So intelligence is not just something that happens inside individual brains, it also arises in groups of individuals. In fact I define collective intelligence as groups of individuals acting collectively in ways that seem intelligent. Now by that definition collective intelligence has existed for a very long time. Armies, companies, countries, families, these are all examples of groups of people acting collectively in ways that sometimes seem intelligent. But in the last few years we've seen some very new kinds of collective intelligence enabled by the internet. Think of Google for instance where millions of people create web pages, link those web pages to each other and then all that knowledge is harvested by the Google algorithms so that when you type a question in the Google search bar the answers you get often seem amazingly intelligent. Or think of Wikipedia where thousands of people all over the world have created a very large and amazingly high quality intellectual product with almost no centralized control and without even being paid. To take advantage of ideas like these we need to understand them much better and that's our goal in the MIT Center for Collective Intelligence. Our core research question is how can people and computers be connected so that collectively they act more intelligently than any person, group or computer has ever done before. To help answer that question in one project we're applying the same statistical techniques used in individual intelligence tests to measure the intelligence of groups. We found that just as with individuals there's a single statistical factor that predicts how well a group will perform on a wide range of very different tasks. We also found that the group's collective intelligence is only moderately correlated with the average individual intelligence of the group members. So just having a bunch of smart people in a group doesn't necessarily make a smart group. But three things were significantly correlated with the group's collective intelligence. First was the average social intelligence of the group members, their ability to understand others' thoughts and feelings. Second was the degree to which group members participated about equally instead of having one or two people dominate the whole conversation. And third was the proportion of women in the group.  Interestingly, that last factor is mostly explained statistically by the first. On average women score higher than men on the test of social intelligence we used. Soon we hope to give this test to groups like sales teams and top management teams to predict how flexible and adaptive they'll be in a wide range of situations. We also hope to use these measures to help increase the collective intelligence of groups by, for example, giving them better electronic collaboration tools. In another project we're letting large numbers of people work on one of today's biggest problems. What to do about global climate change. Of course this is a very complicated problem, but we now have a way of solving complicated problems that was never possible before. As examples like Wikipedia and Google show, it's now possible to effectively harness the collective intelligence of far more people than was ever possible in human history before. Our goal is to apply this crowd sourcing approach to the problem of what to do about climate change. On the online platform we've created called the Climate CoLab, over 10,000 people from all over the world have created proposals on topics ranging from eating vegetarian diets to adapting to sea level rise. They've used computer simulation models to predict the results of those proposals and they voted for the ones they liked best. The creators of the winning proposals as determined by both expert judges and the votes of the crowd have presented their ideas in briefings at the United Nations in New York, the U.S. Congress in Washington D.C. and they'll do so this year in a meeting at MIT in November. In the long run we hope that ideas and work like those in these two projects will help us learn how to connect more and more people and computers in ways that will let them act more intelligently than any people, groups, or computers have ever done on our planet before. Thank you.


Why is that nothing is working out? I don't know what you think and the rest of my friends. Whatever it does, it's only successful. But if I venture into it, it's a failure. I think it's time to write it this. Yes. Wait, wait, what are you doing? What are you doing with this now? Why is it that I don't know?  I get it myself. It's not nothing is working out. For me this is not the solution. It's not the solution at all.  Why? I got you. I'm waiting to die. I'm waiting to die? My asses are waiting for you. I can't go out with that. But let me write it out so that we can pick you when you feel yourself. By the time you go out with it, then man. Wait, wait, let me teach you how to do it. You need to put this on your neck so that you can dive in. I'll let you advocate man.


Well, it finally happened y'all. I finally reached a hundred thousand subscribers on YouTube, I just want to say thank you guys so much for all the love and support over the years on my personal page We know the inter clutch page is already established. We're on the road tonight in the cave there But for you guys to show love and support on a completely different page Mainly wrestling focused is truly amazing like before I even recorded this video, I was on the phone with Doug and He was just telling me how proud he was of me for actually sticking the course staying true to it grinding and really Dedicated my time and energy to my personal page He was the one for those who don't know he was the one that inspired me to really Do my own YouTube page to start it up and actually post my own content and for those who don't know Nisha dubs wife. She was the one that came up with the name kicking it with Ross so I just want to thank them both for believing in me for for Motivating me and pushing me to keep making my own content first for my personal page They believe that I could hold an audience and entertain people without just the inner clutch, you know Being the focus at you know for my personal page They felt like the people from inter clutch with you know Show me love individually and they have and I for those who who found my page from the inner clutch main page Thank you guys so much for rocking with me for those who found my page just off the YouTube recommend it Thank you for joining joining me and rocking with me as well kicking it with me as well I also want to thank you have always glory to God Without him none of this is possible without him. I don't link up with Doug in 2017 I believe she was 2016 2017 and we don't start this YouTube thing without him, you know him without God I don't even meet Doug in middle school, you know a lot of these things Happened for a reason and I'm just very thankful and very blessed to be able to bring you guys content on a day-to-day basis I found my purpose in life and that's entertaining you guys for the longest I didn't know what my purpose was until I Linked up with Doug and we started doing YouTube and It didn't take long for me to figure out this is my purpose This is why God put me on this earth to entertain you guys to you know Bring that that type of Personal connection that we have because a lot of times I see messages of you guys saying yo When I watch your guys content on watch your videos I feel like I'm watching it with a homie and that's what I always wanted and the fact that I'm able to do That with you guys is so amazing. So I definitely got your praise to God give thanks to dub. I want to think my close Family and friends that I'll be so surprised when I go out and about and my homies, but I go I love your wrestling videos. I'm not kidding not making this up. I literally be out just chilling Don't be thinking about videos at the time and somebody I personally know or somebody, you know I may not even met. Oh, yo, I love your wrestling videos.  It's racing right now if you can't tell And last but not least I gotta think y'all I None of this This this setup the shoes that I have clothes The crib that I'm in all of these are blessings from the man above But at the same time all of this is not even possible If it's not for you guys if you guys been with me from the beginning those who have you remember what I was recording on My setup was super basic, but it worked. I got a lamp from Walmart I was using a tripod I got from Amazon and I had my iPhone That's what I started with and I was using a microphone that there was we was using on in the clutch page Oh, when I bought me a microphone from Amazon And to see where the equipment was then to now to see where I was I was Recording in my grandmother's one of her rooms that I grew up in as a kid. I was recording in there, bro room Super small, but I made it where I didn't even have a desk really, you know and now I'm in this situation where I got plenty of space. I'm actually about to move next month if God says the same So I'm moving to even bigger space and all of that is because of you guys supporting me All you had to do is watch the video You didn't have to you could have Took 10 minutes out of your time to do anything else But because you guys chose to watch a video and because you guys chose to keep coming back And because you guys kept commenting because you guys were hitting me up on twitter and instagram Hey, check this video out or joining in on the live streams or you know Making fun of my football teams on the live streams like all of those interactions help me get to where I'm at now So I just want to say thank you to you guys because you guys have changed my life forever forever I I'm at this point in my life where I am at content and knowing that When you finally know what your purpose is and you're able to live out your purpose and I'm Creating content that you guys love and want to see more of I'm good. I'm at peace. All right, and it feels good to be able to say that So yeah, this video is just wanting to say a thank you guys So so so much you guys are amazing And now it's on the road to 200k and beyond man So I just want to say thank you guys so much for helping me reach this milestone. So Before I get out of here, I got some pretty good news. I think I'm gonna do a 100k live stream of smackdown tonight smackdown Be later on so I'm probably going to stream it on this channel It's going to be the 100k live stream to smackdown before some Viver series and I'll be introducing my brand new 100k robe for you guys I know you guys love it when I pull out the robe. So robe Ross will be returning today in his 100k robe I think you guys are gonna love it. Love it. So hey, man, we're gonna turn up tonight tonight. I'm taking shots I'm pulling up. We're gonna have a great time on stream. So make sure you guys join me for the smackdown stream we're gonna set that up and uh And we're gonna go from there, man, but I just want to say once again thank you guys so much for all the love and support you guys have shown me and tune in to the 100k smackdown go home show for survivor series and See your boy robe Ross live in action tonight. But thank you guys so much Row two is it's cool to say Row to 200k. It's gonna take a while to get there. Maybe I get there sooner. Who knows but row to 200k on the way Um, but I love you guys appreciate y'all kicking with me and I see y'all later on tonight. Peace


Hello and welcome back to the craft box. My name is rent and today we're in episode 25 of those 101 Death Walkthrough. If you haven't checked out last episode go do that. We managed to start and finish Newgate Prison and we started off Knight's Court and that's where we are currently but today we're starting by talking to Sergeant Stig. Brilliant, our reports of scratchings have lessened considerably. My thanks to you young wizard. I'm truly impressed. Now that the deadly scratchings have lessened let's look to the case. I see Lady Dalton reported an incident last night. Talk to her. See what she knows about Jock the Scratcher. Okay we leveled up. We are now level 27 I believe. Yep 27. Yeah so that's cool. We are going to Catherine Dalton who is over towards Bone which is yellow which is this one here. Good day. Um yep. Where is your Knight's Court one? Kate's and Sun's Lab Knight's Court. There is. I don't know where it is. Who knows? Amy Brooks is there. Whoop whoop whoop. Don't get pulled. That would be bad. Um where is she? I don't even know. Been so long. Ah here she is. She is over this side. That's good. Why thank you dear for calling on me. I appreciate the concern. My encounter with Jock the Scratcher was such a horrid experience. All I recall is that he carried a black bag.     Which way is it quicker to get back? I mean to be honest it's probably this way. To be perfectly honest.  Um where is he? Down here. Okay. Not too far away. That's good. Um I don't know why. The last two times I've tried to do that I failed. I don't know why but I'm just so bad. I'm terrible. Anyway sudden stig. Excellent work young wizard. Our first clue. We've yet to locate Jock the Scratcher. We need more clues. Lady Brooks reported a scratching not too long ago. She's standing near. Go talk to the young lady and ask her what she remembers. Okay. We need more clues. Go talk to Lady Brooks nearby. Um I know where the cat is here. It is apparently somewhere around here probably. Probably. Probably. There it is. It's in the same place as like another one. It's where they just copy and paste it. That's fine though. Um yeah let's head over to Amy Brooks's place all once more. And we will head on down to Amy Brooks. It was just here. I came home one night and Jock the Scratcher attacked me. I've been scared to go back ever since. Please young wizard do what you can to stop this awful scratching. I want you to ask the constables to come and make sure my place is safe. I loaned Katherine my new spring hat and I'm going to need it for the placement's ball. I'm scared to wander the streets these days. Would you mind fetching it for me? Okay let's head back to Stig. Who is over here? Wrong one. Good damn it. Good damn it. Good damn it. I'm so bad at this.  Oh dear how terrible. Jock and his ruffians are more active than I expected. Thanks young wizard. Your input has been invaluable. My boys and I are still dealing with that prison break. We have the time to follow up with Lady Brooks's request. Can you comfort her by searching her place and making sure it's safe? Mind you her place is in a clock tower so you can't miss it. Okay let's go there then. Amy Brooks's place. What we're going to do is we're going to add just one of you. We're going to add a couple of feints. We're actually going to just go to the death spells. We're going to add one of you just in case. And that sounds good. Yep let's head on in. Ten nine eight seven six five four three two one. Okay. Let's head on in. I really hate Night's Court. I think it's the worst part. We're going to add a poison just in case we're going to take you out just because you're not bad. Okay let's do this. He's easily killable. You are easily killable as well. So both of them are very easy which is good. We just need a blade and a vampire. Just easy. Oh look a shield or a blade. Oh look it is a shield. Oh well it does not affect me. Oh a pass. That is a surprise. Papa thank you. And you can die because you are more likely to shield than anyone else.  I love it. I love the spells so much. That's so cool. Six eight three. Okay then. Boop three four one. And here we go. We will blade. And we will wait until we get four pups again so we can vampire. Oh he's going to pass. Okay that's cool. Papa. Okay that's fine. Pass. Okay boop boop two nine one. Do do do do do do do do do do do do do do. When you don't get any power pups it's actually really sad. It makes me sad. One seven two. There we go vampire. Let's go. Fizzle thanks a lot game. Much appreciated.  Yep you do. Not a fizzle. Okay here we go. That is him dead as well. Yay. Boop five seven eight. Two eight nine. We find a crimpled glove with the initials X on the floor. Okay. We're actually just gonna put you back in. And we will head back to Sergeant Stig once more.  That's right here isn't it. Yeah it is. Yeah it is. It's called a Yard. I'm glad with the initials xx. Oh your sleuthing skills are astounding. This might be the evidence we need to crack the case We're puzzled as to the meaning of all these clues. Oh crank and up could solve it But he's off duty now. He's a regular mr. Burt's bones and biscuits and Regent Square Find him there and see if he's willing to help Okay, let's go and hid to mr. Crank and hop crop thing in my Bobby Let's hit over there load Load thank you Where is he? Where is this place that we're trying to go to over here? Hello Here you are No, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no Boop. Hello. Ah stig sent you an old cop. I like me could use some excitement Hmm glove with xx It's caught and a black bag Exactly. He must be a doctor with the initials xx who lives in night's court Okay, and we will head back to night's court and talk to sergeant Stig There we go that crank and oppie's got it Doctor Xavier Zandros lives in the night's tower. That's near night's core. Great work young wizard We'll be sure to investigate this doctor We've checked all the clues and they all land up Dr. Xavier Zandros is shocked a scratcher who's up ahead in night's tower You've proved your hurry there and defeat him before he menaces another lady Okay, let's head to the hub and here we go lag why do you lag after teleporting?   That's some fear Oh Well, I'll take out his minion and then we'll take out him. Yeah, it sounds good blade. Yay How do I want to take out as many and I'm kind of team did to poison Yeah, I'll poison I suppose might as well, you know, hey, don't use it spell enough And they may be me me and may mean he can get more hits on me, but you know what?  So I mean we should kill hopefully We'll see how much that does over time What we will do. Oh now we get this. Okay, then game. That's cool we will blade skeletal pirate and 240 okay, then that's cool.  Yep, okay 240 yeah, he's dead cool perfect Boop blade We're gonna just cut you for now We will use you and we will pass Just for now Okay, evil snowman. That's cool Can be like 350 400 okay, then I'm like yawning.  This is not even that late what Okay, I mean we might as well he's got 1800 health he's got quite a bit. We will do this He's got two perps. He can't do too much. She's got a blade as well though now. So that's kind of worrying That's fine. It's only 30 Mean let's just see how much this does I speed up. Okay, then that's fine No, I'm 30 cool cool cool Ah One six five two nearly dead. Oh my so close 148 whoa Okay, then I mean I Mean, yeah, sure.   That would be bad. I mean he doesn't have a blade. So I suppose that's good I'm all worried what he's gonna do this round But hopefully he passes all blades, so I don't have to worry too much pop up Who if I didn't get pop up that would be bad as well Don't you dear tower shield again?    My my you're an accomplished detective We could use a wizard like you on our force We couldn't have gotten shot the scratcher without you Let Watson know how you finish off shot the scratcher You'll be waiting for you on the Scotland Yard roof Okay, that is that area done. Yay. Um, so we'll talk to To Watson and we will probably end off the episode there. So yeah Let's get on it through Over to Watson who's just here. Hello. Good to know our fair ladies need not fear shocks the scratcher anymore With the shock the scratcher case self. Thanks to you our detectives have uncovered the scientists behind these metal men Make me in dr. Katzenstein's lab Perhaps we'll find out more about the clockworks and the connection to me. Oh, yeah, I see Okay, so next episode we will head into Katzenstein's lab. So yeah, thank you for watching remember to leave a like and subscribe and if you're very subscribed Press the little bell so you know exactly when I post another video Go follow us on Twitter links in description below and remember craft outside the box


Margo, you and Jaina had worked on a project together to pull in photos from the members' libraries. Right? How many photos did you get? 50, 60 photos? So let's do a thought experiment. Let's cut those number of photos in half and choose the ones that are best, that represent the best library space. So how would you go about doing that? And we can't go there. We can't physically go to that library, look around, see if the young adults are enjoying themselves. We have to look at the photos. We have to look at the digital representation of the space. So that's the assignment I was given. I was offered to go in and figure out a way to look at a virtual representation of a library space and say, this one based upon our rigorous findings has better qualities than that one. So how would you go about doing that? Right? So that's the purpose of my portion, very small portion of a very large grant. So that's what I want to talk about today. I'm not going to try and get you to sign up for Second Life Avatars, because I think that's probably yesterday's news. But we did use some of that technology and it was very inexpensive and very useful for this process of creating a virtual representation of a real-life space. So... All right, this is me. I'm a full-time lecturer. I've been at SLIS. How many of you graduated from San Jose State SLIS? So a good third to half the people in the room, right? There's about 75 people in the room here, so about 25 of you raised your hands. I've been teaching online since 1999 with SLIS since 2005, 2006. And really my focus has been connecting 3D virtual environments and representations with learning systems.  I'm going to show you Second Life circa 06, 07, the big hype time. So let me show you some examples of what we were doing with Second Life back then. We're still doing some of the same stuff, but it's quite a bit more grounded now. This is more like marketing. And my first stop, a virtual class at the Second Life Campus at the School of Library and Information Science. Hello, class. How's everybody today? So that's a reporter on the right-hand side from PBS who came from the Quest Science program, came and interviewed us, and right at the peak of that sort of bubble of Second Life, you're going to be able to do everything. And this is Lily LeWoe, another hero of mine who's an incredible researcher at San Jose State, a ten-year faculty member who went to early tenure because she's really, really quite good. If you have a chance to associate with her or take a class with her, I highly recommend it. Introduce a visitor from KQED, and his name is Shiraz. Welcome, Shiraz. Hi, thank you guys so much for having me here. I'm doing a story for Quest on Second Life, so I'm really excited to be here. In today's class, we are going to do an exercise. You will break into pairs with one student playing the role of the user, another playing the role of the reference librarian. I paired up with Grayland Fairweather. In real life... See, they've got the headsets. A lot of people, a lot of classes in our program are doing live video conferencing. This is video with a 3D component. It's the only difference, really. In real life, she's a graduate student named Robin, who helped build a lot of San Jose State's Second Life Island.  What sort of books have you come across in Second Life? How many books do you own in Second Life? And do you have to pay library fines if you check them out for too long? No. Any books that are in Second Life, you can either buy them or get them for free. I have, for example, the collected works of William Shakespeare and HP Lovecraft. And many books that are in the public domain, people have brought into Second Life. So I have about 19,000 items and perhaps 200 books on me. What if I came up to you and asked you about where I could find information on Second Life about aeronautics? Well, specifically for aeronautics, there is the International Space Flight Museum in Second Life. Or you can simply do a search for places and look up aeronautics or flight. The strange but inviting space made me feel like I was in school again, where everyone was smarter and better looking than me. Well, at least in Second Life, I was able to opt for a full head of hair. Any other questions or thoughts or comments? I just want to say that these are the most attractive reference desk librarians I've ever met. Alright, then. I love the dance, Robin. So that was sort of the naive thought that we were going to be able to serve patrons in a virtual environment who were residents in a 3D setting. All of that sort of fell away, became much less interesting. But we have done two things in Second Life in San Jose State that continues to bring students and have some positive educational outcomes. And the first one is a set of digital humanities courses that we've been running with different topics. So students come in together and create the Renaissance of Florence or pretend to be Tudor, Shakespearean-era people, where they come up here pre-Revolutionary France in fall. And students, 20 to 30 students, will come in and do some digital humanities, content construction, role play. And it's interesting. They can do, let me get back in here, show you some displays. So this is a very cheap and ineffective way to do displays, to practice building displays and talk to each other about the arrangement of humanities content in a physical space. So the students are arranging these things, record keeping in Renaissance Italy. They're talking to each other about how they've arranged the information, how they're telling a story. You can see in the back there they've got the slides, and then interactive items around the edges of the stage. So the students aren't experts at multimedia development or anything. They've gone and purchased these things and sort of put them together. So they're telling a story with 3D objects, found objects. But they get to talk about collection development and arranging spaces and things like that. So it's sort of training wheels. Here's another one. Again, you see the slide presenter on the left-hand side. Some very interesting Renaissance era science tools on the right-hand side. There's a prey. You can go over there and prey in the left, have an animation for your avatar. Might as well use this, huh? Right here you can prey, have your avatar go and prey, all these science instruments, and the slide projector here on the left-hand side. So each of the students gets one of these little lockers or carousels, and they can go in there and build a kiosk about art and medicine with the nuns in Florence in Renaissance Italy. So that's one thing. We've done digital humanities. We've used Second Life. We've had the students go in, and they've really enjoyed themselves and done some interesting work. The second thing we've done is more of the, somebody mentioned Twitter, the social media aspect. So we have a virtual center for archives and records administration. We actually have a full second master's degree, a MARA degree. That's not an MLIS. And that group gets in there and has conferences and presentations, and they do poster sessions, and they really are about promoting this career option of archivist records administrators and doing it focusing on cultural heritage. So that's two of the successful continuing efforts in Second Life. But this grant, the one that I'm going to talk about, the work that we did with, this is a student, Lori Harris, and also Julie Whitehead, who's graduated since, was to do, as Anthony described, surveys of hundreds of library spaces, videos of dozens, and now 3D spaces recreated from, and I'll show you six. We've taken those surveys, he sent videos to the librarians, about, what, about 20 librarians and 20 young adults, yeah, created the videos, then we took those and parsed the videos and recreated these spaces in a virtual environment. And the goal is to say, how do we know which space is better without having access to the space? So when Margo goes and grabs all those photos from all of your libraries, how can we, how can we do an evaluation of those spaces without actually going there? And that's what we've tried to do. So we rebuilt six of them, and the point is to measure and analyze public commentary. And there's a precedence here, actually. This isn't something only done in recently. So here are some, the virtual representations. These, I actually do not know where these libraries are. They are real libraries, I don't know where they are. I think we just anonymized the video and didn't focus on the location of the videos, the location of the libraries that we were modeling. I'm going to show you specifically, if you can see the laser pointer, this area right here, there's a media room, and like Anthony talked about, that trough, so there's a trough there in the window. And we're going to go, I'm going to show you some video going down around this space. So the key questions here, the key questions for my portion of this grant is can we evaluate these spaces using simulation? Does it help to evaluate them? Can we do it? Are there any advantages from taking the evaluators out of the actual spaces? So if we have all the photos that Margot put together, showing them to a person and getting information, getting feedback from that person, is that helpful to separate that person from the actual space? Kind of counterintuitive. You think you just want to put them there and they can look around and tell us how they like it. But there's actually some benefits from separating the people from the space itself. Is there any new field of inquiry? Can we go, can we take this further and build the literature in this area? So here's some precedents, here's some background. At New York Law School, there was an island, the Second Life Island in 2006, where they created a 3D wiki and they rebuilt, how would you like to build portions of Queens, New York? So they rebuilt portions of Queens, New York and brought the public in to show them what the possible, that possible neighborhood in Queens would look like. So that's something. Landing Lights is the name of the island and that was New York Law School. Another one much more recent was a colleague of mine in Scotland, Daniel Livingston, rebuilding, taking a class of students who were more proficient in virtual environments and multimedia construction to have them go in and look at urban regeneration. So we're going to plan the town of Paisley, Scotland and we're going to bring students in to have them sort of build some strawman example of what the town could look like. And here's some screenshots from that. They use all different platforms, so there's not just Second Life, here's Open Wonderlands, another one. This is the high street for Paisley, the shopping street, and you can see that the students had built out, actually this is pretty faithful to what was there. So it's possible to build out urban settings. Here's another one, the Town Hall and Abbey on the left and more of the Town Center and War Memorial here in a different platform. They even used Minecraft. If you're all familiar, if you have an elementary school student, you'll know all about Minecraft. They weren't able to get the kind of look and feel that they wanted to out of minecraft, so it wasn't as useful. So they had to take photographs of the space and then map it on their models. That's not possible in Minecraft. Here's another one, the shopping district there in Paisley as well. Okay. So that's some precedent. This is being done. It's not just our grant. People are doing this all around the world, creating 3D virtual environments and representations and then trying to get feedback about it. So let me show you one of the videos. You didn't show a video, right, Anthony? So this is great. This is a video of an adult. I believe it's an Idaho who has a teen space. Let me show you what he had to say. When you were talking about what they were interested in, it kept ringing a bell, because he talks about the collections and separation and the art. Later on, I'll show you the same space with a teen narrator. You can see her different perspective. Since I started representing the library, is it student? It looks like I don't have the adult. So let me just do the teen. This is the second of the three videos I was going to show. On the left-hand side, over here, you have the actual teen holding the camera, talking about the new space that she really enjoys. And you can tell she talks about furnishing. She talks about how it makes her feel. You can get some of the transcript and the verbatim, the talking from her. And then on the right-hand side, I also have the virtual environment, the second-life virtual environment, the version of the same space. Actually, I'll probably try and play this twice. It's only a few 20 or 30 seconds. So on the left-hand side, she's talking. On the right-hand side is the virtual environment recreation of that space. We made this new room. It used to be the audio-visual room for the handicap, but we have turned it into a really cool teen space. We have art that's been donated on the walls. We also set up three different computers for teens to research and study with, which I think is very, very handy. We also have pretty cool chairs here that are new along with a room to encourage reading comfortably. We also have all of our animated graphic books located in here now. We also have a TV here hooked up to a Wii with remotes that... Okay, so you get a good idea. On the left-hand side was her talking about the artwork and on the right-hand side, you saw the second-life materials that we'd rebuilt based upon this video. One thing that we did immediately is take those videos and very meticulously slice them into one or two second pieces and look for every object that was in those videos. So we found nearly 800 data points from six of the videos, and we took a lot of screen captures of those videos over and over and over again and created a spreadsheet that looked like this. And then you can see this is one example of that mural.  And here's an example of the mural outside of that window. So this is a scene outside the second room, a window mural that said, be more, do more, live more, 14s. We have a screen capture, and then we also... If we were a seating option, we also looked for that same seating option out on the web. So we tried to find the same seat for sale somewhere. So we were able to take those six or seven different library spaces and slice those into 700 individual pieces to find all the different parts of those. Here's some more conversions. You can see there on the top left is the real-life space, and on the bottom right you've got the computer. So we were able to buy the computers in Second Life and for a buck or two and place them in the spaces. All of the cabinetry and everything we found, pretty similar cabinetry, more computer workstations, those were very easy to find. So there's a whole catalog of things for sale in Second Life. A lot of things... One of the things we did is every single sign we could find, we tried to recreate it and place it into Second Life so that people who looked through the space would have a good feeling for what was there, more computer spaces with these walls, carousels, such as over and over and over again, getting as many details as we possibly could exactly the same. So then we had a floor plan. Without looking at the library website or any of that, we went to the videos and created floor plans based upon the videos and then also all of the textures, any carpeting, things like that. So I got five minutes. The folks who we wanted to evaluate this was sort of a convenient sample of our own students. So we took our own students and had them go into Second Life with a possible community of a couple thousand people. We had them go into Second Life with avatars, walk around the spaces, and then complete a web survey about the space. So we had 40 surveys completed, two rounds from May to October. You can see the average age was mid-thirties, so older than our students. Our students tend to be mid to late-twenties and 85% female. So the things that we asked them, we told them the kinds of improvements that we were thinking of, and these are some of the things that they were responded to, this wireless connectivity. This was very important, kind of interesting. Because in Second Life, I mean there's no wireless connectivity, but the students, the ones who went in, thought that this was an important thing for the library to have. Event space, exhibit space, seating options. And this was one too, virtual merchandising in the library. So we asked them if that was something that they thought would improve the space and technology. Storage, all these different things that we've offered them as an option. So two, this is probably important, two main results here was that the age of the respondent didn't make a terribly big difference. Now if they were younger, younger students or older students, it didn't make a very large difference. So here you see the red ones, the bar on the top. These are people 36 to 55. The ones on the bottom, these are our students who were 18 to 35. Generally the same trend line. And here you can see better wireless. Younger folks and older folks, they agreed pretty much with library space you should have better wireless. Generally. So not a lot of difference based upon their age. That was kind of interesting, I didn't expect that. But, okay, yeah, more of that. Okay, look at this, this is the other thing, this is the point of not having the people go to the actual space. Because we can make, we can do AB comparisons. I can actually tweak the space and pull out one single thing and have the same population look at that, those two in an AB, kind of an AB comparison. So here's an example of a space that doesn't say teen over here on the right hand side. That big mural, we just blew it away. So we're going to evaluate these two spaces and the only thing we're going to change is the fact that it doesn't say for teens. It doesn't say it's for young adults. So we can do that in this environment because it's simulated. That's a key point I think of the presentation. You can evaluate a space, but can you evaluate a slightly altered version of that space? And in this case you can. I thought this was really fascinating, that respondents who saw that big teen label in the window, they were less interested in suggesting things like academic technology. They didn't think you needed more computers and printers for teens. If it were a teen space, they didn't think that was terribly interesting. Also, better wireless connectivity. Here, the ones who saw that teen space logo, these are college students, these are MLIS students. They didn't think wireless was so important for the young adults. But for the generic people, the people who saw a space that didn't say young adults, give me wireless because it's my space as a college student, as an MLIS student. I need wireless. I need academic technology. So you really saw some bias in the reviewer, the person who was reviewing the space based upon whether they thought it was a teen space or not. It's the same exact space. The only thing we did was take off the label. So you could see some bias there in the way that the MLIS students evaluated these spaces. So that's really interesting to be able to do this, to look at pretty much the same thing as real life. It's the same structure. It's got the same decorations and everything.  And our students didn't think teens needed better wireless or that teens really needed more academic technology compared to if they thought it was a teen space. So that's interesting that you can take the evaluator out of a real space and start to see some of the bias there. So the key question, can we evaluate library spaces from afar? Yeah, darn right. And we can even do it with photos too. I mean, Margot could have done it with her 60 or 70 photos too. It's more interesting and more hands-on and tactical, if you can get in there and walk around with an avatar. Is there any advantage for separating the evaluators from the real spaces? And there is because you can see some bias. You're able to change that space in very subtle ways and see the bias of the evaluator. And does this open up any new fields of inquiry? I think it does. We have to continue chomping through the numbers and continue throwing different populations into those virtual environments and getting feedback from them on what they think a good library space looks like. But I think this opens up some interesting stuff. Thanks.


The results of this study suggest that a higher protein diet does not significantly affect the gut microbiome or the production of certain volatile organic compounds in older adults. This article was offered by SM Mitchell, E.J. McKenzie, C.J. Mitchell, and others.


This 2014 Ford Mustang Shelby GT500 is stock number 12096Z. We are here at Summit Automotive in Fond du Lac, Wisconsin, you're new and used sports car headquarters. This 2014 Shelby GT500 has the 5.8 liter supercharged V8 motor, which pumps out 662 horsepower. This car has been fully safe and inspected by our service shop, has a fresh oil and filter change, all the fluids have been checked and topped off, and this car is 100% ready to go. It is just about as clean as they come, ruby red metallic is the color. We shoot all of our videos in 1080p, 60 frames per second. So if you have HD capabilities on your computer, tablet, smartphone, or television, turn them on right now because it is definitely your best way to check out the quality and condition of the car before seeing it in person. And if you like the video and want to subscribe to our YouTube channel and the lower right hand part of the screen is a subscribe button, click that, and then click the bell notifications and you'll get updated every day we do videos here at Summit Auto of our amazing inventory. This one has the SVT performance package, this one actually has just about every package you could get as an option on the car, other than I think glass roof and heated seats. So it's really loaded up coupe, has the 19-inch SVT performance rims in the front, no scuffs or scrapes on them, and it has Goodyear Eagle F1 26540 ZR19 tires. These tires have just about all the tread left, all the tread is on the inside of those tires, and this car only has 1600 miles on it. Front fenders in excellent condition, it does have the HID headlamps, the LED running lights, the factory fog lights, and I'll tell you one of the only imperfections I saw in the entire cars, these lower valences here, they always get scuffed up on curbs, just one little notch right there. And then on the other side, kind of the same thing, what's nice about these though is they come off and you can replace those with brand new ones really easily. So that's always a nice option. Those with the grille delete, they didn't put grilles in the 13s and 14s because they had that 5.8 liter in there. The hood is in excellent condition, you get the black matte stripes, or matte black stripes I should say, and they're in excellent condition as well. I like that all the way up to hood, the hood, I didn't see any corrosion on that, sometimes because these are aluminum, they'll get a little bit of oxidization on them. This one doesn't have any of that. Passenger side front fender, absolutely perfect. Ruby Red, it's got just a little bit of metal flake to it, it's really a cool color. And the passenger side front rim, no scuffs or scrapes on there. And as you go down this side of the car, take note of how clean the body is, how reflective and mirror-like that paint is. We take these HD videos, so if you are far away or even if you're close by, just can't make the trip down, but you're still interested in purchasing the car. You can see the car, hear the car, and of confidence in the vehicle that you're looking at before you even get here. So when you do get here, there's absolutely no surprises, and you can make a smart and informed buying decision from the comfort of your own home. And I'm sorry, the roof with those stripes is in excellent condition as well. And down this side of the car looks really, really good. The side stripes all look really good on this car. This back rim looks really good on this car, no scuffs or scrapes. You can see just how much Tritas on those tires. Now if you look a little bit further in here, you can see that rear differential, there's a tube coming off of it right there. That tube indicates that this one has the Track Pack on it, which was a $29.95 option on this car in 2014, and it does have that option on it. Rear bumper is in excellent shape. You get the quad-tipped dual rear exhaust. This thing sounds fantastic. Just look really good. The Shelby GT500 logo on the back looks really good, that black piece, that gloss black piece is in excellent shape. You get the sequential LED tail lamps, and we'll check out the trunk. There's a lot of really cool stuff in the trunk that I want to show you. It has the capitalist fuel fill, no gas on your hands again, and the rear quarter looks really good on this car. For full disclosure, this back rim is absolutely perfect as well. You can see the scuffs or scrapes on there, and the driver's side door looks really good too. Power mirrors with the blind spot mirrors. Before we get into the interior here, we'll take a look at the trunk, and then we'll check out those Recaro seats. So back here we've got a lot of really cool stuff like I was saying. First off, you'll notice that it's got the Shaker Pro audio system with the factory subwoofer. It comes with the car cover that came with these cars. It does have the original owner's manual and case for those books. And then we have the original window sticker for this car. I'm not going to go through everything, but feel free to pause it. I'm just going to go through the optional equipment here. So ruby red metallic tint coat is $395. It has the manual driver's seat, 50 state emissions, 331 limited slip axle over the top racing stripe SVT track package, which was $29.95. Electronics package with navigation is $23.40. The Shelby Man leather Recaro seats are $15.95. The Shaker Pro system was $12.95, and the Shelby car cover was $3.75. The MSRP on this car was $68.85. One of the more expensive coupes that you could get with this in the GT500 package. So it actually gets 24 miles per gallon on the highway, 15 city, 18 average, which isn't that bad for a 662 horsepower car. Safety ratings are all really good. And then it came with this certification from the Ford Special Vehicles Team that this was a limited edition, it was assembled in flat rock assembly plant on 624 of 13, and it was number 2318 of 4816 coupes that were built, and it's number 290 of 614 ruby reds. So really cool stuff that comes with this car, and then you have like a build sheet that tells you all the options and which ruby red, how many were built in ruby red with which options, which is a really cool piece to have as well. And that all comes with the car, there's also a tire inflator kit underneath there. And we'll hop inside, take a look at the interior, check out the seats, check out everything that the interior has to offer. This is a driver seat height adjuster, you get the recaro leather and suede seats, the Shelby stitched Cobra into the backrest. This has the black inserts, they can come with white, red, and blue, I believe they came in on anyways. Back seats are in excellent condition as well, no rips or tears, get latch, child safety system back there, smells very clean in this car, brand new actually, GT500 floor mats, power windows, power locks, and power mirrors. This one has auto headlamps, launch control, steering settings, and then your different suspension settings will hop inside. Take a look at the miles and the radio and everything in here. You can see that this car only has 1,620 miles, you do get a miles to empty, you can do miles per gallon, you can change that gauge to read pretty much whatever you want. Comes with the leather and suede wrapped steering wheel, Bluetooth and audio controls on the right, cruise controls and information center controls on the left, you get the Cobra logo in the center there, and that steering wheel is in excellent condition. I didn't see any scuff scrapes, rips, tears on it. This one has the AM-FM and Sirius XM radio capabilities, it also has the factory navigation system, this is the electronics package, so you get that, also has hard drive for songs and music, pairs with your cell phone, CD player, down here your climate controls, notice you do get the dual climate controls, six speed manual transmission, sync system, this one has the ambient lighting, so you can change the color of your cup holders and on the floor, it changes the ambient lighting on the floor, you can change the color and intensity and brightness, passenger side seat, no rips or tears, and the headliner is absolutely perfect, once again this car has never been smoked in and smells like new inside, home link buttons for your garage door security systems and lane systems, and map lights up there, alright let's start it up, we'll take a look, under the hood we'll also listen to the exhaust, this car sounds so good, we'll take a look under the hood I would personally like to thank you for checking out the video today and hopefully from this HD video you will be able to tell just how clean this car is all the way around inside and out, you get those HID headlamps, the LED running lights right there, factory fog lights, this one does have aftermarket shocks for the hood, which is a nice feature, under the hood we have the 5.8 liter supercharged V8 motor, once again 662 horsepower, this car has been fully safe and inspected by our service shop, has a fresh oil and filter change, all the fluids have been checked and topped off, and this car is 100% ready to go, it looks like it was made by Kerry Bodle and Chad Walla, they etched their names into the plaque there, there's your mission sticker and like I said this car is 100%, ready to go, and to see more pictures of this car, or one of our other 450 new and used cars, SUVs, go to that website right there www.summitauto.com, full pictures and descriptions of every single vehicle from two locations all at summitauto.com, and I would highly recommend this car from a quality and condition standpoint, and if you want to check out more HD videos you can go to youtube.com slash summitauto, remember to like, subscribe, and share on this video, and all the videos that you see there, in fact in a second you will see a link to subscribe to our youtube channel in the upper left, a link to more GT500 car videos like this one in the upper right, a link to this vehicle on our website in the lower left, and a link to one of our latest youtube videos in the lower right, click those, check us out, and we're super excited to help you with this ultra clean 2014 Ford Mustang Shelby GT500 and Ruby Red Tin Coat, thank you so much for checking out the video, remember to like, subscribe, and share.


So again, on behalf of the president of the Einstein Society, Professor Ott, I would like to welcome you to the last of our 2023 Einstein lectures. Now before I start my introduction, let me ask, is there anyone in the audience who hasn't been here yesterday or the day before? Oh, interesting. So in this case, I will still briefly introduce Marina to those. It's a larger portion than I had thought. So this is the 14th edition of the Einstein lectures. We will complete the cycle of five times with philosophy next year. So this is the fifth Einstein series of mathematics. My name is Christiane Treta. I'm professor of mathematics here at the University in Bern. And it has been a pleasure to have Marina already for two evenings, Professor Marina Vyazowska, chair in number theory at EPFL. So her travel wasn't too far. And so Marina sticks out in various respects, not just because of her young age, but also with her life. And we had the pleasure to listen to her already two days. And I think her enthusiasm for mathematics and for basic research in particular has been really transpiring to the whole audience. So I met Marina for the first time actually in the moment of the high point of her career so far, namely when she was awarded the Fields Medal in 2021 in Helsinki. And before this prize, a whole series of other prizes poured upon her after she had published on Archive the free math preprint server her solution of the sphere packing problem in dimension eight alone and then with co-authors the one in dimension 24. So we are very happy to have you here and look forward to your third talk on the sphere packing problem. Please. Thank you very much for the introduction. So this is the third talk. And so today I will speak about the sphere packing problem in high dimensions and the connection to error correcting codes. And so because there are people who have not been to the first two lectures, so maybe I'll start by repeating a little bit. So before we spoke about the sphere packings. And so this is somehow a symbolic depiction of what the sphere packing problem is. So we have a very big box and we have an infinite supply of equally sized hard balls.  And our goal is to produce this densest possible configuration. And because the game we are playing is that the box is much bigger than the balls. And so what happens in the boundary of the box becomes unimportant to us. And they are only focusing on what happens in the bulk and only interested not in an exact number of balls because that might be dependent on some very complicated way on the size or exact parameters of the box. But we are really only interested in the density. And so now an interesting twist to the story. So we are going to consider this in Euclidean space of different dimensions. And so something what I already spoke about last time. So this is how dimensions 1, 2, and 3 look like. And now what we would like to do, we would like to go to higher dimensions. And so how do we do it? So we do it by introducing more coordinates for points in our Euclidean space. So here is the picture we can see here. This is the three-dimensional Euclidean space. And in Euclidean space, each point has three coordinates. And so the thing which we are going to do now, we will simply add more coordinates to our list. And instead of three, we can consider four or eight or 24 or D for any natural number D. And so here we do so. And so this would be our points in the space. And also in our D-dimensional space, what we want to do, we want still being able to compute distance between points. And so we will do it by applying the Pythagoras rules. So just the distance between two points is the square root of the sum of squares of differences of respective coordinates. And so this works, of course, in dimension one, in dimension two, in dimension three. And we can just, by analogy, continue this to D dimensions. And so once we have defined what is a point and what is the distance in our space, we can also say about what is the ball. And as usual, so the ball of a centered point x and radius r, it will be the set of all points in our Euclidean space, which are the distance at most r from the center. And so another thing is we want to speak about sphere packing and density of sphere packing. It's important for us to have the notion of volume. And so here they have this natural one which comes from computing determinants. And it works in dimension one, two, three, and also can be generalized to higher dimensions. And probably I will not go into technical details here. And so what I would like to speak about today is to speak about how this, or how thinking about the dimensional spaces where dimension D is big, how this can be useful in real life. And so here one, maybe there are more than one way how we could use this, but one beautiful example of how the sphere packing, or in some sense also maybe not the exact sphere packing, but also the idea of sphere packing can be used in a very applied field of engineering so-called error correction. And so I'm sure that somehow it's possible that all this, somehow the engineering devices, they would even work without the mathematical abstraction behind it. But what mathematics was good for is actually for explaining this and making this very intuitive and organizing thoughts around this. So the history of error correcting codes starts during and right after the Second World War. And so the ideas I'm going to talk about now they originated in one particular laboratory, the Bell Labs in the United States. So probably you have heard about Bell Labs already because a lot of amazing technology come from that place. And so it happened that the error correcting was introduced not once, but somehow invented twice in that laboratory by Claude Shen and Richard Heming. And the legend is that they worked in the same institution and they had their offices next to each other. And they were both thinking about error correction into different contexts. And they never spoke to each other about it. And so they discovered that they work on the same question only after their papers were published. And so, and actually, so Marcel Gallet, it's another, it's a Swiss engineer who was also working, worked at the Bell Labs. And so his contribution to the field so that he invented one of the very effective early codes that will also play important role in our story. I'm telling you in the story of sphere packing. And so let me start with Richard Heming. So Richard Heming was using one of the early computers and at the middle of the last century, so this is how the modern computer looks like. And this is how a computer looked like back then. So he was not working with a computer. He rather would have to work inside of the computer. And computer programs, they were written on such a medium, which were punctured paper tapes. And I think people stopped using them maybe even before I was born, so it's really ancient history now. And an important feature of this technology was that it was very unreliable. And computer often made a lot of mistakes. And so during the weekdays, assistants worked in this building. And if mistake was made, then the computer could detect a mistake. So there was already a mechanism how to detect a mistake. But if mistake occurred, then the computer would stop. And the assistant would have to somehow restart the process. And Heming often worked on weekends. And on weekends, there would be no assistants here. So then the program would stop, and then he would lose time. And this made him very upset. And so this is how he decided to introduce this error correction and introduce some more codes which could not only detect, but also correct errors. And at the same time, Claude Shannon, he was also thinking about error correction, but in a slightly other settings. So here is his important paper, which actually sets out, as I say, it starts a new field of study, which is information theory. So here he described what he writes about as another situation is when we transmit channel, for example, by radio or by other means. So when we emit signal in one place and then somehow capture it into another, and some noise might be introduced. And so here, he has some important ideas. So this is how the, somehow, this is a very, I would say, vulgarized version of his. So he wrote this, he wrote down the scheme for communication channel, for signal transmission. And this is a much simplified and vulgarized scheme. So you could think of this as signal being sent here, and then it is transmitted by some means. And so while it is transmitted, there might be some noise, for example, some noise coming from bed, whether if it's these are radio waves. And so my signal here, I will depict it as a point inside of the square, because somehow point inside of the square it is some meaningful information that people might send to each other. And so then, when I transmitted it, what people would receive. So they should have received the signal right here. But then because of the noise, it could happen that an error occurred and the signal actually shifted somewhere far away. And so now, the question is how to, yes, if I received this message, first, how do I know that the message is wrong? And also, if I know that it's wrong, is it still possible for me to understand that this was the initial message? So how is this possible? And so here somehow in this paper, actually, Kloschen and he suggests he explains how this can be done. And so what he writes, I think the important thing is here, the first he writes that we like we don't, we will forget about meaning of our signal. So signal, this might be some words or some sentences, some commands. And they are supposed to have some meaning, but let's forget about this. So what we are sending, we are just sending each other numbers. So we encode our signal in numbers and meaning is not relevant for us anymore. And now, another important thing is that whatever signal we are sending, we will just, before we actually start communicating, we will pre-select the certain set of messages that we can send to each other. So we will not send anything what code word goes through the channel. We will only have some pre-selected set of messages, code words that we are going, that's why it's called code. So some code words that we are allowed to send to each other. And then somehow this already helps us with error detection, because if I know that somehow only the final number of code words exist and I received something which does not coincide with any code word, then I will understand, aha, there was a mistake here. And another thing, if I know that there is a mistake, how can I correct it? And so this is where the sphere packing, or at least the philosophy of sphere packing, becomes useful. So what Shannon suggested is to choose these code words to be far away from each other in some sense. So this is where the notion of distance becomes important and useful. So we'll choose them far away from each other. And so then if the signal is corrupted a little bit, I could still think of my distance and could think which of my code words is the closest to the signal. And this is how I could decode the signal. So if you think, for example, I don't know, maybe it's not sure if it's a safe joke to make here, but if you can think of a French language, then maybe this is an example of a bad code because you make a slight mistake, and the meaning of your word is just changed completely. At the same time, the German language is a very effective, at least good in a sense of a distance because somehow words are long. So even if you make a mistake, your vis-a-vis would be able to probably guess what you wanted to say. At the same time, the result of a price to pay is that words usually normally become very long. And actually, the same problem is with codes. So if you want codes to be very safe, then our code words become longer. And this is somehow the whole game of coding theory, how to make code effective as German language. So it's safe as German and effective as French, where you need to say something, you just say a few sounds, and it's already a sentence and it could be the whole story. So how to somehow make true the best of two worlds and mix them together. And so this is where the sphere packing is actually, the idea of sphere packing becomes very useful. So now this is this gray box, this is our channel. These are all the signals in this somehow. In my story, of course, it would not be a very practical channel. But in this story, somehow, every signal it would be two real numbers, probably between 0 and 1. And it's not a great message, but it is a message. So suppose that this message consists of two real numbers. And then what I decided that I will not send any pair of these numbers, but I will send only these code words. So the coordinates of these red points, these are the signals I agreed with the receiver that I will send to him as a transmitter. And so now I know the physical characteristics of my system, and I know that it's likely that somehow some error will occur. At the same time, it's also a reasonable assumption that the error will not be too big, or at least with a big probability the error will not be too big, otherwise my channel is just completely useless. So I assume that, OK, so within this green round of each of my red code words, there is this error bolt. So the cloud of expected errors. And so it means that, for example, I sent this word here, and then because of the, my channel wasn't perfect, so the signal could be somewhere in here. And since it's still inside of this green ball, then I will know that this was actually the original message. And so first I will be able to detect an error because what I sent does not coincide with what I'm pointing to, if this is the signal received, then I will know that somehow, first the error did occur because it doesn't coincide with any of the code words, but I will also know that this is the closest code word, so this is the way to decode. And so now you see that somehow the game, we are playing, of course, we want to have many, many code words to be able to send more different messages and more meaningful information. We also, we want this code words to be far enough from each other, so we do not want our error clouds to intersect, we don't want them to have interior points. And this is where the pecking problem is coming. So this is exactly the pecking problem inside of my channel.  And so I've also told you that the work of a Claude Shannon was similar to the work of Richard Heming, even though, as you've seen, that what Richard Heming was dealing with was this punctured tapes, and somehow each bit of information on this punctured tape, it's either 0 or 1. And so it does not look a lot like my continuous channel that I show to you here. So what is the trick here? And the trick here is that this time Euclidean space is not that useful for us. So we have to think bigger. And we have to, oh, OK, I will stay away from that. So what we should do, we should go farther into mathematical abstraction and lower ourselves, think of other metric spaces. And what is a metric space? I will not go into somehow definitions as if we were in a lecture for mathematical students. But essentially it means that we have some set of points which we have decided to find. And we also introduced some meaningful notion of distance between these points. And this doesn't have to be Euclidean distance anymore. It could be a different metric. And usually the convention is it has to satisfy some properties that Euclidean metric still has and one property that turns out to be very important and useful is the triangle inequality. So in Euclidean space, we know that triangle inequality holds. So if we have a triangle, then the distance, the each side is shorter than the sum of two other sides. Or that the short. And so if you have another in our metric space, we have another distance. But the triangle inequality is something we want to keep because it's very useful and convenient. And so this is the space actually Heming introduced and he was working with. Because his messages, they were not real numbers. They were all sequences of zeros and ones. So something what computers like and can understand. And so what he have done, he also realized that this set of sequences can also have a geometric structure to it. And here somehow it's a magic of number two that this time Euclidean geometry is still not as useful. If you have alphabet with more letters, then it's true it's a totally different space. And it's not easy to find connection between this space and Euclidean space. But with zeros and ones, actually so we can see that. So the Heming space, it consists of all sequences of zeros and ones that have given lengths. And for example, if you write, we can write down all sequences of lengths two of zeros and ones. And there are exactly four of them. And so now what I'm doing here, I will just draw on the plane. I will draw points with these coordinates. And what I will get, this would be just a square. So if you think of a Cartesian plane, and this would be a point with coordinates zero, zero. These points with coordinates one, zero. This point with coordinates zero, one. And the point with coordinates one, one. And so here we do have actually somehow we see that the Euclidean distance between points, it still tells us something useful. For example, if we think how to define a distance between two different sequences, one natural way which Heming introduced was if you have two sequences, let's look at how many different symbols they have. So we compare these two strings, write them one by another. And we look at each place whether the symbols coincide or not. And if they do not coincide, we count number of all places where they do not coincide. For example, if you have this string zero, zero. And the string one, zero. Then here the distance, Heming distance between them would be one because somehow the first position is different and the second position is in fact the same. So here the distance is one and Euclidean distance is also one. And so here the distance between this point and this point. So if we compute the Heming distance of the number of coordinates which are different, we see that the first place in our sequence, now the digits do not match. And at the second, they also do not match. And so there are two, the distance is two. And the Euclidean distance between them is square root of two. So they are different, but somehow still there is a nice relation between them. And we can do the same for sequences of length three.  And here again we can check that Heming distance, it will be equal to the Euclidean distance between points only squared. So for example, the two points that are farther away, the big diagonal in the cube. So we see that the Heming distance here is three and the Euclidean distance between these two points is the square root of three. And so geometry is still useful. And so what I draw here, this is the four-dimensional Heming ball. And so this is also somehow one way one could think about this higher dimensions and higher dimensional objects. And so for the, and so now what Heming introduced was exactly the same. So he realized that when we are sending a code, we just, we have to pre-define our number of code words. And then, but in his case, the points, the centers of the balls, they cannot be located anywhere in the Euclidean space, but they have to coincide with one of the vertices of this hypercube of the length of the code he's working with. And then he will choose this vertices so that he could choose many of them, lots of them. And at the same time, that they are quite far away from each other so that the cloud of errors would not intersect and that he could not only detect errors, but also correct them. And so there was actually another important difference between the work of Heming and Claude Shannon. So what another important thing that Claude Shannon realized is that, for example, when we are sending this type of signal, then many things are outside of our control anyways. And so it means that if we have, if our balls do intersect a little bit or few of our balls intersect, it's not all that terrible because we have these conditions that are outside of our control anyways. So it means that now if we, if we allow our, some of our balls to intersect a little bit, then it means that our error could occur not only because of some outside factors, but also because of the design of our code. But if the probability is small, it's still not all that terrible for any practical application. And so what he actually introduced, he suggested to search not for exact peckings, but for this averaged versions of peckings, peckings where balls do not intersect with big probability. And for this type of problem, it is a much more fruitful approach, which also opens way to many good codes. On the other hand, what Heming was studied, he really studied the case where he does not allow his error clouds to intersect at all when we, when by our design, we do not introduce any errors ourselves. And so actually his problem is more, is more is closer to the sphere pecking problem I was talking about. And so actually another, and so now an interesting, maybe after what you have told you, there will be no surprise that for example, E8 lattice, which is a, as I already told you, it's a solution of the sphere pecking problem in dimension eight. It's also closely connected to the coding theory. And for example, one of the, there is a code, eight dimensional code, which is called Heming code. It is in fact closely related to the E8 lattice. So E8 lattice can be easily constructed from eight dimensional Heming code. And the eight dimensional Heming code can be easily constructed from the E8 lattice. And so there is another marvelous mathematical object, the leach lattice. And the story of leach lattice is very interesting. So the E8 lattice, it was actually known to mathematicians for a very long time. It was discovered at the second part of 19th century and then it played a lot of role in classification of league groups in many, many areas of mathematics. And leach lattice, it was something that mathematicians did not know about yet at the 1950s. And so before, and before it was discovered, so the Marcel Legalle, he has, he all worked at the Bell Labs. He thought about creating these codes after Heming introduced error correcting codes. So there was of course a question of how to find, it's okay, we have this general theory, general philosophy, but then how to find concrete good codes. And so people were working on proposing those codes at that time. And so one code proposed by Gale was a code of lens 24 and it turns out it was an extremely interesting mathematical object, so it had many symmetries and it was somehow what is called the perfect code. So from the coding theory, it was clear that Gale code could not be possibly improved. It was in a sense, if you think of it as a pecking of these balls in the Heming, so Heming balls in Heming space, then it's somehow a perfect pecking where all this, actually it's not only pecking, but essentially all the space is covered by those balls. So it was an extraordinary object in coding theory and in 1960s a Canadian mathematician John Leitch, he used Gale code to construct an Euclidean lattice. So the Gale code, it was a sequence of zeros and ones, which we saw the big number of words which would have a big distance, big Heming distance between them. And so John Leitch was able to take this binary code and to turn it into a lattice in Euclidean space and here what he did was a bit similar to what we have done before with the cube. So we took these elements of Heming space and embedded them into Euclidean space. And so what John Leitch did was a bit more complicated. He had to play with it. He had to first find a nice way to embed Gale code into Euclidean space. Then he would have to span the whole lattice with this embedding. And then what he discovered that this was not a really great sphere packing, but he could take another copy of the same lattice and shift it and then maybe not too, maybe not too, maybe it was actually more copies of that. And so he could take several copies of the lattice and then this created actually a great packing in dimension 24. So this happened in 1960s and then in 1980s. So John Conway started studying the works of John Leitch and what he discovered is that the lattice constructed by John Leitch has a really great group of symmetries. So it's not only a very good packing, but it's also an extremely symmetrical mathematical object. And so this is how he discovered a famous monster group. And so till now this is the biggest simple finite group that we know. And at that point people were very interested in classifying all simple finite groups. And some of those, so for a long time people know of whole families of groups. They were known classically. And then at some point people discovered the, so to say exotic groups or pariah groups. So they were also finite groups. They were simple, but also they did not fit into any of the previously known families. And since they did not have a family they were called pariah groups. And somehow there was a feeling, there was of course this question. So we have found these objects, but have we found all of them or there will be more? Maybe they all fit into some infinite family. And so John Conway, so you were studying the group of automorphisms of Leitch lattice. John Conway have found this monster group.  And now we also have a complete classification of finite simple groups.  So at least we think that we know it. It's a very, very long proof, which, but I think people do have a lot of confidence in it. But now many of my petitions who have written, worked on this was called an Atlas project. So and many people, some of the people who worked on it now already died. So maybe this is also one of the good candidates for formalization and mathematics would be the classification of simple finite groups. Probably this would be an insanely difficult project, but it seems because first it's so important and the proof is the classification is so long and I believe that there is no living person who understands all of it. It would be really nice to have it somehow formalized for the future generations. And so then the study of the Leitch lattice leads to a lot of other beautiful mathematics and theoretical physics. So here's a portray of Richard Borschertz who received Fields Medal for studying Quertex or introducing Quertex operator algebras and resolving what was called the moonshine conjecture about the monster group. So there is a lot of somehow very beautiful mathematics that came from solving difficult engineering problem. And so the Gali code was used in many things practically. So for example, it was used in some of the space missions. I think this mission was launched in 1970s and it was somehow that time it wasn't important to because sending signal from the Voyager was not easy and also there was no ability to pack many things on it. So having somehow a nice small code which helps to decode was extremely important. So also the, for example, Gali code was used in CD disks. Maybe you still remember the shiny things, the CD disks. They also used Gali code in there to somehow so that you can scratch your disk once and it still would work somehow. Then you scratch it second, third time and it's over. And so maybe the last thing I wanted to talk about is one important question in sphere packing and in coding theory is to know what happens with the sphere packing density as dimension goes to infinity. And so as for me for pure mathematicians this is just such an interesting theoretical question but there is also a practical angle to it. So for example, one of the fundamental discoveries of Claude Shannon was that the error correction is most efficient when we send not short chunks of signals but the long one. For example, if you have sequences of zeros and ones so error correcting short chunks of them is somehow, if you do it like that we will not succeed, we will be limited. So it's most efficient if we send long signals and if we send long signals in our geometric picture it means working with big dimensions and the best case if the dimension is somehow infinite, unbounded. So knowing what is the best packing density in very big dimensions it has this practical angle as well. And so what we know here, so it's, so we do know on one hand that the things are not too bad and that if we have dimension D we could achieve density which is at least two to the minus D. And so here is a very simple geometric argument which tells us that if a saturated sphere packing in the dimensional Euclidean space has always density at least two to the minus D. So what is a saturated packing? A saturated packing means that we have a packing of balls so such that we cannot add any single ball to this packing so that it will not intersect with one of the already existing in our packing. So for example, if we think of this balls disks so that is a two dimensional picture because it's easier for visualization.  But now how we see that it has density at least two to the minus D so what we are going to do we are going to make our picture like this. So first because of here for the purpose of visualization of course in my slides I cannot allow for infinite packing so I have a boundary here but we agreed with you that boundary is not important and somehow we think of a boundary as being somewhere very far away but here I colored in this pale red the area where somehow I cannot put centers of a new ball if I wanted to still be inside of the box and don't intersect the existing one so I painted this area around the boundary and if my box is very big then some of this area that I took away it would be very small comparing to the total volume inside of the box. And now I don't want my new ball to intersect with the old ones and what that means it means that I take any of the previous black balls and I draw this red cloud around it and the radius of this would be also cloud in the shape of a ball with the same center and the radius twice bigger than the radius of a black ball and so now if I have a ball with a center inside of the red cloud then the distance from this point to the center of this ball would be smaller than two and it means that if I put another ball with a radius one then there will be an intersection and if I put another ball with center which is outside of this red cloud for example here then there will be no intersection with this ball and so my packing it will be saturated if and only if all the red clouds cover my box completely and if there would be some uncovered spot left inside of the box I could just put a center of a new ball in there and may make my packing even denser but at the same time if all these balls which are twice bigger if they cover my box and again here we forget about the boundary boundary is unimportant so if they all cover my box it means that the sum of the volumes of this big red balls has to be at least as big as the volume of the box and now an important fact is that if I have the d-dimensional ball and I increase its radius twice then its volume will increase to the power two to the power d. So in one dimension if I take an interval which is twice longer than the length will also become twice bigger and for the area of a disc if I have a disc here so the area of this disc is four times bigger than the area of this disc and for a ball for a three-dimensional ball it will be eight time increase and in dimension d the increase is d times and so this is where this two to the minus d is coming from so we know that the volume of all red balls is at least the same as the volume of the box and it means that the volume of all black balls inside is at least to the minus d times the volume of the box and somehow here there is a very many counterintuitive and paradoxical things happen. So first of all it seems that we have got this saturated packings almost for free and maybe if we apply some smart design we could do better and we can do better in small dimensions. However if we think of a very big dimension the situation is opposite that all explicit constructions at least in Euclidean space that we have they actually have dimension less than this one and it's like much like what else. So the best explicit constructions that we know they are exponentially worse than this one. And another question is what's about upper bounds? So in the previous lectures we spoke about upper bounds so maybe this two to the minus d how close is it to what is theoretically possible? So this is also something we don't know. The only thing we do know, we do know that the density of the densest packing in dimension did decays exponentially with the dimension. However the exponent is not like the logarithm of two it's another exponent which is a weaker one. So the difference between the best we can guarantee that exists and the things that we definitely know cannot exist is exponentially big. And so this is all I wanted to tell you about very big dimensions for today. So yeah, so I would like to congratulate you with Christmas, with upcoming Christmas and upcoming new year and also I'm ready to answer your questions about everything what you've heard about during these three lectures.


Albert, how many texts you got, man? Two men in a council? Yeah. What is up? I got a lot of music right now. Who's that from? It's a blessing, man. It's a blessing. It's a blessing. Washington University, Japan State High School. Full council. Thank you. Thank you. You're looking at your phone. How many text messages did you get? 70 or something like that. Where they all from? Where they all from? 70. And then good? What's the most, what's the best one to hear? I don't read them all.  It's nice. What do you think you'll get to them all? What do you think you'll get to them all? What do you think you'll get to them all? Come on.