It's me Ethan Nester from 2015 here to tell you from the past You got to take advantage of the show tickets that are on sale right now But where are they? I'm so glad you asked. There are so many cities around the United States and a little bit of Canada. Is New York one of them? You bet it is. How about Pittsburgh? Yes, Indianapolis. You're too late I have to do this dot show and get your tickets now before it's too late. It's me from the past Go to buy tickets Whoa, whoa, we get to see the How do you turn into stuff? Hey, I don't know dude How do you turn what you you you left click one mouse one. I'm whiskey and whiskey and whiskey. This is nuts I'm by the way. I'm seeing it. Oh wait. Can I help this or can you only do it yourself? Oh, how do you oh space? Get out what the hell's happening? Get the coins and stuff that you see For stuff I'm in a chair. Oh my god. Oh my god. How did you not hear me? What are we? Oh, we're gonna do gents I was just playing hide-and-seek the whole time. I Was not helping at all. I'm down.    You have to find your I'm repairing machine go. Yes. I'm a loaf of bread. Oh Shit, I might be able to escape. I'm gonna come get you. I know I got you up. No, I'm in the chair Okay, I'm gonna get you healing you How do we heal? I don't know. I don't know. I'm a mug. I'm a little We're going one in your inventory. Well g-wagon. Yeah, dude. Whoa. Oh, I'm afraid so funny Alright skill check Wow, how did I get out of that?  I'm I'm pretty spooked out right now Yeah, I like the sounds. It's not bad. I wish the environment was a little more creepy Okay, I'm gonna heal.  This literally is just db. Oh Which I guess makes a lot of sense. Oh, he didn't even do If you remain perfectly still, yeah, you pop the gen real if you remain Uh still like they literally don't They don't know I was a mushroom. He had no clue. Mm-hmm. Do you feel me? Well, she muted this whole time. Not sure if I'm sure if it's your business Oh my god. No, it was totally by axon. Who am I jason sully right now? I was gonna say It was only action over here God dammit. I keep not paying attention to the skill checks I don't want to be like I always feel weird being like, hey, man, you're not talking because it's like I'm about to get chaired again guys For my this is my second chair of the game. Oh guys, you can actually watch Other people while you're in the chair too, which is pretty cool. Yeah Yeah, isn't that cool? Oh my god. There's a tip coming at me Hey, man, how do I get out? Crystal How do I get you? How do I get you? Oh, there we go. So is it three? Is it three seats and then you're done? You think? Yep, I'm dead. Yep. Oh, I gotta I gotta helm it. What's the helmet to? Oh, let's go. God I got a red bull. I wonder what the killer sees like I gotta know I gotta know what the killer actually sees if you're Too long my prop is really really really good. I just want you all to know I'm a frog pillow I'm a frog I'm trying You're not really standing you're kind of like flopping but yeah Yeah, this is a bad. Yeah, this is a bad prop to be because it's loud. You know, yeah, that bunny was Dude, I can't deal. I can't deal with when you're not that it says self reanimation It's so good.    You're going in. Good job, bunny It's all our first time.  Wait, you have like that what we're doing right now Wait, I'm in a random.  I didn't know that that Could happen. Well, that guy's cool Ethan. You got to be that too. That's so This is literally a dbd map Am I wrong? This is actually a dbd map Fortnite Fortnite What's the point of building but you're going night night Yo, who's the Ethan there's corn, dude There's corn dude I can't move. Why can't I move? I got stuck. Whoa. Who is who is this carrots carrot candy?    Yeah, you just were like one you were like chris's character or whoever's character Yeah, you can just keep chasing the same guy back and forth. It's like scooby-doo, bro. Man, this is Greg don't worry. I'm about to do the sickest juke in all of america in all of america Put in a hypno chair I can see you also even Oh, yeah, you literally get propped my butthole right now with your character. Wow. That's mine too by the way That's that's super as much as I love this Wait, I can't oh you dropped me. I'm gonna grab one of you guys. You can turn into somebody else. Oh, you can Yeah, you can That's a special problem. Oh my god, your wiggle stays on that is Around town. Ethan, I thought we were friends. Please don't Yeah, you saw Ethan's face camping I'm tunneling I'm tunneling Ethan's like remember when I said you could come backstage You can't Who's this potato? Why am I so hurt, dude? Yo, let me get some heels. I'm not healing guys get coins fine chest get heels It's easy as that.  Oh, what is the battery dude? Yo, you got him out of the chair. No fair. Yeah, dude. I'm cracked. I'm on this other prop machine Oh, nice. So are you not calling him jens feels wrong. I love the prop machine over here, dude Oh, that's what it's called.  Is that a killer? Come on Who goofed it? Who goofed it will Let's go Ethan Get stunned putting you in the hip. No chair. Wait. Whoa, what? Dude, I'm out here in the streets In the proper streets and prop on streets In the pH streets. He loves your good dude. You're good. You know, I'm gonna hide in the locker Yeah, you can't do that. Why not try to throw Ethan off? Where's my coinage at? Oh, I only have eight eight seventy five What is that shit?  Yo, you walked you walked on top of me brother. I wonder I want to see what the killer can see. He's hey. He's hey. He's hey Chris What dude? I'm trying to help my team. Hey, it's been up me doors. Oh, okay. That's done Hey, man Yeah, oh it works through the walls That was the most effective Dude, you can literally flash your walls out guys.  What are you? He's a tire. Oh, wait. Can we leave? Or did you open our first window tonight? Even though he's coming under me. What do we do? It counts it counts He's coming after me I'm opening a door.  Someone please save me. Oh my god. It's so hard. You'll see it by sterfie Someone save me It's so hard. Whoa No one save me a little guy like where do we go? The hypno chair. I put you in the hypno chair Is everyone out?  I put you in the hip I am not out. Not yet. Come to the come to the red barn and Ethan don't come to the red barn Ethan don't come to the red barn I'm caught No No You know what's interesting to me There's like pirate here There's there are certain phrases that like young kids are saying these days that like or like whatever I don't get it but some that I'm like damn.  I was like, what does that mean like capital punish? Like I don't understand


What are you doing boys. Hey renegade it or renegade it or renegade it. This is water Okay, I'm not gonna. I don't drink pop. Don't even think anything about pop. There's no pop here This is water. All right Sorry, hey quick W Wait Joel. Oh, hey the MSU boys. It's the MSU boys. Let's get it. He's guy This is looking exactly like last game. He's the gas tank and then no I'm gonna I'm gonna self report you Body is in specimens.  We're at in specimens like in the actual like room Yeah, and the actual I just walked out of the hallway like coming from Admin or whatever or the swipe cartage. I just came in that way. It's like right So what has anyone coming in that way? No, I didn't I didn't see anybody Crews and Joel did you see anyone up top besides Poof came from specimen anyone else come up through specimen? Not that I saw I mean deluxe insider in lab at one point So where'd you go? I I've read in my scan right now. I'm I haven't even entered the specimen yet I'm in decontamination almost about to enter specimen where where'd you go because I I thought you went into specimen I'm right by medbay. I didn't go in it. Is that true? I don't know. I didn't look but I was Right Crews was already in there. Poof was coming in. Joel was the next to come in Unless JT somehow already is our killer our killer has to be in decontam top right or in that hallway unless m&g self-replace But that where we're where you think I didn't I didn't walk by anyone on my side. Who's at the rocket? So not the rocket the telescope Okay, never mind then I mean it could have been a cell but I go through my pathing and I didn't walk past anybody either and I also Wouldn't I mean I wouldn't self-report a body and specimen So our killer has to be in top right decontam or in that hallway. Yeah, unless it's m&g I'm on every side. All I know is that the lunch is on admin and Somebody's on cameras. So that's everyone's accounted for but you said I'm I'm in I just did my scan. I'm going into Who does this game by themselves? Me nobody's game by themselves. Did you say that? I'm good. Oh, you should have got us guys.    I'm gonna go wires on top of electrical And do my last task in specimen and then I have o2 canisters again I'm gonna hop on cam see what my other imposter is doing Wait, I think my other imposter got a kill on that. Joel got to kill that round too.   Yeah, that's fine. Okay. Anyway, the body is at the top decontamination I just opened the door doing my wires there going to do my wires there rather and then I didn't even do the wires I reported the body. I'm not the imposter. So it was definitely not cruise or deluxe No question. M. M. G. Why didn't you just go do lights? You just came I usually just don't do lights especially with how much I was talking last round I kind of figured if I went to lights I was just gonna die So wait, where did you find the body side? Uh, right now it is at the top of decontamination as soon as I open the door report button Bam speedy, where'd you go after doing lava? I went to left side of the map I did the download and then possible two downloads.  I'm floating down on cruise saw me and cruise saw me on the tree I'm on the I'm on the download by the tree cruise and I connect to each other We walk up to the lights and m. M. G. Is running away from the lights. Where did where did you come from? I came from med bay. I have scan I'm so excited I think m. M. G. killed the first one self-reported. I think side killed the second one self-reported All right, that's great. Self-reported I don't know. So I came from the left side It's also possible so I could kill the first one m. M. G. found the body and got scared Correct. That's why I already voted for side I actually just the first round I just went into decontamination I don't know why d4 is not saying that so that's kind of fucking weird What do you mean you went into decam? d4 is doing the thing where he's trying to be super smart This happens all the time.  And if I'm wrong after this side, you know what I'm doing. I'm gonna say sorry like a grown-ass man I'm gonna say sorry. You know what? I'm not doing my task.  You always say that when you're in posture That's the most classic in posture line ever. All right, honestly. Hey, that's fine.  Let's go. All right, so I can say that my final task is specimen room I kind of have to lay low here Come with me Joel Come with me for the double. I'm sticking.  I'd say it. I'm sorry. I'm sorry.   They did lights.  No words. I literally said to myself I said to myself Joel's still alive. He hasn't talked all game Let's go. All right. I'm crewmate.  Wow. I never would have made that play I I watched five up and I know that I never would have made that play.  I think i'm a What a good i finally got a good imposter game in dude. Let's go Let's go Oh, bro, would y'all would y'all really be my imposter and then kill me on the next round No, maybe not. Why aren't you jt? Why are you not reporting that body earlier dude? You were gonna walk by that? Um, wait, did you see anybody else? Uh, I saw deluxe up there. Deluxe went right. Yeah, I could have sworn I saw you bro. No, no, no Okay, yeah I don't want to be Fun that I was up there, but you saw jt right next to a body Yeah, yeah, but I was all I reported it. I saw you two of them, bro Okay, listen cruise if you're wrong on this one you have to say sorry afterwards deal No, I was I was up there alone with mmg. He went down to decontam. I and I came off my mid-bay You know who wasn't up there me I'm gonna really though. Can someone help me cruise. Are you do you think it's jt? Where were you then? Oh jt don't get off the hook with trying to vote for deluxe right now I reported it. I reported it.  What are you eating? My bangs are very popular Hey, he's on the body Horrible self-report because mmg just passed me. That's a horrible self-report. Uh, I'm gonna be honest. I don't remember seeing you, but I I believe it. I mean, I'm not saying to you There's nine. I'm not That's what I want to know. That's a bad self-report. I just saw mmg like two seconds ago I mean like it very well still could be um He's very well still could be jt. I just I don't vote on nine You don't want to do the imposter.  Uh, I was pretty good at 20. All right So I feel confident that Joel actually does have a specimen Unless he's like galaxy brain following me I I feel really confident that um Pete is not one Or not p. Joel There's deluxe and jt. Oh, I'm dead Deluxe and jt were with each other. Why would they do that? Those two are Sketches help each other.   Yeah, why were you shooting together? Yeah, because I saw somebody go into specimen and I wanted to make sure there wasn't a kill in there And then I went it up going in and Joel and mmg came out.   I did the same thing last game. Did you record a body or did you press the button?  We square danced around that whole JT, why would you do a task? And deacon to him. Well, this was right off the spot. I went to check on specimen because two people I fixed I fixed lights to ran down south and I just saw him at the very end. That's where I am right now MMG and Joel and david came from specimen and I went in there What for me? That's what I'm saying. I like I could kill me next round. I don't want to be a part of this anymore Thank god. Kill me. I'm gonna be at button. Just kill me. Oh, there was there was no kill here.  My only thing though jt is why why were you dancing with deluxe? Why were you even there? Why aren't you doing tasks or something because I did notice you two just like hugging each other for no reason This is right.   That was a long time for lights to be out That was a full black round. What happened aside.  Yeah, you're right.  That's exactly how I react when I get voted off as an imposter But didn't do anything. I'm like bro. I'm really here trying to get the hit dog and I just got snipe So, I don't know I still don't know and I don't know why he wasn't doing a task. So I'm okay with that snipe, but I don't know it was more of a I don't feel as bad because that was kind of deluxe and uh It was deluxe to jt's fun is my fault. So if they're both crewmates and we goofed there I don't feel too much burden, you know I don't feel personally responsible. I'm gonna keep cranking my task that seismic stabilizers I don't feel like doing that. I don't feel like dying bro. Probably making a bad play by Not going to this but Couldn't have been key. Whoa. She was with me. Yeah, we were chilling. Yeah, this is a cover up story So I uh, I went to admin or uh, yeah the room to the right of meeting room And I did my lava task went down to Admin table saw there was a body or the saw there was a person in weapons And then reaction got called thing around the same time weapons didn't move. That's where the body was That's Joel. Uh, there was one person in O2 that is me still there for a bit currently in Yep O2 canisters whoever whoever this was whoever this was obviously called ratchet to pull people away from there Where was everybody? I was waiting for lights and then I did left reactor. I did the right reactor Where'd you come from sweetie? Lava buddy when earlier in the round I went to the left and then I came back over and did the lava buddy Early in the round because I was that lava was my second task And I went and I went directly to left because all four of my tasks are clustered on the bottom left side So, uh, when did you go left? I'm not saying you didn't I just am confused early in the round I did my download in asteroids that I went over did the lava buddy reacting.     Yeah, I have a super Unfortunate task setup Look at my tasks, bro. We damn near could lose on tasks. Was my padding just bad? You're like did I kind of get cut here? It's bad.  I ain't going through space, but I'll tell you that right now Was what just got is that lights? Because that'd be too obvious There's got to be a kill now. Oh, yeah speedy. Why are you guys checking in there? What are you looking for in there? It's speedy. What are you looking for in there? No, I don't know. I lost just unlucky after fixing lights. That was unlucky, man. I'm sorry, but I'm gonna have to put you off your speed. I don't know what you're looking for I lost the body was in specimen. It wasn't the last body was on med bay. David did it It was not electrical. That was that was just unfortunate. Yeah, we galaxy brain that but Joe Joe just played a trash and posture up, but me and Joe were the ones who won last time too though I'm getting a lot of imposter games. I'm really excited right now. I'm gonna go directly into lab I don't even know what this task is. Oh temperature I know I guess I'll just go I was going to specimen I got to get a kill this round though. This is how I lost last time was by not getting these kills fast enough Soon as I see someone I'm calling electrical again. Dude. Why is David always the easiest kill? I feel so bad. I feel so bad. It's always the easiest kill Someone just went through decontamination. The body is right on the med bay.  All right, sorry. You're double kill, right? At least Besides where's the body the body was right on the med bay skin Where did you come from? I came from the left side after doing left reactor.  Um, so yeah Speedy's dead body was actually in decontamination that room right underneath med scan like right between the doors Uh, I was about to report it. What's that got the report up first? I will say I just saw david on vitals about maybe 11 seconds ago So that like you saw like you saw them there or you saw the body checking vitals That's not mmg What happened with your path thing at the end there because you went to it was speedy. Did you not entered where? Are you talking about med bay right now? No, you either got the color wrong or that was a long time ago I am in bottom left right now. I'm far far from all of this. Oh, Joel. Where are you? Wait, where are you bottom left of mg? Uh trash trash shoot like top right of water wheels and then under the tree I don't it's like the dead center of the bottom left room.   I did but Joel last round. He didn't do anything. I watched him. He didn't do anything Wait, let's not do a screaming match, please. Can we not do this? Let me speak though. So I watched Joel in the mic He just said nothing.  I Why Joel why are you not speaking up when cruise the person you were with about seven seconds before the body got reported died What what's what happened? What was the separation there? I was not near cruise p. I don't know why you're tell Why are you saying? I literally can you tell me where cruise was p and I you were the last with you I I saw cruising hallway weapons to finish my last two Rocks, I you're the last person I saw so I don't know Where I don't even know where the cruise thing came up with and I actually uh, I saw a side fairly recently How come I both saw you guys Who is with who is with you at lights p who are the total people at lights? It was just me you and deluxe came up afterward, but I was alone. It was me and deluxe Oh, it was you too. Yeah, two people came up from there, but I was alone in the lights Okay. Well, I think the kill had to have been out of that group of three as much as I want to vote for d4 I want to vote for beat because I Oh Joel here just trust me.  Get him out of here No first vote up right now. I'll be allowed.  I'm a lot smarter than d4 I will say that yeah, right clear throat again pussy. I'm a lot smarter than d4 Okay, you know what I have to do here. I have to get the lux I think I think I have to kill the lux and then get pete on my side about jp I'm just gonna say I have this node here. Can I fix lights like entirely fix them?  Geez Anybody dead? I was on by those old time. So we're good.  I Oh Never mind then. I don't even know what to say right now. I don't know. I don't know. I have no idea Are you done with test them jt? Why are you sitting on? I'm not. I just know.  I just did my upload. I just did my upload.  I mean like there should have been a kill that round I'm this is for everybody in the lobby in case I die. I think I'm 70% on mmg and 30% on jt I'm 70 on mmg and 30% on myself too, honestly Okay, I don't know well Yeah, I'm fully done. I'm fully done my task On a little uh, little field trip, but I'm fine with that fans So what do I got to do here? I got to call reactor, right? I got to call reactor and just hope someone goes to the right thing I don't know what to do here I don't know what I'm supposed to do here Beautiful Well done, wasn't sure what to do there. Yeah, it's fun. It's tough. It's always a pickle. It was a pickle I'll blow myself off Let's go Oh, I'm a cruise. I'm a cruise I'm so you ripped. Let's go. Let's go. Let's go. Let's go. Where is everybody? The locks just came in security.  Where did you just go?  The kill was in electrical.  Oh my god.  I don't know what I see. Okay. Can I get the rundown of what you guys think happened here? Yeah, yeah, I agree with that if we're on cruise this the spell is in the the spell lights on you Okay, so I go into electrical and I had a quick really that one where you push the knob all the way to the top I push the knob up to the top I look up and Cruz is gone. I am like where'd she go? What but she could have ran down and she followed me to every task that I did Besides that one. I checked in um, I see I want to see if she vented right. I want to see if she vented to um Secure but it was mmg there. Yeah, she definitely At least Electrical so I don't they probably wouldn't have just ran out. So they either came out or somebody that came in there after me And I don't know who it was. I it was Joel for maybe but I don't know who killed him in there for sure So, I don't know Right now, so I don't think yeah Cruz. Where did you go? You still haven't answered that question. Where'd you go? I told you where I don't think she vented and got zero. Okay.  I don't like God dammit. All right, whatever.   Looks like Cruz is going for a kill Jesus Cruz. Do you have something you want to say? I'm mj. I both saw you murder Okay, listen, why are you running with your nikes on?  I just threw me into that but yeah, I don't know if you saw that deluxe But Cruz just killed right in front of both of us at the at the bottom I did not and I did not man. Is she come on man. That's the way how jc just died No Before is there any chance it's a failed double kill. I don't know man. I'm so confused I don't think d4 just saw her, but she just killed did you see jt right next to us at the button? I love that. Yeah, I'm wearing like you right now.    I'm about to throw hands I think I'm gonna wait here.  Go ahead Pete Wait, why were you gonna say that?   I don't know here's a pitch Do we think that uh Cruz was not an imposter? No I watched Cruz kill. No, no, no, no, no, let's not even go down that path I watched her kill JT as deluxe to click in the button 100% In the middle of cafeteria in and mmg's defense this could have not been him He could okay. Well, can you tell me where you came from then mmg? Yeah, absolutely Um, I was I was first an electrical and then I realized that I hadn't fish admin like I went straight to electrical I saw Pete there or not Pete. You know, it was Pete. Yeah. Yeah, Pete, right? This is taking too much time. Hold on. I don't care. I'm not gonna I'm not gonna be right now The two people who pushed on a vote for Cruz last round was deluxe and mmg Deluxe, how come you're running to the right side of Storage away from electrical while the lights were off where the body was. What are you talking about? I don't I don't okay. Listen, Pete. I don't want to be You're running from the you're running from the left to the right side You weren't running from down. You're running from the right side of storage You're running away from where the body was. I'll be honest. I don't even know I forgot that lights were even What if we kill d4 and mmg I also believe that was the wrong play though because d4 called the button and Cruz was definitely an impostor Okay, so like that's 100% sure. I'm gonna I'm gonna call the button. I'm gonna like triple galaxy ring this Just just hear me out on this. I might just get voted off here, but I don't fucking care I was just I wanted more I want to I want to go back over this p I get what you're saying like the potential that there was two imposters left I I follow that completely, but I I'm not running away from where the body is even if you didn't know which which but like the body on last round or first round Yeah, last round Well, yeah, I mean, I know well, I know that it's not over Well, I know it's not over. So d4 was definitely wrong and Cruz is definitely one We're gonna shoot If anything I would have said it's sidearms I was about to clear sidearms and then sidearms randomly said that it was me Maybe he thought that I was gonna throw him out for doing something, but it didn't make any sense to me No, I saw the vent open in med bay while I was doing wires And then I ran up to try to catch whoever was and you were the one there I mean, they're probably whoever it was probably still sitting in that vent and med bay then Like after all I mean is we don't know for certain that Cruz got the kill No, I'm serious, like I watched okay number one She said she vented so either is the absolute we can lose to a horrible third imposter There's nothing wrong with that. She said she vented. She didn't have any defense and she killed right in front of me Yeah, she did claim she vented one time, but I think she said it anyway though I think she was third impostering for d4 to help him out and I'm sorry if I'm wrong in that but I might be a little critical No, but I saw Cruz kill guys like it that was one of them.  She did not realize that deluxe By the way, mng if it's not you. I'm sorry. It's just steady timing. I love you. Oh my god. This is bad This is really bad. I don't know what your reactor play is but go do it I don't know Woo Hey, well played mmg. I like that. Thank you Cruz. I'm about to throw hands.  I'm about to catch a guy in case The one who's doing a good job of third impostering like you know me And we're in Joel and then you did a good job of ninth crew mating.  Why are you talking about? You said you vented and then you threw me under the bus. Damn it. You were like yo, mmg saw me not killed Bro!  It was funny. That was kind of nose Hey, I love you guys. I'll see you soon. Goodbye. It's please the old clock, baby


False doors are undoubtedly one of the most perplexing mysteries of the ancient world. Found all over the globe, legends regarding these enigmatic doorways, seemingly leading nowhere, actually once having been active portals of unknown origins, have permeated the many native cultures still found at many of these ancient anomalies. The toppled obelisk of Axum, for example, is not only one of the largest megaliths found on Earth, weighing many thousands of tons, once cut, transported, and subsequently erected within an obelisk field in Ethiopia, is drenched in false doorways. Found in peculiar locations within Peru's mountain ranges, one in particular found within a unique location within a rock face containing a rare element now used to increase radio frequencies. Yet the most intriguing and well-known of these doorways is the Gateway to the Gods, also known as the Midas Monument, once perfectly carved into one face of a slim outcrop within this ancient site, literally translated as inscribed rock within the Eskisehir province in Turkey. Predictably, any circumstantial evidence that would suggest a date of creation within new or known world history have taken place by the academics tasked with dating the monument and the surrounding relics. The crude inscriptions, which we feel, due to the difference in quality and ability of their creators, we believe, dated at a more primitive time, have been used to age the monument to know earlier than the 6th century BC. This inscription, translated as, Atis, has dedicated this monument to Midas, Levactus, and Van Ex, being used to date the entire site. Quote, the name Atis, a variant of Atis, is a prominent name in Phrygia, associated with royalty. The fact that the dedication is made to Midas may indicate that he had received posthumous ruler cult. Various indications place the date of the monument's construction in the early to mid-7th century BC. The inscription probably indicates that the monument was erected after the death of Midas in the early 7th century BC. Another inscription, on the right side of the monument, includes the letter Yad, which was added to the Phrygian alphabet in the mid-6th century BC. No consideration has apparently been given to the possibility that, like many other, as yet unexplained ruins we have shared, may have simply been re-inhabited and subsequently claimed as this people's work, giving a false perception of abilities and power. We find this curious. Who built the Midas monument? Could these false doors have actually once been portals to another place? We find such hypothesis, and indeed the monument itself, highly compelling.


Are you ready to party right from the comfort of your TV screen? The rundown's here to save the day. From freshly baked videos to the classics to the youngins and dope conversations, all in one charge. We got you covered. Just tune in to The Rundown every Friday, 10.30 p.m. Waste the African time. The Rundown. Let's turn it up.


Okay, so we are looking at binary dch codes, a few things I want to emphasize which I think might have been missed out, let me go through this in some detail now. So essentially if you want length n, you have to begin with an element beta and some expression 3, the order of 3 bars is greater than or equal to n. So this is how you have to start constructing a binary dch code and why does such a beta exist, it always exists, it's easy to see why it has to be so. So once you agree on that, things are fine and then you can construct a parity So first you want dn equals, let's say greater than or equal to b. Then you have to do 1beta, beta square all the way to beta dot, n minus 1 and then the second row is good. Beta square square, beta square, oh sorry, this is just beta square and you have beta square all the way to beta square so beta square plus 2 power and minus 1. So now put, we just involve the way down, beta power b minus 1. So that's that, that's that construction method and we show why it satisfies both the properties you want that satisfies the property on n, but really what also looks at gives you a minimum distance at least d. So one thing that this construction does not give a direct candle on is the dimension. To find the dimension, you have to do some more work. The best way to think of the dimension is using this generator matrix. Then there's a polynomial, d of x. What is the LCM of all these? Minimum polynomial. And then we know that n minus k is going to be equal to what? Degree of d of x. So that's the handle you get on the dimension. If you don't compute the dimension directly, you have to find the LCM of the minimal polynomial. But then we saw that beta and beta square will have the same minimal polynomial. So only the odd colors here have some purpose of producing distinct polynomial. So it's very common to take this d minus 1 b to be equal to 2 b plus 1. The minimum distance, the design distance. d is called the design distance. So the reason why it's not exactly equal to the minimum distance is, the minimum distance is greater than or equal to d. You can't be sure whether it will be equal to d or not. You say that it's equal to d, you have to actually produce a weight d code word. In most cases, it will be true, but we don't know that I could have done it. So it's very common to take the design distance to be 2 b plus 1, and this d is called the design variable. A direct connecting capability. That makes sense, right? So you have small d as the minimum distance that is guaranteed, and clearly d equals d minus 1 by 2 can be corrected. So that's your design error connecting capability. Like I said, you will get a minimum bound of the minimum distance, and then you get an expression for the dimension. So it's not very clear how you can quickly bound it, but then you know that since... So remember, this is d minus 1 terms. So d minus 1 by 2 of them can give you non-trivial distance minimal polynomials. So what is d minus 1 by 2? That is small d. So out of these d minus 1 guys, this is actually 2t, t of them are guaranteed to give you the state minimal polynomials. And assuming the worst case that the d of them will give you a degree m minimal polynomial, you can get a bound on the... So you can see that the degree of g of x, what gives us that is smaller than or equal to... Smaller than or equal to m times t. So that's the main result that I was driving at. So that's clear, right? There are 2t terms here, and only the odd power terms have some purpose of giving you distinct minimal polynomial. The even power one clearly will be the same as that by 2. So because you have characteristic 2 here, so you can't get more than that. So that many of them will give you different ones, and the degree can be less than or equal to mg. So this is usually a tight bound. So small t equals to state. What do I mean by saying equals to state? Actually, equality is satisfied. There are some exact calculations you can do there that usually for small t, this is tight. So using this, you get a bound that is greater than or equal to minus m. This is usually true, and like I said, for small t, this is also tight. So that's a useful motion to have, and we saw some examples, and we were able to compute the smallest t for which this bound can be violated. So we had a way of computing that. I showed you an example, and I showed you for what t will this bound be violated up to some t it will be satisfied except for some t will be violated and there's a way to compute it. So you can do that. So remember, there is a statement here that I'm going to make which I think is very important. You have to pay attention to this statement. I think there was some confusion about this statement before. How do I define my binary dph code? It's basically set up all the code words and look at gf2n, to emphasize the operation of the code word that stands to transfer with 0. So this is my constraint, and I said to compute the dimension of the rank of h and related to the dimension you cannot think of the rank of h in gf2rn. So if you think of the rank of h in gf2rn you will get misleading answers because you're forcing c to be binary. On the other hand, I can also define a code over gf2rn with h as the parity check matrix. So look at this other code. Another code can be defined as cn, cheer, 2rn and subscribe, which stands c transpose is 0. So these two codes are very, very different. So clearly this code is contained in this code. Is this correct? This code is contained in this code but for this other code, what is the dimension? How do you define the dimension? What is the dimension? Do I have to do minimal tournaments at this point? No, how do you define the dimension? m minus rank of h, right? Is that clear? And now we compute this rank of h. How can I compute this rank of h? You can do personal elimination. You're right. So I've been making this statement about how for binary BCH codes this condition is redundant. Where is that condition redundant for binary BCH codes? If any code read satisfies the first condition, it will also automatically satisfy the second condition. There's no need to have, enforce that condition again. Can I say that the second row and the first row are linearly dependent? They are not linearly dependent. So I think a lot of people made this statement particularly in the first row. The second row and the first row are not linearly dependent at all. They cannot be linearly dependent. They are very different constraints. But if you first the binary BCH code on it, the condition implied by the second row is redundant. That's the only statement I can make. I cannot say the second row is the some scaled version of the first row. It will be a scaled version of the first row. It will be beta squared. There's no way one beta, one beta squared. One beta squared can never be a scaled version of one beta. So keep that in mind. The second row is not linearly dependent on the first row. On the other hand, if I replace each entry of this matrix by the m bit column vector, suppose I do that, replace each entry of this matrix by an m bit column vector, the first row will give me m rows. The second row will give me m other rows. Once I do that, I can say what? What can I say? Once I do that, I can make some statement about linear dependence. In that binary matrix, binary equivalent matrix, the second set of m rows will be linearly dependent on the first set of m rows. That statement is fine. There's nothing wrong with that statement. But if you look at these two rows as elements of gf2 power m, then there's no way these two are linearly dependent. That will not happen. Once you replace it with m bit column vectors, it has to turn out that this second set of m rows has to be linearly dependent on the first set of m rows. Now we are in a binary way. We are looking at gf2. Everything is in gf2. That has to work out. That's why the second condition is in gf2. There's a subtle distinction here. Think about it if you are so confused. Take some simple examples and work it out about gf16 or something. You'll see that because of gf16, if you replace it with the fourth bit equivalent column-wise, you'll see that the second set of m rows become linearly dependent on the first set of m rows. That's something important to think about. Condense yourselves about that. We have any other questions on this construction? This point is a little bit subtle here. Why we are restricting here to the binary constraint? Here we don't have a binary constraint. We'll come back and look at this another code. Another code has another name. It's called the Reach Solomon code. It's also a very, very popular code. The Reach Solomon code is also very much used in practice. We'll come back and look at this soon enough. You'll see the computations in the Reach Solomon code are much much simpler than the computations in the BCH code. But we'll begin with the binary BCH code. It's also useful in practice. Many, many systems use binary BCH codes. There are some advantages to binary BCH codes. Finally, we'll compare these two and the disadvantages are later on. We'll begin with the binary BCH code. Any questions? Things are fine? Are you comfortable? Let's do another computation. Just to drive home the point here. Let's take an example. Let me take N to be 2,000 from 37. There's a reason why I picked 2,000 for this one. Why have I picked 2,000 for this one? What? It's 2,000. 11 minus 1. Is it okay? So maybe this is not such a great example. So let's pick another number. Let's pick 3,995. What have I picked? 3,995 again. Right? 12 minus 1. You should know the powers of 2 to some 64,000 or something. What's 2 past 16? Sorry? 65536. Up to that, you should know the power of 2. It's important. It's an instant. Several communication contexts show up again and again and again. So let's say 3,996 is easy enough to remember. So it's 2 part 1 minus 1. Is it okay? So what I want to do is to construct BCH codes. So of course you don't have to exactly compute any minimal polynomial. But let's just try to find out for p equals 1. Which gives you d equals 3. You can quickly conclude k will be what? What's the answer? I'm sorry? 4083. 4083, is that okay? How do I get 4083? Degree of GFX is going to be 12, right? So first of all I should pick a beta. So let's say we pick beta to go into GF2 power 12. What's the nicest thing we can pick? Why can I pick that? What's the other way of beta now? 4095, which is what I want. So if I pick 4095, it's a very nice number. We can just go to 4096 and then pick up beta and it's primitive. And then what will be the minimal polynomial of beta? I don't know that. But what will be the degree of the minimal polynomial of beta? It will be 12, right? So most likely like I said it's going to be 12 most of the time. If you want to go really down, before it will not be 12. So the next case is to pick p equals 2 and d equals 5. And then once again, d is not the minimum distance of the code we are designing. We don't know that ahead of time. We only know that it's a bound. So usually it will be a tight bound but you have to be careful with the statement you make. Unless you show an explicit code of that weight you are not proved the minimum distance is that much. So what is this? So remember the real, roughly k is n minus mp. So n is 12. So that's the main thing. So once you just do that you can just keep subtracting 12. So it's a very easy thing to do. What do you get here? 471. So what about p equals 10? So here it could be a little bit fat but believe me if you hold till 10 let's just say. So what would be k? 4095 minus 120, what would that be? 3975. So let's pass at this point and see if we have achieved something which sounds very non-trivial. So I know a code now n equals 4095 and k equals 3975. So what does it mean? I can give you 2 power 3975 code words in web n 0 1 4 0 9 5 So you take the set up all possible 3095 length binary like this putting this noise and stop good. So you are able to come up with 2000, 2 power I think it needs some action. You can take whatever you want and you can look at it and it makes noise. Sorry? I know it really. Ignore the noise as we ignore everything else in this great country of ours. So let's say 2 power 3975 How big an number is that? Who can tell me how many digits it will have if I put 1, 3, 2, 3, 4? Roughly. Sorry? You know how to compute that? How many digits does it have? How do you compute that? Yeah, so Roughly you can do it. Let's take log 10 of this. What do you need for log 10? What's log 10 of 2? 0.3010 0.3010 times 3975 It's very big. It's going to be more than 1300. So a huge number of code words we can produce in this 0, 1, 4, 0, 9, 6 But anybody can produce those code words. So what is special about these code words? Anybody can come up with the list of 2 power 3975 It's not so hard. You'll get it. What is so special about these 2 power 3975 code words that you're producing? Any 2 of them will be found in at least 21 places and I can guarantee that. So that's something quite non-privileged. So at the beginning, if I don't do this, you may not believe. So it's very hard to come up with code words that are always so much distanced apart. But here it is, I can do it. I can produce 2 power 3975 code words Any 2 of them are at least 21 bits apart in different 21 places. So it's quite a non-privileged seed that we have accomplished. So in terms of this, I have a very, very simple description for each of my code words. So it's not that I'm saying this is a very complex description you run some computer algorithm for like 3 days and come up with this thing. So no, I'm not saying anything like that. What am I giving? I'm giving a very precise computation for the code word. So how do I describe the code word? I have to simply produce this gfx. What will be the degree of gfx? 220. So you take any polynomial of degree less than or equal to 3974 with primary coefficients. Then multiply it with this specific 120 degree 120 polynomial you will get the code. So what can I do very easily? I can do encoding very easily. So if I have to do encoding all I have to do is take this 120 degree generator polynomial and multiply it with whatever message polynomial that's coming out. So I think of these things in polynomials, I can do encoding very easily. So not only I'm giving you a guaranteed minimum distance in the construction I'm giving you a very simple encoding procedure. This is very important in practice. If you don't have a simple encoding procedure nothing is going to work. So you have a very simple encoding procedure for addressing this 2975 code word. So it's quite a non-privile phenomenon. So you can do this for anywhere n. For instance if you want to pick 65335 at 355 which is 2 power 16 minus 1 then you take a primitive element in gf2 power 16 and you can just repeat the same process and get all these numbers. In fact if I'm not wrong one such code is used in the digital video work as satellite standards. So they use these things everyday So that's something which I want to convey there's something magical about this construction. It's a very simple construction and it gives you fantastic results in terms of what is possible. So it gives you a handle on going to very very large propellant without any great difficulty. So that's something that's important. We'll come back and address these issues later. So let me talk briefly about the n product. So this is quite important. So like I said if you have an nk nk equal to b equals to b plus 1 binary dph code So remember whenever I say d equals to b plus 1 in the context of binary dph code we have to understand that we have to design this one. So let's say suppose g of x is another problem of n and what would be its degree? Degree will be equal to n minus k I know that's for sure. So every code So what is this code? I know this code has a simple description. Every code word is basically So every code word can be described as m of x times g of x. So this is another interesting result of the number. So this is the code word This is the generator polynomial and this is the message polynomial. And now do I construct this message polynomial? So it's going to be m0 plus m1x plus 0 until mk minus 1 x power k minus 1 and each of these ma's are binary. So I can take 2 power k message polynomials in this fashion multiply each of them with the generator polynomial and I will get a code word. So this is a very valid encoding. So you might just do one. So if I have a message m which is k bits how do I produce a code word? m of x times g of x and you produce a code word see with mx. So this is a perfectly fine encoding. But what is one possible problem with this encoding? Is there any disadvantage to this encoding? Any reason why you may not like this in practice? Anything that you notice? Sorry? It's not that expensive proportionally. n minus k So for every bit that you are producing of the code word, if you are doing something like n minus k operation you can't expect anything less than that. It's not that. So the one problem with this is it's not systematic. That is a crucial defect to this problem. So with this encoder. The reason why this encoder is not so good is because of this non-systematic character. What do you mean by non-systematic? It's not true that the message appears by itself in the code word. So that's an advantage. Why is systematic that's an advantage that's important in practice having a systematic encoder. Why is the systematic encoder nice? Sorry? So then on the decoder side you can directly take the message out. So once you do the decoding, the message is already available. You want to do a division by g of x or something. On the other side, you want it to be multiplications at few bits. So you only have to do multiplications for both n minus k parity. Which is better. But also more importantly typically what happens is there might be some other conditions that are satisfied by your message. There might be some other reasons why you might want your message to be in a certain form and you don't want some encoder to change all the characteristics of the message. When you do multiply the g of x the message might change and I may not like it in practice. I might want the characteristics I have in my message like for instance random positioning of one inch or whatever characteristics I put into my message to be retained by the encoder. I may not want it to violate. It can violate it for a small number of qualities. That's okay, I live up to that. I live up to that. But not for my message. There might be some reasons for that. So maybe you want something like that to be satisfied. So if that's needed, then also systematic encoding is very nice. So we like a systematic encoder. What we are going to talk about now is how to do systematic encoding for this h-coder. That's also very easy. It's a little bit trickier than this one but it's also very easy. So we will not map m of x to m of x times g of x. We will map m of x to some other multiple of g of x so that m shows the itself in the encoder. So this is how you do it. It's very easy. It's not very hard. So here is the systematic encoder. So what you have to do is you have to take m of x and in the first step multiply it by x power of minus k. So what kind of a multiplication is this? This is quite a trivial multiplication. So all you are doing is shifting all the coefficients of m of x to the left. So it's quite easy.  So that's what you get when you do this multiplication by x power of minus k. So of course this is not an encoding. I'm not in any encoding. But this has a nice form. So if I think of this as the code web. So of course it's not the code web but if I map it to a vector what do I have? So I'm sorry. I have 0's for the first n minus k positions m1 to mk minus k. So I have a vector where the message appears by itself. So this is nice. The message appears by itself. But now all I have to do is to compute some n minus k bits and put it in the first position so that this whole thing becomes a multiple of gfx. And if I do that I'm done. So I've found the systematic encoding method. So what do I have to do to make x power n minus k mfx a multiple of gfx? It may not be a multiple directly but probably I get to some multiple which is not a multiple. First step is to divide by gfx. So that's what we do. So you divide x power n minus k mfx by gfx. Remember gfx has degree equal to n minus k. So that's very important. So what will you get if you do that? Some quotient times gfx plus or minus k. What do you know about the degree here? It's strictly less than n minus k or less than or equal to n minus k minus 1. So this quotient I don't really care about. Some quotient times gfx. Now I have rfx here which has how many bits? n minus k bits. Now if I move this k to this side what happens? I get a multiple of gfx. So when I move rfx to this side what am I doing? I'm doing x power n minus k mfx plus rfx. But what are the first n minus k coefficients of x power n minus k mfx? They're all 0. So rfx will definitely occupy these first positions. So instead of these 0s you put rfx here. When you put rfx here you can guarantee to get a multiple of gfx. And that gives you the input. If you derive x power n minus k mfx by gfx you will get a quotient which you don't care about. You will get a reminder which you care very much about. You take that reminder and put it in the first n minus k positions you will get finally a code goal which will be a multiple of gfx. And that's systematic. So when I go from nfx to this multiple of gfx it is systematic. The message appears by itself there. How do I know that there won't be any repetitions? How do I know that two mfx will not give me the same code goal polynomial in this procedure? Yeah, where the mfx appears by itself there. Clearly the two code goals will also be different and they're all multiples of gfx. So it's a very trivial way to ensure that nothing very large will happen. So this is the systematic encoding procedure for bcx codes. Then it will be c++. I wonder how to divide by gfx. I don't know if you've seen this linear feedback shifted with this circuit. So it's very trivial to achieve the D-slip flap division. So the basic idea is to repeat the long division method. So you put a polynomial inside. You put the quotient there. You find each thing. So you can implement it with a D-slip flap shift register about any problem. So it's very easy to do that. So once you do that this division is done. All right? Any questions? Okay? So that's how you do this. Okay? So that's the encoder part of it. And the final thing I want to talk about is the generator matrix. Okay? Before we move on. So how do we have... How do we define a binary diffuse code? We defined using... using a... So suppose let's say mk e equals 2t plus 1 binary diffuse code. We defined using a 2t plus m parity check matrix over what? Over... some 0 to power m. So some extensive fee. We had a 2t plus m parity check matrix. Okay? And you know a method to go from here to mt plus m binary parity check matrix. How will you do that? How? Replace each element by this m bit column equivalent. But how do we get to mt, not 2mt? Do all the... Yeah, do all the... Get rid of all the... Maybe depending on m even the odd power bonds may not be needed but we know mt plus m is possible. Okay? So we can get that. So it would be nice to get to a generator matrix which is k cross m for instance. Suppose you want a k cross m generator matrix binary generator matrix, how do you do that? Okay? So it's quite easy. We've already seen it but I want to emphasize that once again. It's also possible to get a k cross m generator matrix. Any ideas on how I can do it binary, okay? How can I do that? Any ideas? We've already seen it. The answer is already there in our discussions. It would be more specific, okay? So it and all is general find. For the binary dch code for the generator matrix, m, k, d everything is given. So how do I do that? What is the critical thing that is needed? What do I use to get a generator matrix? The word itself should be a clue. You have to use the generator polynomial, right? So see, that's what gives you... So how do I... See, remember what is a generator matrix? Just giving you a set of linearly independent code words, right? I have one code word already. What is my first code word that I have? GFX, right? GFX is a code word or not? And I give you multiple of GFX is a code word. So you take GFX itself, convert it into one vector, you get a code word. That's my first and simplest code word I can generate, okay? Remember that. So that's very important to remember, okay? So GFX which is, let's say, g0 plus g1x plus random g1 minus k x bar n minus k remember this will not be 0. So g will be equal to x bar n minus k last time will not be 0. So you can just put it right by minus k. And I know from here from here I know so I would like I know g0, g1 g n minus k 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 1 is a code word. So this is a term that's quite important and you should remember that. Code words are all multiples of GFX, you might know that by heart but if I ask you to quickly produce a code word is a code word. In most cases, the minimum weight of this might be equal to d. So, which means what? Which means what have you shown? If for instance I compute this and I see that the weight of this is equal to d, then minimum distance of the bandwidth is equal to d. So, that is a quick way of checking that it should be. If the minimum distance here is not, minimum weight here is not equal to d, you may not be able to say much, but it will give you some tools as to maybe how I can combine these things. So, now, how do I quickly produce other code words? So, let me give you an idea of what is the easiest next code word I can think of. Of course, there are all kinds of multiples of gfx. Which multiples are easy? Yeah, shifting is the easiest multiple. So, you multiply it with 1, it is easy. Next thing you multiply by x or x square or x bar 3. So, any multiples or x is very easy because you are just doing shifting. So, that is an important notion to keep in mind. So, all you can do is, what you can quickly do is to come up with one code word and then other code words. So, other code words can be even defined by shifting. So, of course, if you want to go beyond shifting, what should you do? You should have some columns. So, the shifting is over, it is a good way to start. Remember, g n minus k is actually equal to 1. So, I wanted to remember that g n minus k is equal to 1, where the degree is equal to n minus k. So, what happens when I shift one code word after the other and put them in a row? I would get g 0, g 1.  How many zeros will I have here? Let me see. k minus 1, right?  So, when I shift what happens? I will get a 1 here. I shift a 1 there, a 1 here and so on.  So, along with the first one, you will have how many rows here? Right? So, every row of this matrix is a code word of my binary DCH code. And how do I know that no two rows are linearly dependent? Look at the right hand structure. You have 1, 1, 1, 1 along the diagonal along that path. So, no way any two vectors here are linearly dependent. So, this is a generator matrix which is k-trap in which you can easily come. So, this is a generator matrix. Now, it is also binary. Is that clear? Any questions? How do you question? Sorry? Yeah, it is not in systematic form. But you can convert it in systematic form. How do you convert it in systematic form? You can do both in elimination and convert it in systematic form. That is one answer. But if you want the systematic generator, the systematic encoding procedure to work here, it is a little bit more complicated. Let us not go there. So, you can convert this to systematic form by both in elimination. You want it, that is okay. But this is a valid generator matrix. There is nothing wrong with it. It is worse space is equal to your code. No problem. Okay? So, we are going to go for another 10 more minutes today. We are going to have to go anywhere today. Is that clear? Okay? So, one thing that this will help you is if you have to sometimes show in a course, for instance, that the minimum distance is exactly equal to 5 or 7 or something, then this will help you. Okay? So, you can quickly try to find some code word of weight 5 or weight 7. This method will usually help you. Okay? So, in small numbers, you can do a small n, small p. Okay? So, I am going to stop here and move on to discussing your quiz papers, entertaining your answer sheets. Okay? So, before I return, let me discuss, let me discuss the answers. I think most people have done okay. It is not proven to be a very difficult example. Except for the last question. I think last question, enough people have made mistakes. So, maybe I should point out what is going on. Okay? So, the first question we are going to see, it was about coming up with the table for BF16. I think everybody got it right. So, everybody got 6 marks yet. So, it is a DC shift of 6. Right? So, everybody got 6 marks. Nobody missed out on this. The second question I saw all kinds of statements which I wanted to clarify about in class. Okay? So, I have said that I have an NKD code over GF16. So, this is very very important. Okay? So, when I say over GF16, you cannot assume that the code words are only binary. Okay? A lot of people have made that assumption. At least from the reasoning that you know. So, you cannot assume the code words are binary. Okay? So, for instance, a paradigm matrix is given to you. 11, 12, 12, 12, 13, 14, 15. 12, 14, 15. So, the paradigm matrix is given to you. The first question is N, of course, the MS6. That is very easy. Okay? So, for K, how do you do this? How do you do K? Okay? For instance, a lot of people made this. So, quite a few. I think only 18, 17 people involved also. At least 3 or 4 people made this claim which is a large percentage. The second row is linearly dependent on the first row. So, the rank is only 1 for H and N minus K is equal to 1 and K is equal to 5. So, what's wrong with that? What's wrong with that conclusion that K is equal to 5? Okay? The second row is not linearly independent of the first dependent on the first row. Okay? Right? So, why is that true? You can check it. How do you check for sure that the second row is not linearly dependent on the first row? We do this in elimination and show that there's a non-zero term in the first one, followed by a zero on the second one. There's no way you can quickly complete. There are so many other ways of showing that here. It's not very hard. But that is the definite way of doing it. Okay? And you have to be there. Okay? So, if you don't, particularly in a case like this, we just say the two rows are obviously linearly independent. Looking at this, it's not obviously linearly independent. If there is a 1 there and a 0 there, then I agree it's obviously linearly independent. If there's nothing like that, it's not obvious. Definitely not obvious. I can show you some interesting examples. But here it's quite easy. But there are some more complex cases where the only place where you can say obviously linearly dependent is if there is a non-zero term, followed by a zero term. So, otherwise it's not obvious. Okay? So, you can do quick version elimination to check that these two are linearly independent. Okay? And so, that will tell you n minus k is 2. And from there, you can compute k is 4. Okay? So, in the gradient, I will expect some reasoning for linearly independent. Okay? So, you can't just say claim linearly independent. So, there is a way to check for it. So, you have to do version elimination. You can quickly make this 0, right? So, you just simply add the two rows. This becomes 0. Here, we'll get something else. And that shows linearly independent. Okay? That's the first part. And for the minimum distance, what is the definition? The minimum number of linearly dependent columns. Okay? So, remember again, when you earn NGX16, linear dependence is not the same as summing to 0. Is that clear? Okay? So, in the binary case, we can say that best mission is equivalent to minimum number of columns that add to 0. We can say that in the binary case. In the GS16 case, you cannot say that. Okay? So, in this case, it turns out both of them are the same. Okay? But it may not in the general case. Particularly, when I say the code is over GS16, you cannot make the difference. You cannot say the minimum distance is the minimum number of columns that add to 0. That's not correct. That are linearly dependent. That is the correct statement. Okay? We're clear. You have to think about that. There's a very subtle difference there. It's very important to remember. Okay? So, if you do that, okay? So, you have to realize b equals 1. Okay? No one column is all 0. So, b equals 1 can be easily ruled out. Okay? And you have to realize b equals 2. Okay? So, there is some proving needed there. Okay? You have to show that no two columns here are linearly dependent. Okay? So, I think I don't think anybody has bothered to even think about it. You just claim that any two columns are linearly independent. That's not enough. You have to show that no two columns here are linearly independent. I'll be sure that. So, we took out the four. One is alpha 2A. Another one is what? Alpha 2A. Am I right? So, this has to be equal to some constant times this. What should happen? Alpha 2A should be equal to 2 times alpha 2A. Alpha 2A should be equal to, sorry, alpha 3A should be equal to C times alpha 4G. 2A should be equal to C times alpha 4G. Okay? Okay? So, you can quickly manufacture the problem here. So, what will happen if this is true? Then alpha 2A equals C squared times alpha 4G. And if this is also true, then what should happen? C squared is equal to C. The only possibilities for C are 0 or 1. And then you realize that if you multiply any column by 0, you won't get another column. Any column by 1, you'll definitely not get another column. From there, you conclude that no two columns can be linearly dependent. Okay? So, that's a complete way of giving an answer. You can't say the inspection. This is not like an objective type paper where I only look at the last answer. Okay? So, I need the steps. You have to say some plus is equal to C. C is equal to 1. And that is not possible. Okay? So, only then I'm convinced that B equals 2 does not work. It's quite important. Okay? So, you might say it's not important that I do some marks for such steps also. Okay? Not all the marks, but one or two marks will be for that. Okay? And then finally, for B equals 3. Okay? So, D equals 3 is very easy in this case. Okay? You can argue that B has to be less than or equal to 3 by the single term. So, D equals 3 has to be 3. That is one quick way of saying D equals 3 is true. Or you can also quickly find several code words of grade 3. Okay? So, people have tried to find boundary code words of grade 3. Okay? It's also good. It's also easy to find. But non-binary code words are very trivial to find. Okay? So, if you just do Gaussian elimination, pick one column, the other two automatically pick themselves. Right? So, finding non-binary code words of grade 3 is very trivial. Okay? So, you can quickly find non-binary code words of grade 3. Is that clear? What do you mean by non-binary code words of grade 3? So, you do the Gaussian elimination. You will get I here. You will get some other column. You pick this to be non-zero. And then you pick the parities to be 1 and 1. So, it's very easy there to come up with it. The single bound is exactly satisfied. It's easy to do that. Okay? So, that's the final step. Okay? So, once you do that, you have to have D equals 3. Okay? But you cannot claim D equals 3 without proof. The other side of the single bound is to produce an explicit code word of grade. Okay? So, I think this has confused people a little bit. So, spend some time thinking about it. What are the differences between this and the other case? So, if I say binary BCH code. Okay? What will happen for the binary BCH code by this matrix? What is K? Yeah. Yeah. So, if I say, if I say binary BCH code, right? I have to do something else. I have to look at the minimal polynomial of alpha. What is the degree of that? 4. 4. Okay? And then I have to do N minus 4. 6 minus 4, which will be 2. I'll only get K equals 2 if I do binary BCH code. Okay? And the minimum distance will still be 3 only. Okay? So, it's a different kind of code. Right? So, think about that. That's something important. So, I would suggest that you replace each element by its 4 bit equivalent and check that the second row produces linearly dependent copies of the first row. So, you can see that it's not really hard. Okay? So, the third question I did not really expect such kind of confusion. I think almost all answers were interested except for I think one person. Pretty much everybody gave me precise answers and I'm not giving too much to everybody in the bad question. It was probably just a really easy question. So, more I think people made some very serious mistakes when I was very confused with them. Okay? So, let's take an n minus 1 through repetition 4, even though it's code. Okay? So, the important thing to realize is five-digit matrix is complete at once. So, when you make the statement as per the recap, how many bits are there in your syndrome? Those are just two bits. It's either 0 or 1. And how do you find the e-cap corresponding to 0? The least greater vector that gives you 0, which would be all 0. And what is the least greater vector between the syndrome 1? There are several of them. N of them, but you can't pick all n. Okay? So, people claiming that all n can be picked. You can pick only one e-cap. You can only pick one e-cap. So, I'll put my one in the first question. Okay? And then you have to apply the standard formula. What is the standard formula for problem-poor problem? 1 minus 1 minus p power n for this guy.  So, that's the problem. So, if you just follow the standard method, you get the answer in like three steps. There's nothing more to do here. And I think people are going round and round. And all kinds of confusion about what it corrects when people are claiming d equals 2. You can't correct any error. Of course, you can correct one error vector. Okay? So, okay. I have one book syndrome. You can correct one on zero error vector. Okay? Of course, it doesn't have any error correcting capability. That's not correct. All the way to one error. So, it doesn't have any error correcting capability. Because it corrects one error vector. Okay? So, do it. Do it. That's the least. Okay? So, don't say it doesn't correct anything. Okay? And the next one is the 1 comma 1 comma n repetition code. So, here if you do the syndrome method, it's a bit more complicated. I'm not saying it's not possible. But it's unnecessarily complicated. But you can go back to the main distance description. What is the main distance description? You have just two code words. Right? So, don't make your problem harder by going to a much bigger 5D check matrix and look at 2 power n minus 1 syndrome. Why do you do all that? You have just two code words. What are the two code words? The all-zero code words. The all-zero code words. Any vector, what do you do? Just compute the distance between these two. The closure to 0, you go to 0. If you're closer to 1, you go to 1. That's a much bigger description for the MLB quota. But people do some syndrome description. I have not sorted it, but it's certainly not advisable. Okay? So, you simply do this very quickly. Okay? But now a lot of the error vectors that can be corrected. Okay? So, this requires some careful path. It's not so easy. You have to carefully do it. Okay? So, what are the error vectors that are correctable? Okay? So, this gives me two cases. If n is odd, it's very easy. Okay? So, if n is odd, the rate of e less than or equal to m minus 1 by 2 is correctable. Okay? The rate of e greater than n minus 1 by 2 is not correctable. Okay? Both these statements are true. So, n odd. Okay? And you can quickly find the probability of error. Okay? What happens when m is even? m is even is a slightly more complicated case. Okay? So, one thing you can definitely conclude is the rate of e less than n by 2 is correctable. Can I conclude the other thing? The rate of e greater than or equal to n by 2 is not correctable. No, I cannot conclude it. Okay? The rate of n is okay. But what do we do? What do we do? So, there is a confusion there. Right? So, we are going to say I toss a coin and half the time I decide which is fine, which is optimal or you pick any one. If you pick any one, the computation is a bit more complicated. If you pick any one, your decoder is not symmetric anymore. You can't just happily assume all zero previous transmitted. You have to do zero first and then one first. Anyway, you will get behalf. Okay? So, the best thing is when you have equality for your analysis, you always flip a coin and choose any one which is closest. If you do that, the analysis becomes very simple. So, the MLB decoder will transfer the rate of e equals n by 2, if you correct half of the orders. Okay? Any half you can pick. It doesn't matter.  And so, the rate of e greater than n by 2, what does it do? It does not correct. Okay? That is also good. Okay? You always make an error. So, that's the MLB decoder. Okay? So, when you write down the expression, travel to the blocker will be distance or odd and distance or even. You cannot get one expression for both. I think almost everybody got one expression for both, except for maybe one or two guys. So, only those guys got that. So, I will do some marks here. Okay? So, there are various ways of thinking about this. Okay? So, let me also give you one more way of thinking about it to clarify this thing to what's happening. Okay? So, you have 2 power n minus k sub 1. Okay? Right? To each syndrome, you can associate a distinct error vector. Okay? So, you keep counting from weight 1, weight 0, weight 1, weight 2, so on. Right? Why am I counting from weight 0, weight 1 and all that? That is the layer weight in a vector. Right? So, of course, you have some minimum distance problem. You'll get stuck. But for the repetition code, you have no minimum distance problem. Right? So, you have to keep on counting till you come to minimum distance. Right? So, beyond this, only a fraction can be corrected. Okay? So, of course, it also could be greater than 2 power n minus k. Is that right? We're clear. Okay? So, think about this very carefully. So, you're looking at 1 and choose 1 and choose 2 and choose t. So, we're going. So, now for the repetition code, minimum distance is n. Okay? So, you can cover up to n by 2. But then, before that, after that, it's fine. But at n by 2, you have to take half to make sure that you're equal to 2 power n minus 1. Okay? So, the sum has to be equal to 2 power n minus 1. And when you have to minimum distance, you can correct for sure. Beyond that, you have to add some things to make it equal to 2 power n minus k. So, it's almost as if you're filling your syndromes with the error vectors, one after the other, and trying to cover as many error vectors as possible, so that you can add up to 2 power n minus k. That's another way of thinking about this problem. Minimum distance is important. Beyond that, something else. Okay? All right. So, let's stop here for now. I'm going to distribute the answer sheets. Okay.


بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والصلاة على سيد المرسلين وعلى آله وصحبه جمعين عود بكلمات الله تهاماتي من شرمة خلق بسم الله الذي لا يضره مع اسميشن في الأرض ولا في السماء وهو السم العالي ولا حولة ولا قوت إلا بالله العالي العظيم وصلى الله تعالى لسيدنا ومحمدن وعلى آله وصحبه جمعين برحمةك يا رحم الرحمن أولا شكرا لك for joining this session شكرا to MCC for putting these programs together بسم الله الرحمن الرحيم إن شاء الله what we are planning to do in the next few nights that we are going to be together go over some of the councils from one of the great sages of the 5th century إن شاء الله we are hoping they will benefit all of us during this blessed month of Ramadan one of the secret of Ramadan we all know about the faraida of Ramadan we have been into this month almost half way through this year one of the secret of Ramadan is because it is prescription just like in medicine you have over the counter and you have prescription drugs and Siam is prescribed this month of fasting is prescribed so there are mysteries in this prescription that Allah has written for the human being and one of the mysteries of this month is that we will get a chance to actually spend time with ourselves throughout the year people they don't get a chance to spend time with themselves or with their Lord here and there we go to the prayer we go to the Juma but Ramadan is a time that really we can concentrate on our relationship but Allah SWT and these two things are very important إقبال رحمة العلي the great poet of Lahour he said in a beautiful line in his Persian D1 and as you all know إقبال wrote both in Urdu and in Farsi in his Farsi collection Nasrara Khudi Mysteries of the Self is really one of the masterpieces of the Persian literature and he said از همك از كنا رغير صحبة عاشنا تلب هم از خدا خودي تلب هم از خودي خدا تلب هم ازخص كله وانتظار فإنه وحفظ فهذا ونقل ونقل ونقل ونقل ونقل ونقل ونقل ونقل ونقل ونقل ونقل إذا دخل شهر الرمضان when the month of Ramadan enters فتحة أبواب الجنة. The doors of paradise open. Right there, this relationship that we built with Allah سبحانه وتعالى that he's opening the doors of paradise for us in this month. وغول قد أبواب نار. And then he closes the doors of the fire, his punishment.  وصفر ذات الشياطين. And out of his mercy, he locks up the shayateen in the chain, in prison in this month. Because of the love that Allah has for his servant. جل شعنه. So this month is a time that we actually take a few steps back in order to jump further ahead. And this is the step back is to go into seclusion. This is why a lot of the علماء and the أولياء in the past and even ordinary people, they didn't take off. They in the last 10 days, they went into seclusion and they all they did, they talked to their Lord and they talked to themselves. One of the tragedies of our time is that people don't talk to themselves. Only in this country, only the mad people talk to themselves. But traditionally people talk to themselves, especially to your heart. The Prophet ﷺ said in a beautiful hadith that asks your heart because your heart would never lie to you. Human beings are disconnected from their hearts. This is what our Shaykh told us. He said, people are not disconnected from Allah. They're disconnected from their hearts. And if we connect people back to their hearts, they will see the light of Allah سبحانه وتعالى. So in this month is a time that we go inward. We go and we actually start communicating with ourselves, with our hearts and with our soul. Because Shaytan is not there to put waswasa into our head. And we have that freedom this month. And we have the ability this month. And Allah is there. It's so manifest. Allah is always there. Bahlul, one of the great Sufi master, he said, look, Taqwa, he was given the definition of Taqwa. He said, what is Taqwa? He said, have Taqwa of Allah. And he said, have Taqwa of Allah. He said, have Taqwa of Allah سبحانه وتعالى in your private gathering, when you're alone. And when you're in public. In your privacy, in your public. He said, فعلم بأن الله حاضر في كل مكان. Know with certainty that Allah is there wherever you are. Wherever you go, Allah is there. And that is the definition. Indeed, Allah is always there. But our understanding of that, that Allah is always with us, that is Taqwa. And in this month, we actually come to this. We can see that Allah is with us. The power of Allah, the hand of providence is on us. That we can go throughout the day without food, without drink. And without any complaints. Alhamdulillah. I haven't seen anyone. There's a Ramadan complain about the long days or about the fast. What about anything? Everybody's saying سبحانه وتعالى. So easy. Allah has made it easy. So, Abul Al-Ansari, which we will start tomorrow night, he has 10 advice for the believers. He has 10 advice in order to be successful in the dunya and successful in the hereafter. Majority of the advice of the علماء are أخراوي. They are successful hereafter. That how to win the آخر. Which is the greatest advice is to win the آخر. But Abul Al-Ansari is one of the unique characters in the Muslim civilization. He was a giant of the 5th century. He died in 481. Left behind a beautiful تفسير كشف العصرار. Left behind many great books in Arabic and in Persian. منازر سعرين سيد ميدان. Many books he has written. I am blessed to have most of his collection in my library. And one of the things that he said, he said I give you 10 advice. And if you practice these 10. If you practice them. He said you will be successful and happy in the dunya. And you will be successful and happy in the hereafter. And that's something that really a lot of us, a lot of people especially living in a modern time. It's really difficult to find سعادة. Find happiness in the dunya. And to secure your سعادة. Your happiness in the hereafter. And as Aristotle said, all of us are searching for one thing. Every human being on this planet. Whether they are Muslim, Jew, Christian. Whether they are black or white.  Men, women, children. Every single human being is in search of one thing. And that is a thing you cannot trade with anything in the world. You can't get it to buy something. It's not money. It's not wealth. It's not health. It's not friends. It's not family. What it is, it's happiness. It's سعادة. Everybody is looking for happiness. And he's going to give us the 10th habit of successful people of the dunya. And the hereafter. Insha'Allah we start that tomorrow night. And we hope that this is a blessed month of Ramadan. These are the time of reflection. These are the time that we need to spend some portion of the day or some portion of the night for ourselves. And indeed another portion for Allah سبحانه وتعالى. And that portion of ourself is reflection on our lives. And not about our past because the past is gone. مرنا رومي said, don't look at the past. If you have done something wrong in the past, Allah will make it straight. If you did cricket things in the past, Allah will make it straight. If you get on the straight path now. So now it's to put the milestone. Where are we going from here? What am I going to do until next Ramadan? And what am I going to do after Ramadan? How is my life going to change? Those are the milestones. We have to set some real serious goals for ourselves. Insha'Allah that we are people of success in the dunya and people of success in the Akhira. The greatest losers are the ones who lose both dunya and Akhira. And many people are like that. And then there are other losers who win in the dunya. They think they won but they lose Akhira. And the successful people are those who actually win Akhira. That's the successful. But the dunya is أولايكم الخاصيرون. They are losers in this world, the Quran says. There are people who are losers. But in the winning in success that Abdullah Ansari is going to talk about in the next few nights. We are going to be together. Insha'Allah is not about money. It's about the success based on virtue. It's virtue success that everyone appreciates it. Whether they are Muslim, Christian, Jew, atheist. And everybody loves virtuous people.  He is generous. Everybody appreciates generous people or people of temperance, of Haifa or people of justice and people of wisdom and people of knowledge. All of these virtues everybody loves them because it's universal and everybody appreciates universal truth. And everybody doesn't matter where you come from. We meet Christians that are virtues that people of virtue. And we appreciate that and we benefit from them. How many of us listen to the lectures of Dr. King and we benefit from those lectures? Why do we read Aristotle in Socrates? Because there is benefit in wisdom and we appreciate the Prophet صلى الله عليه وسلم said that wisdom is a lost treasure of the believer. Wherever he finds it, he takes it. So wisdom anywhere. We take the wisdom from anybody anyone who has it. Knowledge and wisdom. We take it from them. Insha'Allah. So we'll continue tomorrow night with the first two advice of Abdullah Ansari on the path of salvation and success in the dunya and Akhira. وصلى الله تعالى لسيدنا وحبيبنا وقرة العيوننا ومحمدنا وعالي وصح بجمعين برحمتك يا أرحم الراحمين تقبل الله. May Allah accept the fasting and عبادات. Insha'Allah.


This is Thambon Becky, South Africa's president between 1999 and 2008. He became famous for his denial of the link between the human immunodeficiency virus, HIV, and the immunodeficiency disease, AIDS. Despite overwhelming scientific consensus that HIV causes AIDS, he suggested instead that the causes of AIDS were related to overall low levels of health care and poverty in the country. He denied treatment to AIDS patients and suggested alternative cure such as garlic, beetroot, and lemon juice. His policies are now estimated to have led to more than 300,000 preventable deaths. Thambon Becky belongs to the growing number of people trying to deny, vilify, and reject scientific claims in a movement generally referred to as science denialism. Science denialism is not a new phenomenon. Think of Galileo Galilei, an Italian scientist from the 17th century that is considered to be one of the fathers of modern science. In Galileo's time, people believed the earth to be at the center of the universe. Galileo tried to demonstrate with his astronomical observations that the earth and all of the other planets move around the sun. This led into a conflict with the Catholic Church that forced Galileo to deny his ideas in a now very famous trial. Unfortunately, similar claims such as that the earth is flat are well persisting into the 21st century. Flat earthers may not pose such a big risk to society, but unfortunately this is not always the case. For instance, establish and secure cures such as vaccines are now being put in doubt in a movement referred to as vaccine hesitancy. Vaccinations help prevent between two and three millions childhood death every year, but the growing number of non-vaccinated children is rising more than one concern. The World Health Organization declared vaccine hesitancy as one of the biggest threats for global health in 2019. And this is even more the case when we talk about measles. Measles was an illness that was once thought to be eradicated and is now surging back all over the world. In this chart you can see the number of measles cases in the United States in the decade going between 2010 and 2019. It is clear that there was a huge explosion in cases in the United States that led in 2019 to an increase of almost 20 times the number of cases compared to 2010. We are witnesses of a constant degradation of the scientific endeavor. In order to fight this trend it is necessary to understand what science is and why we should believe in science. In order to do so today I would like to show you what a scientific theory is, how scientists get to a scientific theory and how it is possible to distinguish between scientific and non-scientific theories. But before doing so it is important to understand what scientists mean when they talk about a theory, which is slightly different than how the world is used in our everyday life. Commonly we talk about a theory as an idea or a guess that we have about something that has happened and that might not be really connected to reality in any way. In science we refer to the world theory as a description or a story that allows us to interpret observations and facts.  But how do scientists get to a scientific theory? Let us imagine to have two magnets in our hands. Once we put them close together we might observe two different phenomena. The magnets might repel each other or the magnets might attract each other. Imagine how to do so with more and more magnets and always to observe the same effect. We might wonder why do we observe such effect? Is it possible to extract a general rule that allows us to predict the outcome of such experiment? What we just did was to start from a real empirical world observation and try to extract a general rule. This approach has been used in science and in scientific discoveries for ages and is known under the name of scientific method. As just said, the scientific method starts from an empirical observation that leads to an hypothesis. In our case the hypothesis might be that there is a force driving the two magnets close together or further apart. And that this force depends on the orientation of the two magnets. Once we have a hypothesis we must be able to perform and design new experiments that might prove or falsify our hypothesis. Once we get the results of these experiments they might go in two different directions. They might deny our hypothesis and in this case we might need to reformulate and go through the loop once again. Or our experiments might confirm our hypothesis. And thus we would be able to elevate our hypothesis to the role of a scientific theory and accept it as a valid description of the phenomenon we are studying. In our case the fact we observe with magnets are due to magnetic fields and now we know that each magnet has two different poles, a north and a south pole. Same poles repel each other and opposite poles attract each other. But what makes the magnetic field theory scientific? The crucial feature of every scientific theory is that we must be able to test in the real world what the theory predict is going to happen. This means that we must be able to have real observation and real experiments that prove and show what our theory wants to tell us. This feature is called testability and it allows us to distinguish between theories that are scientific and theories that are non-scientific or pseudo-scientific. Today I will focus on three different characteristics of a testable theory. Falsifiability, repeatability and reproducibility. Let me start with the principle of falsifiability. Once again please bear with me because we are meeting a world that has a slightly different meaning in science than it is in our everyday life. The principle of falsifiability states that a scientific statement is one that could possibly be proven wrong. This means that we must be able to think of a real experiment that might show that our theory is false. The keyword here is possibly. Possibly means that the principle falsifiability doesn't state that our theory is necessary false, but only that we must be able to think of ways to prove it false. In order to make this principle easier to understand, let me give an example. Let's pretend to have a theory and let's call it theory number one. Theory number one states that there is a planet between Mercury and Earth. This theory is falsifiable. Indeed we can think of experiments that might prove whether there is actually a planet between Mercury and Earth. For example, we might think of having a telescope that looks what is before Mercury. Of course what we know nowadays is that there is actually a planet there and it's called Venus. This makes the theory real in practice but also falsifiable since we were able to think of an experiment that might have possibly proven our theory wrong. Having a theory that is falsifiable makes it easier for us to justify and believe in such a theory. Let's now go to the other end. Let's take theory number two. Theory number two states that there is a China teapot orbiting around the sun. Between Earth and Mars. Theory number two also states that this China teapot is undetectable by any telescope or technology known to human. This is of course a problem and this makes theory number two unfalsifiable, not falsifiable. Of course we cannot detect the teapot if we have no instrument to actually see if the teapot is there. This makes it difficult to justify and believe in theory number two. As you saw with theory number one, scientific theories are all about taking risks. We have to think of ways that might prove our theory wrong and then test if the theory is actually wrong. Moreover, scientific theory makes both predictions. We try to falsify our theory and until we cannot do that we think of the theory to be true and we believe in our theory. There are theories that do not take any risk. They are not falsifiable. In science this is considered to be a weakness and not a strength of the theory. Finally, let me highlight once again that falsifiability doesn't necessarily mean that our statement is wrong. Falsifiability allows us to keep in mind that there could be a new observation coming in the future that proved our theory to be wrong and false. If this happens we would be able then to change or modify our theory and this is our science advances. We said that for our theory to be testable once we have a scientific statement we need to be able to think of experiments and the results that might falsify our theory. In order to get really scientifically valid statements these results must be repeatable and reproducible. The principle of repeatability means that we must be able to perform the same experiment over and over starting from the same observation going through the same experimental setting and using the same instrument. If this is possible and we always obtain comparable results we have a repeatable experiment. Repeatability ensures that you as a scientist can trust your own results. Let me once again go back to the example of our magnet. A scientist would be interested to take two magnets and keep on putting them close together in order to observe whether they attract or repulse each other based on their orientation. If this happens the theory and the results are repeatable. Once we have a scientific statement that is falsifiable in our opinion and for which we have identified experiments that might prove it false we expect these experiments to be universal or reproducible. This means that if we have different teams of scientists scattered all around the world they must be able to start from the same question use their own observations and their own instruments but get to comparable results. Once again if we want to see whether the magnetic field theory allows us to have reproducible results we would have scientists scattered all over taking their own magnets putting them close together and observing whether they attract or repulse each other based on their orientation. If this happens the results are reproducible. We now have all of the instruments that might allow us to evaluate whether a theory is scientific or pseudoscientific. Allow me to give you one last example of a very famous scientific misconduct case that led to devastating consequences and that started one of the main trend in the vaccine hesitancy community that vaccines may cause autism. In 1998 British doctors Andrew Wakefield stated that vaccines that were supposed to cure measles, mumps and rubella the so called MMR vaccines were supposed to cause autism. Of course this piece of news and of research quickly spread all over the world and led to almost immediate drop in vaccination rates. But there was a fundamental problem. Group of scientists immediately tried to reproduce and find whether there was actually a link between vaccines and autism and they were not able to. Wakefield's results were not reproducible. Therefore from a scientific point of view his statement was not valid and could not be considered more of a normal personal opinion. Eventually what was discovered during an investigation was that Wakefield was working after being paid from private law firms that wanted to force a link between vaccines and autism in order to open lawsuits against vaccine manufacturers. Here I come to an end. Today I showed you what a scientific theory is and how common language and scientific language may differ. I showed you how scientists get to a scientific theory using the scientific method. Finally I hope I demonstrate that there are a few instruments that might allow us to evaluate whether a theory is scientific or not scientific and this would be whether a theory is falsifiable, repeatable and reproducible. Thank you very much. Thank you. Any questions? Raise your hands. There is one over there in the front row. As you're also a neuroscientist, do you find some strong correlation between the people who tend to go for anti-vaccinations, conspiracy theories, anti-migrants as well and they tend to be on the right side of the spectrum if you know what I mean of the politics? Do you find a strong correlation in all of that? Importantly, what's the main reasons behind it? Is it how their brains are wired? Also religion comes into place as well but let's move it out. To be honest I think it's quite risky to affirm something in that direction and I honestly wouldn't feel like doing it also because I have no numbers in my hand that confirm in any direction what you have just suggested. For sure there are different reasons for people tending not to believe in science and scientific theories or in vaccines in particular. And this might be related to education, that might be related to religion, prior beliefs, the society they are born in which of course plays a big role but I think it's very difficult to find a common denominator in all of these kind of trends and behaviors. Yeah I have no numbers you know so I mean again as a scientist if I have no numbers and especially then deriving casual relationships is always kind of tricky so I wouldn't they're saying something especially now in some situations. I think that was a great example of sticking to the scientific method. Any other questions? Don't be ashamed. There is one over there. There is a little bit of an idea that science is also a social process and basically boiling it down to the very strict philosophical principles is maybe not doing the real scientific process as it happens at a university and in the journals of justice. How much do you think do you see this in your own life and in your work or in the reality of science so to say? So I agree that often these two aspects are considered to be quite different and to a certain extent they must be considered to be different. But I do believe that in order to have meaningful scientific results that can have a real impact it is necessary to have this principle in mind and unfortunately I'm not sure how many people actually either in science or outside of science really know this principle and that's why I deeply believe it is necessary for everyone to have a basic knowledge whether you're in science or not doesn't really matter to have an understanding of what it actually means to do science or do experiments. Thank you for this answer. I would advise you to find him after the event for your other questions. Ask our time for questions on the stage is up. So thank you very much. I would give him a warm applause.


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Hey everyone, it's Mike from When I Work. Today, I'm going to show you how to create positions on your iPhone. Positions are used to tag employees and shifts to a particular duty, skill, or qualification. To add positions to be used on the scheduler, tap the More button. Select Positions from the Toolbox menu. Then tap the plus icon to create a new position. Type the position name and assign it a color code. If you want to save this position, without tagging it to an employee, tap Save. A confirmation screen will pop up and ask you to tap Save again. If you don't tap Save, your options will not be stored and you will need to start over. You may add as many positions as needed for your specific environment. Adding your positions is an important step in building your When I Work framework. Once they're added, you can get started on the schedule, ensuring you have the right people in the right places at the right times.