I think we are, you know, we are, we're alive on the metal voice and part two, again, with the Mark Stodaceae, I learned to pronounce your name properly, I learned to pronounce your name properly. You can say Storaceae, I'm used to hearing Storaceae. But I practiced. I practiced. In the USA it's Storaceae. All right. The voice, we'll just say the voice. That's it.  But now we've actually heard the album and it's coming out soon, at least sometime in February in Canada, USA, but it's already out in Europe. So maybe you want to just explain that to everyone. Yeah. And I suppose a lot of people across the Big Pond have heard the whole thing already as well. So, and I'm really happy with the reaction, by the way. Thanks for all your nice compliments. I'm really happy I didn't let you down and I hope thousands of others will think the same. Yeah. So how did it get to the album? You mean, well, it's thanks to COVID actually, you know, something positive and everything. It gave me the time when lockdown started out to look into my drawers and files and come up with all the stuff I'd been collecting over the years and Live and Let Live is a song which was written 20 years ago with a friend of mine, Charlie Pricell, lives down the road here, a good guitar player, he's really into total, you know, and we wrote about 20 songs over a period of a year and a half when I was not in Crocus anymore. And then we reunited and that took me away from my solo stuff again. So then it took a while, you know, the whole thing goes back to 2008, 2009, when we reunited and released the Hudo album and started touring again, the Big Crocus reunion. And the last, it was the last round, unfortunately. But it went really well and especially 2019, the whole tour, festival tour in Europe, ending with the final concert in Zurich in the Hollandstadion, which is the holy ground of rock in Switzerland on the 7th or 9th December. And then it was like, I have been in Grand Canaria working with these two guys who produced a series for television called Sing Mine Song, in which there were seven musicians and seven singers and each time one singer had to sing six songs by the other guys or one of his own, rearranged and reproduced the way he liked it, you know, and the 7th song was always one of your own, so I sang Hellraiser as a tribute to Crocus and that came out during lockdown, this series thing, and it was very popular and people saw me in a different light, they say, because you know, I wasn't being the rock star the whole time. We really all came down to earth and talked about personal stuff and about our career and so on and so forth. So Mark, I'm going to stop you for a second. No, no, it's all good. Go ahead. Yeah. Yeah. Did you say that it's done, Crocus? You guys can actually, and I'm just trying to change your gears for a second, is Crocus not coming, is it like done, it's over, it's finished, or are they coming to the, like, is it over? Okay, it's over in Europe because you've done your dates, but is it not happening now? Like it was postponed the Canadian North American tour, but now is that sort of finito done? Yeah. I think the last time we talked, I had high hopes and in the meantime, those high hopes have become quite dusty and have crumbled and I don't know what to think anymore, but I kind of lost hope myself. Everyone's gone in different directions and it's like, you know, what's going on? Nothing. So I'm concentrating on my stuff, my thing, I'm having fun and, you know, and I'm even planning on coming over things I'm being looked at now as we speak in the USA. Yeah, I'm happy about that. So Storace will be in North America, the voice of Crocus will be playing Crocus material, is that what the plan? In full, in full. Well, I'll be playing almost my whole album, Live and Let Live, and obviously that won't be enough to do a headliner gig, you know, it's only 10 songs, so I'm gonna fill the rest with Crocus songs, you know, and some of the songs, no covers, no covers, and some songs which, of Crocus, which I've wanted to do but never got the chance to do again because Like what? Name one of those songs. Name one of those songs. Midnight Maniac. Midnight. Oh, yeah. There you go. Look at this. This album right here. I love this live album because, because, yeah, hold on a sec, hold on a second, wait a second. Yeah, that's it. Yeah. So, and you know what, Mark, the only reason I'm sort of like changing subjects is because last time we interviewed, we went through the whole creating of the solo album, right? I just don't want to. It seemed like it was only like two weeks ago, but it was three months ago when we spoke to you. So things do change quite a bit in three months. So disappointed to see that Crocus isn't going to be moving as optimistically as we thought, but glad that you're coming over to North America, hopefully eventually so. But Mark, I'm even more excited that you're coming because you don't have the sort of the chains of Crocus. You could play whatever you want, right?  But there's some other songs which I've done so many times and I'll be happy not to do them and do something else which I've been wanting to do. Hot Shot Heroes. Hot Shot Heroes. What do we think? I don't know. I don't know. Tokyo Nights. Tokyo Nights. I love it. Tokyo Nights. Wait a second. You're making your set list as we speak here. Anything off this album? I love this album, Mark. Heart Attack. I love Heart Attack. Well, they're screaming in the night, which is like one of my favorite songs, my lifetime favorite songs, so I'm going to have to do that one. And I'm looking forward as well with the new band. It's going to be really exciting and I hope now we'll get enough gigs to fill up a whole month and looking forward to that. But in the meantime, we start the package tour on the 18th of March here in Switzerland. It's a Swiss package. Yes. Yes. You know the band Gotthard? Yes, of course. Yes. The lead guitarist Leo Leoni, he's got a band as well called Corey Leoni and he's got a new album out and we're going to get together and tour, do a few dates, about seven to eight dates. And when you do those dates, are you playing crocus material mixed with your live? What are you doing? Well, not really. We've played two dates so far. We had the baptism of the CD and this legendary nice place called Mühle Hunzikum, try to say that one. The struggle was thoracic. That's right. I can't even say Stonacci properly. So anyway, we had a great gig there and my two kids came out with a platter and the drinks and my daughter held the CD. My son gave me a bottle of Prosecco and we did the bits and everyone was a great audience.  Wow. It was the Balois session here in Basel. We played in this club where I had met my wife for the first time 33 years ago called Atlantis. So it was nice playing there again. And yeah, a couple of crocus songs, yeah, one of them's Midnight Maniac. I love Midnight Maniac. It was a big song in Canada. It was a big song in Canada, yeah. Even in the States. I mean, the Blitz album went gold and it was right after Headhunter, yeah, exactly. And yeah, there's a couple of great songs on that album and it was even released as a video and was up on MTV, like on, you know, what do they call it, high rotation or something like that. I love that sort of chord, you know, I just love that sort of harmony guitar, sort of arpeggio I guess, kind of, and it's just picking away, you know, that's a great. It's got that drive, you know, I don't know where Fernando got the idea from, but it definitely was a great idea, you know, it's kind of going up and down the scales. I'm going to ask everybody here what song they would like to hear you play live from Crocus. Of course we want to hear the new album, but let's hear it. I'm saying one guy saying playing the outlaw, Cecile saying hot stuff, hot stuff, which is my suggestion, hot stuff, you like hot stuff really from the change of address album. I got it right here somewhere. I got love to suit you, babe. Guarantee hard luck heroes. It's hard luck heroes, right? Hard luck heroes, hard luck heroes. That's a great song. Hard luck hero. Yeah, yeah. That's a great song. Yeah. We wrote that with the what? Are you getting like a radio frequency? No, no, no. It's my head is buzzing. Oh, look at this.  Okay, Electric Circus and with Rich Hall says Russian winter. Hey, that's a great tune. Russian winter. Oh, Russian winter broken hearts. Yeah, cold winds in the dark. I love it. Everybody rocks. Everybody rocks. Axe attack. Everybody rocks. That's from the Blitz. Down the drain. What about down the drain? Another one I'm doing is to the top. You know. Yeah. Great song. Yeah. Be a real beefy gang. Cuckoo cuckoo cuckoo cuckoo cuckoo cuckoo cuckoo cuckoo. Gang, it was that top. Yeah, Greg Adams. Greg Adams is saying everybody rocks. Where's everybody rocks from? Everybody rock the Blitz, the Blitz, the Blitz. Yep. Yeah, that rock the nation too. The fans here are speaking.  Oh, you have them in your ear. Well, no, no, they're they're sending, they're chatting. They're they're they're sort of texting, they're texting. I see. Okay. Yeah. Live and let live. Come on. Let's talk about the new album. I've been waiting here for how long now. You guys, you guys are reminiscing. Well, okay, we know about the history because that's what we talked about last time, right, Alan? Okay though. Yeah. So let's go into the songs. I love the new song. It's a great way to open the album with live and let live is a good message too for these days. Especially. Yeah, it fits actually for any any day. There's always some something worth singing that song for. Unfortunately. And for those of you out there, you know, it's not it's kind of like a hybrid hybrid crocus album where there is some sort of crocus vibe. But there's also a little more, right? Well, I have more freedom because there's not the crocus straight jacket if you like, you know, no boundaries. I mean, that's what that's why people do solo albums so they can spread their wings. Take these broken wings to fly again, you know. And yeah, it's it's it's nice, you know, live and let live is is also it's got that nice drivey riff, which could remind you of Midnight Maniac, but has nothing to do with it as a song. And it was based on the lyrics, which came first, you know. And what else? Yeah, then there's that kind of southern rock, groovy, the second song high on love. Yeah. Yeah. Yeah. Yeah. Steel guitar there. I wrote that slide with Adrian Fisher from Newcastle. He sent me the music. I picked that one up. And yes, it's got that slide guitar. The guy did a did a great great thing on it. And all the guitar was played by a studio musician who is actually not on the road with me in the band because because he had contracts, he signed with other acts, you know, so I've got someone else who's really great, great replacement, you know, Tourie Vicky. And he's out with me live now and will be coming to the USA as well. So looking forward to that. It's great. High on love for me. It's it starts out kind of like could have fit on a hardware album. And then towards the end, I'm like, well, I could have been on Dirty Dynamite, you know, it just got a real cool vibe to it. Yeah. Yeah.  It's easy to get hooked, you know, and then you're in trouble and, you know, morally or maybe financially later on. You know what I mean? So it's a kind of subject which is a common subject which not many like to talk about. And so it's a bit of an exposure there. And I've been through it. So I learned my lesson. And no, it's a great song. It's a great song. It definitely is. It's a lady of the night. Lady of the night. Kind of a darker kind of a dark feeling to that one. Yeah, that's a really good song. Yeah, well, you know, it's tuned down one whole note. And so see, that that's why it's so dark. The music is dark. It starts with an explosion, you know. You know, it's it's it's got this great groove. And this was also another song from which came from Newcastle, you know, from Adrian Fisher. And the boys immediately swallowed it up, you know. And I only gave them the demo of what Adrian sent. And what I do is just I put rough vocals and rough lyrics over it. And we took it to where it should have gone in the studio. And a great message and a great message, right?     And I did a similarity to that only instead of them being war victims, you know, which needed 24 hour attention. I'm thinking of the COVID guys that need to be turned over and you have to check the equipment if they're still breathing and whatever they they do. The agony of the guy going through this plus the love he's feeling from from this maybe one nurse just to romanticize it a little bit, you know, and then he gets well and he looks into a brave new world, thanking his lucky stars, you know, it's like what we're doing right now, you know, we're it's beginning to ease. And we're looking back and thinking a lot of people who caught caught the infection or the disease or virus. They they all said, in all interviews I've seen they all said, I wished so much that I had gone and taken the jab, you know, instead of trying to be the hero, yeah, I don't need it, you know, because I went through hell, I didn't think I was going to live through it, you know, so he goes through that and then looks at the sun coming up and walks into the sunset with a smiley. That was like the second video off the album that people can watch. Yeah, yeah, yeah, yeah, yeah. Yeah, I'm really thankful for this for my partner, Joseph Sutter. So we call him Seb Sutter. He's this film director who approached me to do the documentary of my career, which we actually started last November, because we were also blocked, you know, through COVID, no traveling and stuff. We flew down to Malta where I was born and grew up and started singing at the age of 14 with my first band. And so we went down into that first rehearsal room, which is today an Italian pizza restaurant. Hey, Mark. I'll have a grub up. But actually, it was closed when we went. So we had the freedom of, you know, doing what we wanted to do in there.  So it's a nice place and quite sentimental journey for me. And so we got that. And actually it was Seb who he volunteered. He said, you know, we're not working on the documentary, but I want to do your first videos. He first did the short series of trailers, just announcing that the album is coming and so on. Then he did Live and Let Live, you know. And I didn't know what was coming. He said, turn up at this place then, you know, and I turned up and saw this huge wall of LED. And then the whole thing came behind it, you know, the big storagy logo, all new stuff. So I got really excited seeing it for the first time that big. I said, wow, it's larger than nice. And with the flames and stuff. And I have Charlie on there with me, Charlie Price, whom I wrote the song with. So it was really fitting because I didn't have to band by ready yet by then. So I invited Charlie and he came with flying colors and a shitty eating grin. So happy to reunite just for the video, you know, it was it was fitting, you know, it really helped. It was nice. And the second video just was just released, right? Is it out there yet? Yes, it's out there. Yeah. The first Live and Let Live and the second one is Lady of the Night. Lady of the Night. They're both out there. Yeah. And those were made by SEP. Good job. Cut Heart. Cut Heart. His company's called. Yeah. Great. Just a quick hello, Gabriel says hello, Mark. He says hello, Mark. Hi. How are you doing? I like the Broken Wings is another strong song off the album. I mean, it's got a kind of a dead daisies feeling playing. He was I mean, it's just got such a groove to it's really a pleasure to listen to. Yeah, yeah. It's, it's also got that heavy riff, which I love. It was very inspiring. And I kind of, you know, there was so much energy in the music. This, this was an idea which came from Cyril, guitar player and Massimo, you know, the guys that I met in Grand Camaria. We, we worked on this series together. Yeah. And they came up with, with five of the songs on the album. And this take these broken wings. You know, I, the music has so much energy in it that I could lay back, you know, I'm very laid back on that, that one. And letting the music doing the talking, leaving gaps and stuff. It's a kind of less, less is more attitude on that one. And the deep, deep song, deep words in it, you know, that could have been a crocus song. No place to hide. When I was listening to that one, it's amazing. You know, I'm thinking about the early crocus, your voice on the early albums, and your voice on this song in particular. How do you still do it? You sound as strong now as you did back then. Um, I really don't know. Maybe it's the coffee. No, I, you know, I'm always, I can get pretty hyper, you know, I'm an energetic kind of guy, except, you know, and when my, when my heart starts pumping, you know, I was always told by various doctors and so on that I have a sportsman's heart, you know, so I pump a lot of red stuff through the veins, you know, and that helps, of course, to get the energy going and hit the notes. But then you have to be careful of when you're going with such power on this little, little vocal thing here with those chords, the muscles and everything that you don't burst anything or screw anything up, because then you're like, you're done for months, you know.  I'm talking about soccer and so on and so forth. So I like to stay in touch with, with my art and I give it all I've got in the right place. And I guess that keeps me on that level, but I'm not on the same level I used to be like on one vice at a time. There I was like hitting, oh, my pitch was really high there, but I was younger and my voice, my voice was the kind of thinner. And even on the headhunter album, I'm boy up there and soaring high as an eagle and landing on my two feet, you know, finding the rhythm, coming back in and going, you know, how, how can you, how do they say nowadays, I hit the, I hit the floor running. But just the texture of your voice, you know, it's so similar. It's, you know, we're all aging and that you tend to lose it a little bit. But I mean, listen to that song and it's like, three, four years ago, you sound that, that like you did back then. Thanks.  No way. You know, Bon Scott sounds like me. All right.  And he said, why is that me? I sound so strange and most people don't like it. Neither did I. So it took me a while to overcome that and accept the fact that, you know, yeah, well, because it resonates in our heads and we hear it different than the way it goes out, I suppose. Whoa, whoa. Who cares? I don't care. Main thing is, main thing is that I enjoy singing because it really gives me a buzz, you know, when, when everything's functioning as it should, it's like, you know, fine tuned and everything. And I'm going for notes and I'm hitting them and, and having a good time. I'm sitting on the rhythm and see the band and enjoying themselves. So it's like, I'm in heaven. It's like, nothing can pay that, not, not, not the biggest yacht.  Something else. It's, it's you're in your own body, you know. And my, my second favorite song off the album is Don't Want to Go. It's a great ballad. Great. I love the guitar solo on that one. Yeah, amazing. The way he hit it, he, he tried about nine times. And then when he did that one was like, we all got goosebumps. That's the one, you know, it was amazing. Yeah, it was amazing. And, and that song, you know, when I first played it to my wife and my daughter, you always have to play balance to the girls first. They, they had tears running down their eyes. Don't want to go faster than the light. You know, if it's like, even, I don't know how that line came, you know, don't want to go faster than the light. The road to ruin lies in darkness. You know, it's far faster, faster than the light. It's like, I'm going to go on a limb and say, that's your best ballads and screaming in the night. Thank you very much. It's, it's just a fantastic song. My ears can't believe that. Thank you very much. You're going to get more than a beer when we meet. Two beers. No, you could have any whiskey you like. Love over money, you know, that's got that once been twice try feel from it, you know, especially in the chorus there. That's a very 80s 80s. That's a very, very 80s. Yeah, yeah. Well, it's kind of, you know, not exactly a boogie, but it's getting there. And yeah, we have to have a song which is like a good time on core song to play, you know, when you come back on stage and you don't want to be too serious anymore, let your hair down, let the whole band do a solo, you know, that's like we break it up in the end, you know, everyone does his solo and it's because it really gets you on your feet and it's repetitive, you know, and it's amazing. It's just one of those songs which just came and, you know, it's a serious subject, you know, love over money. Yeah. And it has to do with all the greed today, you know. It's like a party song. It's a party song but with a serious message in it, you know. And that's also a little bit romantic and stuff. There's a long story behind it, but yeah, it just hit me straight away. It came from Cyril, you know, down, down, down, down, down, down, down, down, down, down. I even think it could have been a Springsteen song, you know, maybe arranged slightly different. We have a request here, Mark. Quick little interjection here. George wants to know, can you sing screaming in the night a little bit? In the corner of a valley, we took her by surprise. The sound of steel rang loud. Above the battle cries, what I found her lying lifeless. I got through her home. I picked her up and held her hand. And I swore to be avenged. Scream. I can listen to you all day. I can listen to you do this all day. All right, keep going. Side two. I need a pastille. Well, yeah, I mean, to be fair, when you talk, it kind of burns the voice, you know. Yeah, you know, I get more tired when I talk for an hour than when I sing for two hours. Wow. I don't know. My favorite track is definitely Paradise. I love that closing track. What? That's your favorite, your favorite track. I thought the other one was your favorite track. Really? Hey, you're a West Coast man. West Coast. You know, I'm a big fan of Saturday Haver, and he's doing this whole thing about beaches and drinking and tequila, and it kind of just right into that. You know, you're singing about paradise. Is that your idea of paradise? Well, yeah.  Yeah, that's, I love it, but I didn't think you'd pick that one up as your favorite. I think the lyrics are universal, and it's just got such a relaxed feel to it, just such an enjoyable track to listen to. Yeah, I think it's kind of a happy end feeling after all the messages and politics and romantic stuff, which is like more serious, and then you end up, it's like, you know, it's a good way to... It's a good closer. It's a good closer. To close, you know, you close with a smile on your face. Exactly. Yeah, I agree. Mark, so a few people texted, what happened? I mean, we've heard this story so many times from you, like the ACDC audition in the early days, maybe just quickly, quickly, fast, fast, just say that, a few people are asking. People always ask, were you, one person says, let's clear this up once and for all. I've heard a lot of rumors about ACDC when Bonds got passed away, sadly, and you were asked to join.  Well, I wasn't asked by ACDC. I was asked by this production manager who was up in Birmingham in England, this big production company building all these backdrops and stuff for various bands, including Crocus and Lightshows, you know, and they brought our Lightshow down to Solaturn, which is the birthplace of Crocus in Switzerland. And this guy, Steve Dockx, he was the CEO of the company. He came down because they had this computerized lighting desk, which I've never even seen in my life before, you know. And he took me to the sign and said, would you like to audition for ACDC? You know, because I'm very close with the guys and I said, Steve, I'm too happy with Crocus. These are my new buddies and we're going places. And I don't want to change my horse in the middle of a race. It was like, thanks, you know, and that's it. So it was an offer. It was just an offer to audition, not to join the band. No, no, no, no. I guess I don't know if the other guys knew anything about it to tell you the truth. You know, I don't know what's behind it. And in retrospect, about 10 years ago, Steve told me, you know, you did the right thing. Money isn't everything.  I love, I love Brian Johnson. I was sad to hear that he was having engine trouble. You know, he's always driving with his voice. And I'm glad he's back now and things are getting back to normal. You know, it's great. You know, it's sad. Always sad to see a singer or whoever, other musician have a problem having to give up, you know, I'm using in years, you know, I've been using in years now for a few years to protect my my hearing. But my hearing's been screwed up since since a young age. Because a singer always stands in the middle of a stage in front of a drum set. And sometimes there's no no room to go away from those symbols. And the symbols, the high pitch of the symbol is what kills your ears. Oh, wow. Another text says, have you cleaned? Have you guys made peace, you and D Snyder? We've talked about this too. But just fast fast. Have you made peace after all these years? Yeah, you made have you broke bread? Well, I've always made my peace.   And at the end of that tour, we were supposed to play one concert in Vokken with this whole orchestra, the band and everything. And I was thrown off because D Snyder came into headline.  I wanted I wanted to actually I was looking forward to asking D if we could go to the side and have have a beer. And so I could maybe apologize and say, Hey, let's bury the hatchet. It's not worth it. It's a few hundred dollars worth of clothes, which your wife, whatever we didn't accept. We didn't like those clothes. Sorry, stage clothes. And it's as simple as that. I don't know what else what had happened. I was not in the room when, when this thing happened, you know, so I don't know if there were any dirty words spoken or the attitude in which things were said. But I don't think it's worth, you know, like going to the grave carrying a burden like that. You know, I'm, you know, I would just say the D night right now if D was watching, what would you say right now? Hey, hey, D, I'm looking forward to meet you not to get in into into big arguments. We know the whole story. But I think now we're mature. We look forward. You love your wife. I love mine. And let's just sit down and I don't know. Move on, move on in life. You want to move on, leave all these negative burdens behind, you know, heal, heal those broken wings. Yeah, exactly. I like that. Hey, Mark, you remember the group Kicks is just into Steve Whiteman a couple of months ago. He released his solo album, right? He was a part of Kicks forever. Now he's got a solo album. You have Tony Martin, there was a Black Sabbath. He's got his solo album. So, you know, what is your expertise? They were saying it's a bit of a struggle. It's a bit of a labor of love. We're not expecting to make a lot of money. What's your expectations for this album? Well, it is a labor of love.  And all the whole organization and even financial responsibility. In my case, I don't have a record company behind me. But I have a great manager, Rolly Egley, and he's actually the drummer of Tee, you know, the progressive band that I started out with back in the 70s, did three albums with the producer of Scorpions. And yeah, financially, it's just 50-50. And we're happy with the reaction that the albums been getting so far. And as I said, we're looking forward to a tour. The band is great, great musicians. And we just hope it's going to grow and that we can go places and have even more fun. And Crocus has left a vacuum behind, which I'm not trying to fill with Crocus songs, but I want to contribute new material. This is the first album. And I'm looking forward one day doing the second one. But first, I want to have some fun with this round. And just hopefully, you know, COVID will go away now forever. And we can do what we want to do. And enjoy doing it. Yeah, we'd love to see you in Montreal, you know, in Montreal, Canada. It'd be great. I'd love to. I don't even know. Alan, when was the last time Crocus even played? Eighties? In Canada. Yeah, eighties, 1980, something, five, seven. Yeah, yeah. With Accept, maybe? I don't, Grim Reaper. Was that the tour? Grim Reaper, Accept, and Crocus? I can't remember. The Blitz, I think it was the Blitz tour. That's what it was. Or maybe even Heart Attack. It could be Heart Attack. I think we played this small club somewhere called Spectrum, maybe. Spectrum, Club Soda. Or Toronto. Maybe you played Toronto. Maybe you played the Massey Hall or something. I don't know. All I know, we've discussed this before with Mark, but I saw you open for Def Leppard's first major headlight tour, Piramania. Gary Moore opened before you. And guys, Mark is one of the greatest frontmen to ever be on stage. You got to check him out if Storace comes to your town. Thank you. You could say Storace. Well, no, we're trying to do it right. Mark, Cecile wants to know, can you ask Mark if he had any bad experience when they were signed to MCA? A lot of acts have said MCA was a terrible, you know, a label to be signed to.  And here we were touring. I mean, Fernando and I had never stopped since I joined in late 79 for metal rendezvous and I carried on, on and on and on. And this was 1988. And I was slowly burning up, burning out with all the psychological games and negativity within the band as well, between band and management. And then we end up with this record company, which for me was like anonymous, you know, I don't remember anybody from there. Oh, you know, and I was happy to to leave the band and call it a day after that heart attack tour. That's all I can say, you know, and when I look back now, I think hell, that was a great album and we had some great songs on it. Yeah. 699. They were getting harder and harder to find as your career progressed throughout the 80s, maybe that's one of the reasons why so have the backing of the record company. I think they all started to lose faith in hard rock and heavy metal. You have Iron Maiden there behind you. And I remember we played up with Iron Maiden in New Orleans. And we didn't sell out the hall. Yeah, this is the largest hall, the big round one. Oh, yeah. In New Orleans. And it was only like half full. And I remember we were sitting there eating seafood with with Iron Maiden guys. And yet the atmosphere wasn't so happy. You know, business wasn't as great anymore. What year was that? What year was that? 88. 88. Yeah. Wow. With Iron Maiden, with Iron Maiden, it must have been the 90s with Iron Maiden, like when things were sort of going. Or maybe it was the start of the waning waning out. But I remember that vividly. Yeah. Yeah. Yeah. Yeah. Wow. So that's all Brian. That's all Brian's. You know, did you ever when you're making change of address, did you like say, you know what, guys, maybe we're going the wrong way here? Was there any sort of, I like the album, but at the time, right? Yeah. Did you like, did you second guess yourself or what you're saying, guys, we got to do this? Or what was your, what were your feelings? I think there was too much hairspray and color, color, stage clothes, and the music wasn't crazy enough. And it's kind of got toned down. Everything got too polished. And for me, for me, this was a difficult time. We had, we had everything ready, though, that, you know, the songs and everything we were in the studio in LA. And staying, we had these apartments and kind of rhythm going, the band was recording, and then I got this phone call, my dad was in hospital, had a stroke. So I left the following weekend and flew down to Malta to see him. And yeah, and spent a week there. And there was nothing anyone could do. And returned to sing the album, you know, like, like I came back had a two day rest. And then went in to sing change of address, you know, so the parts I enjoyed most were the bluesy parts, you know, the, the more melancholic parts and bringing up a lot of aggression was kind of a little difficult to do. But, but the songs didn't even really ask for, for that kind of headhunter kind of songs. It's a different, different cup of tea, you know, and it was trying, trying to be more commercial, really, which, which really didn't fit. And somehow we were guided up the wrong alley, you know, that's the way I felt. And there was nothing much you could do. You know, because every, everyone was like, like following blind, a pipe, Piper, with the bags of money, you know, that's the way to put it. You know what I mean? Of course. And because, because that, that was a huge budget behind that, you know.  And but, but everyone, you know, it was like management booker and record company.  And, you know, I just, I missed those beefy guitars, you know, and but then the album's released, right? And then it kind of like goes up, then it goes down, like really fast. Was that was disappointing? Like after all that money spent, all the sort of band dynamics, yeah, was, was that like sort of like, guys, what did we just do? Like, why did we do that? Like, I mean, yeah, yeah, well, what can you do?  But the, the problem is you lose a lot of your hardcore fans, because they kind of take it personally, you know, but, you know, but when you look, when you compare to bands, even Queen or ACDC and ELO, that's like even the Beatles, you know, they have bad albums, bad albums, in my opinion, maybe you would think that's a good album that I think is a, was a bad album and the other guy things, you know, but, but actually, but to put it, to put it in general, we, we went out of our normal, you know, we put on the wrong boots that day. You put on sandals, that's what happened really. Yeah. And it was raining outside. So things got really messy. Yeah. But, you know, I, I guess lesson learned and yeah, yeah, yeah, yeah. I mean, you and everybody else at the time, then not only Crocus, but all the bands were sort of getting glossy and hair spray and getting more commercial. Yeah. So I mean, we should never have jumped on the bandwagon, you know, on that one.  Yeah. It was amazing, you know, but what's done is done. That's right. That's right. You know, the good news is we all like Midnight Maniac. That's the good news. We still want to hear it live. So that's a, I'm going to tell you, for us in Montreal, that song was played on the radio non-stop, non-stop when it came out. I have all of my members. And I literally just saw Ballroom Blitz on TV the other day. They were showing hair metal. I think they called the hair metals show and they were playing Ballroom Blitz. Holy moly. Crazy video by, I think, Martin Cahan, his name was. And that was, it was crazy. The idea he had. So, yeah, I just want to wish you the best. The best on the new album, the best on the new tour, and the best on coming to North America. Thanks a lot. I'm looking forward. So we got live and let live. Everybody go. It's coming out exactly what day, do you know? Ooh, I didn't make a note here. So sometime this month it's coming out, right? Sometimes in this month in February, I know that much. Yeah. I'm not sure if it's the 20. That's okay. It's coming out very soon. I know that much.  Perfect. All right. Thank you so much, Mark, looking forward to see one tour. Okay. Thank you guys. I'm looking forward and fingers crossed that everything goes as planned. Two beers for Alan. Okay. We'll talk soon. Great album. Congratulations again. Thank you very much.


apparently climbing now in the Canadian Rockies and is not listening to this talk. I'm at a hotel and using the internet connection there and hopefully that'll last for my whole talk. So practical numbers. One story begins with Fibonacci in the year 1202. In his famous book, Libre Abachi, the same book where he introduced the Hindu Arabic numerals to the West. He was interested in unit fractions, sometimes called Egyptian fractions, one over N. And he noticed that some numbers like 12, every fraction, up 112, 12th, up to 11th, 12th, or even 12th, 12th can be written as a sum of distinct unit fractions where the denominators are divisors of 12. So it's distinct unit fractions, denominators, divisors of 12. For example, 5th, 12th, you can see is 1, 6th plus 1, 4th. It's also 1, 3rd plus 1. I can't get the sound. Why? Did someone say something? Anyway, if you take these equations and you multiply them through by 12, you can see that the numbers from one to 12 can be written as a sum of distinct divisors of 12. And that's the definition of a practical number. Or you could take Fibonacci's definition if you'd like, but he didn't call them practical. They were called that by Srinivasan in a short article that he wrote in 1948. And he had a dig at the metric system, I guess what he didn't like. He said that the subdivisions of money, weight, and measures were often done with such numbers as 4, 12, 16, 20, 28. They're usually thought to be so inconvenient as to deserve replacement with powers of 10. But he liked these numbers, such as 12 and so on, because of this property of, I suppose, I'm not sure why it's so practical to have every number from one up to N being represented as a sum of distinct divisors, but that's what he called them. And maybe it was the Fibonacci thought as well. Anyway, he began a study of the multiplicative nature of practical numbers. And he didn't come up with a criterion. And this was done independently in 1954 by Bonnie Stewart and Vatslav Serpinski in 1955. And essentially, this is what their definition is, their criterion is. It's a recursive definition of a set of numbers. And the recursive definition says that the set contains the number one. And also, if it contains a number M, then it contains all of the numbers M times P for all primes P up to sigma M plus one. Sigma of M is the sum of divisors, of all of the divisors of M. So, and this recursive definition gives a set of numbers, and that's the set of practical numbers. Here's Fibonacci, Srinivasan, and Serpinski. So from the criterion, we can see that every power of two is practical, because I guess because one is practical and the criterion says you can go up to sigma one plus one, which is two for the next prime. And once you have a prime, you can put in any power of it you want. So the powers of two are practical. The fact that you can represent numbers smaller than powers of two by divisors of powers of two, is just the binary representation of a number. Also, the criterion shows that every practical number after one is an even number. So let's see if we can prove this elementary criterion of Stuart and Serpinski. So first, we should note that the criterion is obviously necessary. If the prime P is bigger than sigma M plus one, then you cannot write P minus one, which is bigger than sigma of M with divisors of MP. You can't use a P itself as that's too big and all of the divisors of M together add up only to sigma of M. And that's smaller than P minus one. So there's a necessary condition that P is less than or equal to sigma of M plus one. And then to prove it, we're going to look actually at a stronger statement, improve a stronger statement that not only can numbers up to M be represented as sums of divisors, but every number up to sigma M P to the alpha. So we're going to assume, we're gonna prove in fact that for a practical number M, you can get every number up to sigma of M and then we're gonna prove that by induction. So let's start out by assuming that every number up to sigma of M is a subset sum of divisors of M by way of induction. And let's let P be a prime not dividing M with P of the right size, less than or equal to sigma M plus one. And we're gonna prove it for all of the numbers, MP to the alpha again by induction on alpha. So this is a double induction. Okay, so if alpha equals zero, our induction hypothesis is that everything is cool at M, so M is good. Now we'll assume it holds at some alpha and we'll look at this interval, I sub A. Here A is just an integer less than or equal to sigma of M. The left-hand endpoint of the interval is A times P to the alpha plus one. And the right-hand end of the interval is that number plus sigma MP to the alpha. Now you'll notice that A times P to the alpha plus one, A being less than or equal to sigma of M by our induction hypothesis means that A is the sum of distinct divisors of M. And here P to the alpha plus one is a divisor of MP to the alpha plus one. So this is a divisor, this can be represented as a sum of divisors of MP to the alpha plus one. Plus, if we throw in divisors of MP to the alpha, by induction hypothesis, we can get every number up to this point, we can hit every number in this interval with divisors of MP to the alpha plus one. But does that get every number up to sigma of MP to the alpha plus one? Well, first of all, note that since we're getting all the numbers up to MP to the alpha plus one, it means that this interval wraps around to the next interval at A plus one. And so let's look at sigma of MP to the alpha. It's greater than or equal to P to the alpha plus one minus one because of our assumption that sigma of M is greater than or equal to P minus one and this formula for sigma of P to the alpha. And so these intervals, I sub A can be glued together and they keep on going until you reach the end at this point and this point is equal to sigma of MP to the alpha plus one. Maybe a little garbled here, but this is how this criterion is proved. So one can wonder if it's a practical number theorem giving an asymptotic for N of X. So that's the notation I'll use for the number of practical numbers up to X. So Srinivasan began this also. He computed that N of 200 is 50 and he wondered if maybe this fraction, 50 over 200, whether that is gonna be going to zero when you count up to higher levels or not. And 1950, Erdisch claimed that in fact it does that N of X is little low of X. Erdisch didn't supply a proof but I believe this is what he was thinking using some ideas that he used frequently. So he was quite familiar with the theorem of Hardy and Ramanujan that number N is usually close to log log N prime factors. And this is true whether you count distinct prime factors or not, you can count with or without multiplicity. So let's look at a little bit higher than log log N, 1.1 times log log N. So the Hardy-Ramanujan theorem says that asymptotically all integers have fewer than 1.1 log log N prime factors. And there's only density zero of them with more than 1.1 log log N prime factors. So let's assume now our N is in the majority set with at most 1.1 log log N prime factors. That means that the number of divisors event is at most the power set on these primes. I'm assuming these primes occur with repetitions. Nevertheless, I can just take the power set on a set of this size, two to that power and I get the number of divisors, an upper bound for the number of divisors. And so now let's look at the power set of the set of divisors. Look at all possible subset sums of divisors. So that's two to the two to the 1.1 log log N. Certainly a big number is of the double exponential, but log log N is pretty small. So how does this compare with N? Well, if you bring the two up to the top as log two, you have a 1.1 log two. 1.1 log two is less than one. And if you bring log N down to the middle here, so you have two to the log N to an exponent smaller than one. So that's even smaller than entity epsilon. So they're just not enough divisors to have enough subset sums to be equal to all of the numbers up to N. And so if it has at most 1.1 log log N prime factors, it's not gonna be practical. So that's a proof of the Erdisch claim. Now, this just says little O of X. However, here are our heroes, Ramon and Sean Hardy and Erdisch. If you look at a more quantitative version of the Hardy-Raman and Sean theorem, you actually get X divided by a power of log X as an upper bound for the number of practical numbers. The exponent here, eta is this expression, which is actually sort of famous in the anatomy of integers about 0.086. So upper bound is X divided by log X to the 0.086. But point, that's not the right exponent to have here. And Gerard Tenenbaum and a couple of papers in 1986 and 1995 show that it's basically one. The exponent here should be one. It's X over log X, you had a positive power of log log X, upper bound and a negative power of log log X in the lower bound. But the main shape of this is X over log X. A couple of years later, Eric Seah got rid of the log-log factors. This notation here looks like a smile and a frown is some notation in analytic number theory. That means that n of X is less than a constant times X over log X. And it's also greater than another positive constant times X over log X. So its order of magnitude of n of X is X over log X. That is the correct order of magnitude. Now this is all going towards a conjecture that Maurice Margenstern had made a few years earlier in 1991. And he did some computing. He computed up to 10 to the 13th and found that the number of practical numbers up to that level was looking like a constant times X over log X, where the constant is about 1.341. And so he made this conjecture that there should be some constant and n of X should be asymptotically a constant times X over log X. So this was proved in 2015 by Andreas Weingartner. And he didn't compute the constant in his 2015 paper, but just earlier this year he published a proof that the constant is actually very close to what Margenstern thought it might be. He said 1.341, Andreas shows 1.33607. Here is sort of a closed form for the constant. It's not closed because it involves an infinite sum. And the sum is over practical numbers. And at first glance you might even think that this sum is a divergent series because if here you have a one over n ranging over practical numbers, the practical numbers are distributed sort of like primes, constant times X over log X, the sum of the reciprocals of the primes is infinite. However, this one over n is multiplied, well, see what is it multiplied by? It's multiplied by this thing. Well, what is this sum? Well, by essentially the prime number theorem where Margenstern's this sum over the primes up to sigma of n plus one is the log of sigma of n. So here's the log of sigma of n minus log n. Well, that's the log of sigma n over n. So that actually can be pretty big, making this divergence look even more troubling. However, here we cut it down a bit. Now we have a one over log sigma of n and that's enough cutting it down to get it to converge slowly. It was somewhat of a triumph for Andreas to get so many decimal places for this series to compute that series, some because it converges so slowly. So you gotta use some extra cleverness. So Lola Thompson in 2012 and her dissertation gave a generalization of practical numbers. So we don't consider numbers, we consider polynomials. So here we look at the polynomial t to the n minus one. I'm calling the variable t rather than x because I'm using x as a bound to count up to. So you have t to the n minus one and we can look at its divisors over the integers. For example, it has the divisor t minus one. And we'll notice that t to the 12 minus one has divisors of every degree up to 12. How can we see that? Well, let's look at the irreducible factors of t to the 12 minus one. These are the cyclotomic polynomials, phi sub d of t where d ranges over the divisors of 12. So one, two, three, four, six and 12. Those six cyclotomic polynomials have degrees one, one, two, two and four. And the question is, can you use these weights to make up every number up to 12? Well, it's obviously, obviously you can. That's easy. And so this polynomial has divisors of all degrees up to 12. So she called such a number n to be phi practical. This is the Euler phi function. The reason she called it this is because phi of d is the degree of the d cyclotomic polynomial. So the criterion, the arithmetic criterion is that for every integer m up to n there's a subset of the divisors of n such that if you add the phi of d for d ranging over that subset, you will get n. So you can ask if there's an analog of the Sierpinski-Stewart criterion for the phi practical numbers. And it turns out that it's quite tricky which means that it's not just a simple analog. So for example, with practical numbers, if you have one and you peel off the top prime, it's still practical, but it's not true for the phi practicals. So for the number 315, three squared times five times seven that is a phi practical number. But if you peel off the seven and are left with 45 that is not phi practical. In fact, around 22, 23, those degrees cannot be represented as divisors of t to the 45 minus one. Another example is nine. Nine is not a phi practical number, three is. So this is an example where if you increase a prime from a phi practical, it doesn't stay as phi practical. So that's not true for the practical numbers. So nevertheless, Thompson was able to use say a machinery to show an analog of its theorem that the number of phi practical numbers up to x is a border of magnitude x over log x. And she conjectured that there is also an asymptotic and she did some computing and it seemed like here the constant was near to one. So she even wondered if, in fact, it should be asymptotic to the number of primes up to x. So a few years later with a Weingartner and myself, the three of us proved Thompson's conjecture and we didn't actually compute C but we gave the heuristic that it is close to one but not one, it's slightly smaller. So another application of the ideas behind practical numbers is numbers with dense divisors. These were defined by Tenenbaum and written about by Seah and Weingartner. Number with dense divisors. Here is the sequence of all divisors of n. Start with one, go to the next one and so on up to n. And look at the ratios of consecutive divisors. d sub i divided by d sub i minus one. If all these ratios are less than or equal to two, then that's the definition of a number having dense divisors. These are, in fact, we're used in the studies of practical numbers and it's not very hard to see that any number which has dense divisors will be practical. Now this condition on dense divisors is similar to the Erdisch-Propinquity problem. So Erdisch wondered about the density of integers which just has two consecutive divisors, d d prime with the ratio between one and two. Is that true? Well, it's obviously true for a positive proportion of numbers. For example, it's true for all multiples of six because every multiple of six has divisors two and three and the ratio of three over two is bigger than one and less than or equal to two. So there is a positive proportion of numbers that have such a pair of divisors and Erdisch conjectured that in fact it's density one. This was finally proved in a joint paper of Meyer and Tenenbaum in 1984. But then again, dense divisors is not that there should exist one pair but that every pair of consecutive divisors should have that relationship. So there's a multiplicative criterion for the integers with dense divisors and this criterion is useful in the study of practical numbers because it's very similar to the criterion of Sierpinski and Stewart. So for Sierpinski and Stewart, if M is practical, you can take every prime P up to sigma M plus one and throw it in. With numbers with dense divisors, you can take every prime P up to two M and throw it in. In the study of practical numbers, one can generalize this where you replace two with a larger number and that also plays a role. We now know after their work that there's a distribution for numbers with dense divisors, it's again of the shape constant times X over log X. So because of this expression X over log X, it seems natural, X over log X is so much associated with prime numbers, so it seems natural to ask similar questions for practical numbers as one asks for prime numbers. So for example, the famous conjecture is are there infinitely many twin primes? So let's ask for twin practicals. Well, the practical numbers after one are even numbers so we can't expect N and N plus one both to be practical infinitely often but we can expect perhaps N and N plus two to be practical simultaneously infinitely often. Morgenstern proved that this is in fact the case that there were infinitely many. And then in a new paper that I have with Feingartner, we got estimates for how many there are up to X. The conjecture is that the upper bound is tight except for the constant. By the way, this notation less than less than an analytic number theory is the same as big O where this says that N sub two of X is less than or equal to a constant times X over log squared X. And it means it's greater than or equal to a constant times the slower bound. So you can ask how we prove these theorems. So for example, on the upper bound, I can't see my screen here. Are we looking at, oh yeah, good. So we're looking at the upper bound. So we write a pair of twin practicals. We pull off initial divisors of N and N plus two by an initial divisor, I mean all the primes in M are less than or equal to all of the primes in Q and the same thing for M prime and Q prime. And I'll choose M and M prime to be in this interval since these numbers are practical, they have divisors in this interval, X to the one seven to X to the one third. And then we fix a pair M prime of practical numbers in this interval. And we then count primes, sorry, numbers Q. Q has all large primes, because they're all larger than the primes in M such, so Q satisfies a few properties. That satisfies the property that QM plus two is a multiple of M prime. And it satisfies the property that if I divide that QM plus two by M prime, I'll get a number that purports to be a Q prime and that only has large prime factors. So this argument would get X over log squared X times the power of log log X. And we have some technical hurdles to overcome the power of log log X and get the X over log X squared. So how do we show, how do we get the lower bit to show that there are X divided by that power of log X number of twin practicals up to X? So we do it as follows pretty much. We choose two practical numbers in this interval between square root of two, sorry, one half square root of X and square root of X. And we choose a pair of practical numbers in that interval that are almost co-prime. Their GCD is two. And which is essentially as low as a GCD can be between two practical numbers larger than one. And so given such a pair, there are going to be a one and a two such that a one M one minus a two M two is two. And a one is small, a one is smaller than M two and a two is smaller than M one. And so we have multiples of practical numbers. And the multiple is small enough to guarantee that the product is again practical. So these are twin practicals. Well, that looks like we've proved an even stronger theorem. We have X over log squared X pairs of practical numbers in this interval. With this GCD criterion and for each pair, we choose a one and a two, and we get twin practicals up to X. So why doesn't this give X over log squared X? Well, the trouble is, is that we could be over counting that the same twin pair could arise in multiple ways from this expression. Well, we, we know that there are a lot of things that handle this by first not choosing any practical numbers in this interval. We only choose those which don't have too many prime factors. And we can use sort of analogs of the Hardy-Romanijan theorem to show that we can keep the total number of prime factors of M one and M two. That's big omega counts the total number of prime factors with multiplicity. We can keep them under control. And this function that takes M one and M two to A one is going to be more or less one to one. In fact, it's at most two to one using the inequality that we have and the fact that we have the practical numbers in this interval. So it means that we can again discard we're not gonna hit numbers too often with large values, large numbers of prime factors. So we can assume that the number of prime factors of A one and A two are under control. So with those two under control, it means the total number of divisors of A one M one and A two M two is power of log. And that tracing effect gets that power of log we had in that previous theorem. So another connection between primes and practical numbers brings in the primes themselves. So a couple of years ago, Gwo and Weingartner looked at shifted primes that are practical. So P is a prime number. P minus one is the shifted prime, one less than the prime P. And we wonder if this even number is practical. And they proved the count for that again with the lower bound and upper bound. You might recognize this exponent which we saw earlier. So in the same paper that I have with Weingartner recently, we showed that this exponent here on log X is not 0.086, but in fact one. So that's the upper bound. Presumably again, this is the truth and the lower bound we improved the exponent there. For our upper bound proof, we write a practical number as M times Q. We're now Q is the largest prime factor event. And if N is one less than a prime, then plus one is prime. For a given number M, here we have M. We ask for primes Q going up to say X over M with MQ plus one also prime. So here we have a sieve with two primality conditions. And this essentially gives us a log squared X. And you can see that this expression is just X over log squared X. So again, there are some technicalities because Q might be small. And then the sieving interval was not so long but we handle those cases where M is smooth and therefore Q is small. Or when this is a factor that comes up in the sieve, you don't have to wonder when that's large. So we have to handle those technicalities to prove our upper bound. So for the lower bound, here's how we did that. So we take a number N that's practical. We take, we look at primes up to N squared where P is one mod N. Suppose there are plenty of such primes. And if we write P minus one is A times N, that'll be practical automatically because A is going to be smaller than N. N is practical, so this number is automatically practical. However, we don't know that if we take primes up to N squared, we don't know even if any of them will be one mod N. However, if we're just a little bit below for our modulus, it's just a little bit below square root of X like square root of X divided by high power of log X. Then we can use the Bombiery-Vinogrado theorem to show that there are many pairs P and N where P is one mod N. But the trouble now is that A is not going to be smaller than N and it could be a bit bigger than N. Well, that's still okay so long as A doesn't have any big prime factors. So we use an upper bound in the sieve to rule out the case when A has big prime factors and we are home. Now, we could have used instead of the Bombiery-Vinogrado theorem, a new theorem of James Maynard which is an improvement of the Bombiery-Vinogrado theorem in the case when you have a fixed residue class, which is the case that we'd be looking at. We're looking at the residue class one. Actually, it was sort of hard to find this photo of Vinogrado on the web. There's another Soviet number theorist named Vinogrado, I am Vinogrado, he's more famous, has more photos on the web, but apparently this is our AI Vinogrado. The notation less than less than that we've been using is often called the Vinogrado notation. I'm not sure to whom it's due, it might be to him or to I am. For prime numbers, we have the Goldbach conjecture. Even numbers should be a sum of two primes. So, a Morgenstern conjecture, well, he tried to conjecture that for practicals. Practicals are even, so if you take two practicals, the sum will be even. So he conjectured that every even number is the sum of two practicals. And he wanted to say, well, what about odds? Don't leave them out. He said that every odd number should be the sum of a prime and a practical. So Giuseppe Melfi proved the Morgenstern conjecture for the even numbers. He proved that every even number is the sum of two practical numbers. And now in our paper with Von Gardner, we essentially did the odd part. We did it for sufficiently large odd numbers. So we're trying to prove that a large odd number is the sum of a prime and a practical. So let's let A be an odd number in the interval between X and two X. And let's let N run over the practical numbers that are a bit smaller than square root of X. And use the Bambieri-Vinogrado theorem to find primes P up to X in the residue class A mod N. Okay, so you notice here that A is bigger than X and P is less than or equal to X. So we have these double inequalities. And so therefore A minus P is greater than zero.  So it means that A minus P is a multiple of N. This multiple B is not much bigger than N. And again, we can use SIV methods to rule out the case where B has a large prime factor. So this proves that A is the sum of P and BN. And when B doesn't have a large prime factor, BN is practical. And that proves the conjecture for sufficiently large odd numbers. So you might wonder if you could use these ideas to prove the full conjecture that there aren't any exceptions. Well, that would be tricky to do with the Bambieri-Vinogrado theorem. I'm not sure if it would be tricky with Maynard's theorem, I'm guessing so. But the Bambieri-Vinogrado theorem depends upon Siegel's theorem. Siegel's theorem is the quintessential non-effective, ineffective theorem in analytic number theory. You cannot make the constants explicit unless you assume the extended Riemann hypothesis. And if you assume the extended Riemann hypothesis, we actually have a very strong prime number theorem for residue classes. We have this wonderful inequality for the number of primes up to X in the residue class A mod N. That's what you'd expect when over the Euler-Phi function of N times logarithmic integral of X. And that difference is smaller than square root of X times log of N squared X, starting right from the beginning. So if you assume this prime number theorem, we can prove that the Marginstern conjecture holds perhaps at some starting point like E to the 10,000. So now, for the computationalists in the audience, your job is cut out for you. Just check all odd numbers up to E to the 10,000 and see that they're all the sum of a prime and a practical. Well, Tomas Alevera, a silver, got it started for you. We can show it up to 10 to the nine that it holds. But actually, we were able to get further than that. And let me describe this neat method of going further. Take a power of two. And for each odd residue class A mod that power of two compute the least prime in that residue class. So for example, suppose K is four. So we have two to the four is 16. And we have the odd residue classes up to 16. There are only three residue classes up to 16 that are not prime already. Those are one, nine and 15. And if you look at the first prime that's one mod 16, that's 17. The first prime that's nine mod 16, that's 41. And the first prime that's 15 mod 16, that's 31. So the largest of these least primes is 41. So that's gonna immediately imply our theorem in intervals we'll see in a minute. Linux theorem says that the largest of these least primes is bounded, but it doesn't give us that it's small. Numerically in practice, it will be small. Say smaller than this bound, K squared times two to the K. So that might be tractable to search up to this point for K of moderate size. So once this largest of the least primes is found, we've proved the Marginstern conjecture for every odd number in the interval above P and up to this next power of two to the two K plus one. Because if A is an odd number in this range and look at the residue class A mod two to the K and take a prime in that residue class that's less than or equal to P and look at A plus Q times two to the KB, B is small and this is gonna be practical. So we have the odd number A as a prime plus a practical. So in our toy example, just doing that mental calculation to get 41, we immediately have that every odd number up to 512 is representable as a prime and a practical. We actually implemented this up to two to the 53. If we could prove that every number up to two to the 53 is sum of a prime and a practical. You don't have to even go to this height K squared times two to the K. If you only go to three K, two to the K, then it should be conjecturally only a small fraction of unrepresented residue classes, one in 5,000 or less. And then in those find those classes and then search over them individually. Finally, let's look at this problem. So Landau has a famous conjecture that between consecutive squares is always a prime. Can you prove this for practical numbers? Well, this was done in 1984 by Miriam Hausman and Harold Shapiro and a small improvement was found by Melthy. One can ask, in fact, if there's always a practical number in the short interval x up to x plus x to the epsilon and we don't have that. We don't have that for any epsilon smaller than one half. So that would follow from an argument based upon conjectures about smooth numbers. And so Granville has a famous survey about smooth numbers and in it he has a featured conjecture which says that in the interval x up to x plus x to the beta is going to be an x to the alpha smooth number here alpha and beta are any fixed positive numbers and x is sufficiently large in terms of alpha and beta. If we have that, then we, we're looking at x up to x plus x to the epsilon. We can take the first power of two above x to the epsilon over two and consider the multiples of that power of two that in this interval and we want this d to be x to the epsilon over two smooth. So by this featured Granville conjecture though there will be b's in this interval that are so smooth and then that b times two to the k will be practical but this may not be the only way to prove the conjecture about short intervals. Anyway, going to these number theory web seminars week after week, I see that people are doing really wonderful things. I'm not sure what I'm talking about is so wonderful but at least it's practical. Thank you for your attention.


Good afternoon, everyone. Okay, great. So I will be talking about the NCI Cancer Genomics Cloud Pilots, but before I do that, I'm going to also talk about the genomic data commons. So we'll start with that. So the Center for Cancer Genomics of the CCG has three major projects in cancer genomics, TCGA, Target, which is the childhood cancer genomics project, and the CGCI Cancer Genome Characterization Initiative. And is this... Yeah. Okay. So they're represented here. All three of these projects each have their own data coordinating centers as well as their own data portals. So you have to go to three different data portals to get the data on these three projects. In addition for the sequencing data, the BAM files for all three projects are stored in a second location, not the data coordinating center. You will not be able to get that data through the data portal. You would either need to, for TCGA, Target and CGCI, come to the Santa Cruz site CG Hub to get your BAMs. The Target and CGCI BAMs are also available at the NCBI Sequence Read Archive, SRA. But if you want the higher level data, while the BAMs are at CG Hub or SRA, the VCFs and MAFs are again at the DCC. So this is kind of confusing for users, I think, to have all of this data all generated from the same CCG, from the same division CCG, to have it all in so many different locations. So the goal of our genomics data commons, or the GDC, which is currently in production, is to unify this fragmentary repository at NCI, so that all of the cancer genomics projects that we have at the CCG, and in the future hopefully all the projects we have at the NCI, will be available from a single repository. There'll be a single sign-on for all users. You won't have to go to multiple places to get the data from multiple projects. Now a secondary goal of the GDC is to harmonize the diverse standards that we also see in our data. So here on the left-hand side of the slide, we have just the representation of the BAMs being aligned to various different references.  This causes a lot of difficulty in analysis, of course. On the right-hand side, we have a representation of the Venn diagram for mutation callers with very little overlap. Again, if you've got your mutation calling from two different pipelines that don't overlap very much, again, it's going to make it difficult for analyses. So what a secondary goal of the genomic data commons is to go ahead and harmonize some of these data standards. So BAMs will all of the BAMs that go into the GDC will be aligned to one reference. And they will all also get the same mutation calling pipeline. So the genomic data commons is a contract. It was awarded to the University of Chicago and the PI is Dr. Robert Grosman. The go live date for full functionality for the GDCs should be around late spring of 2016. So that's when you can anticipate being able to log on to one location to get all of your data and finally, it's not a commercial cloud. The photographs here represent the actual data warehouse that's at the University of Chicago and one of the benefits of not being a commercial cloud for the storage of this data is that it will be free to download the data. So speaking of clouds, I'm going to move on now to talk a little bit about the cloud pilots. Right now the standard model of computational analysis is of course, you've generated your local data, you keep it locally stored. You, if you're interested in TCGA data or other public data sets, you have to go ahead and download that locally as well. You've got your locally developed software and then any software that you've pulled down from other locations. Everything, again, is local to your university or research lab. And as a user, you're doing everything locally. And this works fine until the data sets get quite large. So there are definitely some limitations to the standard model when you're dealing with much larger data sets. So assuming that we have approximately 2.5 petabytes of TCGA data towards the end of the project, the storage and data protection will cost about $2 million a year. Downloading the TCGA data at 10 gigabits per second, which is really a best case scenario, is going to take a minimum of 23 days. So you can probably guess more like two or three months to download all this data. And at this point, really only large institutions have the ability to utilize all of this. And moreover, these data types are going to continue to grow, right? We're going to have new projects after TCGA is closed, new projects at NCI, other projects, for example, Target and CGCI. So we anticipate that the data sets will just get larger and larger. Okay, this slide does not look like it should. All right, that's okay. So the answer, of course, is to co-locate all of the compute and data in the cloud. And my cloud is very fractured, you see here. It used to be like this. I don't know what happened. All right, but in any case, what we want to do is we want to have everything on the cloud. We want to have our core data set. In this case, we're just talking about TCGA at this point. We want to have user uploaded data. So instead of storing all your data locally, you would upload it to the cloud, which should be a much easier task than downloading an entire TCGA data set. You would also, of course, have some standard tools that would be available in the cloud, as well as some user uploaded tools. And all this computational capacity would be here in the cloud. And as the user, you would come to the cloud, you would do all of your analysis, and you would then, at the end, download only your results, which, again, should be a much smaller data set than the original large data set, including TCGA. So here you can see the data generated from a project like TCGA. Going into the data coordinating center where there's QA, QC validation, as well as aggregation of the data. And once that's done, we have the authoritative NCI data reference set. This data set is being loaded into the genomic data comments, which is one of the reasons I mentioned that at the beginning of our talk here. So all of this data is coming into the GDC. This is going to be the main repository for all of this data. The data is also being copied to our NCI cloud pilots. Again, they're fractured here. Sorry about that. So the data set will be replicated in the NCI cloud pilots. Now, why is it replicated? So here you are as the user. There's really one, there's different reasons to use the different tools. So you would come to the genomic data comments of the GDC if you were interested in searching, retrieving, or just downloading the data. Because this is the authoritative data reference set. However, if you were interested in doing high performance computing or analysis, instead of coming to the GDC, you would come to the NCI cloud pilots. And you'd be able to upload your user data. You'd be able to upload your own analyses, and then run everything on the clouds. So as I mentioned earlier, it's really only the largest institutions right now that can download three petabytes worth of data and run analyses on them. So this is NCI's effort to democratize access to this genomics data. It's managed through CBIT, where I'm from, in partnership with the CCG, and we're coordinating closely with the genomic data commons. We've awarded three contracts, one to Broad, one to Institute for Systems Biology, and one to Seven Bridges Genomics. Our period of performance started in September of 2014, and it goes to September of 2016. If you're interested, this link takes you to a CBIT page, information page on the cloud pilots. And our anticipated launch date is actually January of 2016. So fairly shortly, you'll be able to start analyzing data using this. So some considerations for the cloud pilots. First, the designs must be released under a non-viral open source license. So everything's open. For extensibility, the initial clouds need to focus on a set of core data types that I'll mention in a few moments. But they also must extend to additional data types without major refactoring of the existing system because we know that there'll always be new data types that will come up. As far as sustainability, we have cost assessments for operating at the current scale, which is on the order of 2.5 petabytes. And also at 10 and 100-fold increases in storage, compute, and usage. So we have an idea of what it would actually take to get to the next level. Once that data is so large. And then finally, for security, these systems need to be FISMA moderate. All of the cloud providers need to be fed ramped. And the three cloud pilots must all obtain trusted partnership. And this is an NIH trusted partnership agreement which allows the cloud pilots or any other trusted partner to share controlled access data. So in this case, controlled access TCGA data. Finally, we have the open access data versus the controlled access. So the open access data, everyone will be able to use and analyze at the cloud pilots. For example, some of the open access data would even include CCLE data so that you could work, do some analysis on BAMs. If you do not have controlled access, dbGaP approval. However, if you have controlled access, you'll be able to utilize all the data. Okay, core data sets. So all three awardees have to host a common set of core data that includes all DNA-seq BAMs, RNA-seq FastQ and BAMs, SNP array cell files, somatic and germline mutation calls. That'll be your VCF files and your math files. And we'll also have the clinical data. In addition to that, each awardee was required to have at least one additional TCGA data set and they all chose to do more than one. Broad chose to add validation BAMs, MyRNA-seq and methyl-seq. ISB is adding MyRNA-seq as well as all level three data across all of TCGA. Seven bridges has added whole genome and exome DNA-seq FastQs, MyRNA-seq, data and methyl-seq. Okay, so the project schedule and deliverables. We have just about a month ago finished up our design build phase one. That was six months of initial design and development. We've just started design build phase two, nine months of completing the design development and implementation. And then right around January of 2016 again, we'll be in our nine month evaluation phase. And this is where we're going to need the community member's help. So we're going to be opening up the cloud pilots to allow the community to evaluate. NCI will also be evaluating the cloud pilots. But we really need researchers in the community to try these systems out to tell us what is working. So what are some things that are common to all three cloud pilots? We have the core data sets, as I mentioned. Some use cases that everyone has to have are running pre-loaded pipelines on TCGA data. Uploading and processing, again, that user data that you can upload your own data. Uploading and running custom algorithms so you're not forced to use what's available on the cloud pilot. You can upload any algorithm that you choose. And finally, these pilots need to serve both the biologists as well as the bioinformaticians. The common workflow language is being considered as a workflow language for all three pilots. And that's not finalized yet, but we're looking at that. All three will be using Docker containers for improved portability and reproducibility. And all three will be using the emerging GA4GH standards. Finally, they'll all have the same authorization and authentication process. This is, again, to make sure that only people with controlled access, dbGaP approval, get access to things like BAMs. Okay, so I mentioned what the three have in common, but what makes them unique? We chose three cloud pilots because we wanted three different solutions. We want to see what works. The first is the Broad Cloud Pilot, led by Gatti Getz. His collaborators are at University of California Berkeley, as well as Santa Cruz. They've chosen to use Google as their cloud platform. And some unique technologies they're using include Adam and Spark. And they've incorporated Firehose, and they've chosen to call their cloud pilot FireCloud. So each of the three cloud pilots have their own website, which I'll be showing on these slides, as well as the very end slide today, if you're taking notes. Each of them have a link that allows you to go and sign up for notifications and news on what's going on, and the opportunity to evaluate the system once it is open. Okay, here's the FireCloud slide.  And then put them all in either a user or a team workspace, where you can securely track and manage your metadata tools, job execution, and results. And it also allows you to capture the providence for each run. There's versatile job executors, as I mentioned earlier, Docker, Adam Spark, and Google Cloud Dataflow. And the data can be stored in these distributed stores, called ReadStore and Variant Store. From ISB, we have the PI is Aaliyah Shmilovich. His collaborators are Google and SRA International, so of course his platform is Google. He's using the Google Genomics platform as one of his unique technologies. And some of the tools they've incorporated include Regulom Explorer and GeneSpot. And ISB is really focusing on the interactive data visualization, exploration, and analysis. And again, the CloudPilot website here is cgcsystemsbiology.net. And I'll be, again, repeating those. Again, this is just a slide showing some of the highlights from the ISB CloudPilot. The interactive tools allow you to explore all tumors or a subset of tumors. Allow you to define custom cohorts, focus on specific molecular data types or platforms. Finally, we have programmatic access, including REST APIs for cloud storage, SQL-like queries for BigQuery, and the GA4GH API for Google Genomics. All three CloudPilots will be having tutorials and ways to learn more about the system and how to use it. Finally, we have the Seven Bridges CloudPilot, the PI is Dennis Karal. There are no collaborators for this contract, but they, unlike the other two systems, are using Amazon Web Services. Their unique technology includes the Seven Bridges Genomics platform. And they've incorporated already over 30 public pipelines that you can see here at this URL. And finally, their CloudPilot website is sbgenomics.com slash cancer dash genomics dash cloud. And here's their last, here's their slide. So at the Seven Bridges Cancer Genomics Cloud, you'll be able to wrap your tools, mix your data and match it with other data, including the TCGA. Analyze the data and then finally collaborate and discuss what you've discovered with your colleagues through the Seven Bridges platform. Okay, so I'm out of time, but we also have a CloudPilot workshop this evening for additional details. All three PIs are here to talk about their specific pilots. It will be from four to five and repeated again from five to six right here in Nature Auditorium. So I encourage you to please attend if you are interested in learning more. And then finally, we just have the project teams that make all this possible. And once again, I've repeated the URLs. Thank you. You ensure that the economics after two years would be affordable to most of the users. That's a good question. So one of the things that CloudPilots need to deal with in the next nine months is how to allocate use time for the evaluators, right? So right now, we're really just looking at the evaluation phase and how to fund that. So that the evaluators do not have to put money into the system. But so I think we need to see what happens in the evaluation phase before we decide what happens outside of the two years. And it's beneficial to bring in more commercial CloudProvider. Three out of the two is Google. So there are other provider, I think it would be great to have a competition so that they can make it more competitive in terms of overall. Yes, I believe the systems will actually be able to run on other CloudProviders if necessary, yes. Thank you. Just a quick follow up, and maybe you can't answer this now, but you just said let's see what happens in the pilot phase to see how that carries forward. But so is there a tentative plan as to what would happen in the spring of 2016 in terms of people getting access free of charge to those clouds to run their jobs? Yes, so. The limit of capacity, or what's the rough plan for that commitment? All three CloudPilots I think are going to come up with their own system. But everyone who wants to help with the evaluation will be given a certain number of hours or credits or something like that to utilize. And I think if you exceed your credits or you meet your credits, you could ask for more credits. And the helpers with the evaluation will be organized by your team? Yes, okay. That's right. All right, thank you very much. Thank you, Tanya. So our last speaker for this session is Andrew Gross. He's going to talk about paired tumor and normal analysis using TCGA data.


With Wimbledon only a day away, let's go have a look at the updated withdrawal list of the players that are not going to be playing at Wimbledon this year. And also let's have a look at the players that are actually injured going into Wimbledon because that list has also grown over the last week. The players that are definitely not playing Wimbledon this year. So on the women's side of things, we've got Samona Halep, of course, suspended, Anissa Mova, Rodo Kano, who's still getting through surgery, Van Udvank, Tomanovich, Kalenskaya, and Covenich is the latest to withdraw from the women's side. On the men's side, of course, Rafa Nadal, the big one not playing. Jack Draper also not playing. Marin Chilich, Pablo Karina Buster, Karina Hashinov also not playing. Monfice, Strouff is also not playing, which is such a shame because he was so good over the clay season. And Krayanovich, he's also pulled out of the draw for 2023. Now, let's go have a look at the injury list for Wimbledon because there are so many players coming in with injury concerns. On the women's side, Kudupatova, she put out of the tournament last week due to a hip injury. So keeping on her earlier Wimbledon. Rabakena still struggling from that illness that she got at the French Open that forced her to withdraw there. So keeping on her as well. But Osa has a back problem that's forced her out of a lot of tournaments in the last couple of months. So keeping on her as well. And Ikes Fiontek, she got food poisoning last week, having to pull out of a tournament in Germany. So keeping on her as well because food poisoning is not fun and can really mess with your routine and sleeping patterns. So keeping on her in her first couple of matches, hopefully she can get back quick. On the men's side, we've got Beratini. He's coming in with some injury concerns. Still not fully back from his abdominal strains. Nick Kerios also coming in with that knee problem that's kept him out of the tour for so long. Yannick Sinner. He's also coming in with an adductor injury. So keeping on him in the first couple of days. Felix Ojaliusim has also pulled out of tournaments over the last couple of weeks due to knee pain. But he did play an exhibition over the last couple of days. So maybe he'll be okay for Wimbledon. But there's a couple of guys there that are coming in with a bit of an injury cloud. So there you have it. Those are the players that are not playing Wimbledon. Some of the players that are playing Wimbledon but have a little bit of an injury concern. Let me know down in the comments below. Who are you most sad about not seeing a Wimbledon who are you most concerned about going into Wimbledon with some of these injuries? I mean, Nick Kerios made the final last year. He's got a really tough round in first round against Goffan. He's going to have to run a lot. And if that knees on 100%, it's going to hurt. So Wimbledon starts 24 hours from now. Hopefully we don't get any more withdrawals.


ويجب أن نتعرف عن صورة التوحيد ، الصورة من المناثيز. أنك ستفهم أن الله سبحانه وتعلم عن صورة. ويجب أن نتعرف عن صورة نور القرآن. وbefore we start even speaking about the Surah and before we get into it we seek refuge from the one who wants to take us away from the Qur'an and wants to take us away from the Surah that was revealed to our beloved Prophet ﷺ the one who doesn't want us to appreciate the Surah and doesn't want us to realize how important it is. So before we start we say عَوَظُ بِيلَا هِمِنَا الشَيْطُّانِ الرَّجِيمِ نرى رفج من الشيطان الذي يحدث ثم بعد نرى رفج منه نبدأ with the name of Allah ونبدأ with the two most beautiful qualities of Allah بسم الله الرحمن في the name of Allah the most compassionate, the most merciful and this name of Allah is known as Ismul Jamia ونبدأ with the name of Allah that encompasses all his qualities and all his attributes those of Jamal, those of majesty and those of Jamal those that are beautiful such as his anger that's the quality of his majesty and then of his compassion and his love that's of his Jamal that's of Allah's beauty and then when we start Allah first of all and then he gives us two of his most beautiful qualities we know that this we recite this every single day that Allah is the most compassionate and the most merciful that everything we see is a manifestation of Allah's mercy and of his compassion and that the biggest manifestation of Allah's mercy and his compassion is the fact that we were given the Prophet ﷺ because Allah says that we haven't said to accept his mercy to all of mankind and the miracle of this mercy the Prophet ﷺ was the Quran and Imam Fakr Dina Razi said about the Quran that it's like an oyster and we know that oyster has a germinate known as a pearl and then he said that the pearl of the Quran is Suratul Ikhlas and so that we've been given this pearl as a mercy and as compassion from Allah we've been given a source to know something of Allah and so the first ayah starts saying proclaim that Allah he, Allah is أحد the one the uniquely and the singularly one the indivisible the one that nothing can be subtracted from and nothing can be added to that it can't be divided into parts that it can't be multiplied into more than one but that is Allah Allah is he didn't say that Allah is one because the one that can be counted the one that can be divided the one that can be added to and subtracted from but Allah is the absolute one in all of his aspects in his essence and in his attributes and in his actions that Allah is is absolutely one that none can compare to him and that only Allah the one has the right to describe himself with these lofty qualities that he's given himself of mercy and of and of compassion and of power and of absolute will that we haven't given the ability to describe ourselves with these qualities only Allah is the absolutely powerful and the absolutely compassionate and the absolutely merciful and the absolutely willing then he starts with his he starts with the pronoun he he Allah is one and then who is this one Allah the one Allah is eternally sufficient unto himself that Allah doesn't need permission to create He doesn't need permission to take away to give and He doesn't need permission to do any of his actions that we need permission to do what we do that Allah doesn't need permission and that Allah didn't need permission to create us and Allah doesn't need our worship and He doesn't need our praise and He doesn't need us to seek mercy from Him that if Allah needed something then He would be dependent on someone else but Allah is not dependent on anyone else and He doesn't need any of this and He doesn't need us to worship Him that we need to worship Him and we need to praise Him and we need to ask is to fall from Him we need to we need to seek forgiveness from Him because if we don't Allah can easily replace us Allah can easily show us how dependent we are on Him and how much we need to worship Him because on the Yom Al-Qiyana He's going to show us whether we worship Him or not and if we worship Him perhaps He'll show some mercy on us and He'll let us into Jannah but if we did anything then Allah can even if we did worship Him He can throw us in the Hellfire but if we have some excuse for Allah to put us in the Jannah for some reason to Allah to say that I will give you Jannah because of this or because of that that we ask that Allah gives us that and that Allah that we realize that we're dependent on Allah for that that He isn't dependent on us He is Aslamad the one that doesn't need anyone that He himself created He didn't need anyone to create Him and He doesn't need to create anyone like Him so then He says Allah says لَنْ يَنِيدُ وَلَمْ يُولَدُ that He didn't beget that He didn't have any children any sons or daughters that the Christians we know that they ascribe the son to Allah and that the pagan Arabs they ascribe daughters to Allah and they said that the angels were daughters of Allah and we know that Allah makes none like Him if Allah made any like Him that there would be something that can go against His will but we know nothing can do Allah's will and so when He says وَلَمْ يُولَدُ that He didn't create and He didn't beget that He didn't decide that He wasn't begotten that He wasn't in need of anyone to create Him that He is above space and time He is transcendent of space and time that He doesn't exist in the location and He doesn't exist in time that our language is not even even capable of describing Allah when we say that Allah had created we are saying that which is in time or Allah is creating that Allah is creating something that's in time or Allah will create that's from our perspective that's from the way we see things but Allah doesn't see things in time Allah is and that is that's it that Allah creates and it's always in a moment it's not in a moment that Allah when He creates the way we see it we see it in moments but Allah is above that He doesn't need the limitations of time and space that He doesn't need the limitations of when something is created and so we know from that that when He doesn't need when He doesn't need anything because nothing is like Him and He doesn't need to answer to anyone and only we need to answer to Him then the next ayam He says وَلَنْ يَكُلَّهُ كُوْفُوَنْ أَحَادِ and this is one of the most important ayat of understanding something about Allah this is the ayat that points to they say everything in His shape nothing is not a single thing it's like Allah وَعُبُواَ سَمِيْهُمْ يَلُسِينَ yet He is all seeing it all merciful and all seeing it all hearing that though Allah sees and He hears it's not like the way we see and hear that it's not the way that when He has power or something it's not the way that Allah will something that's completely different and the way we will something and the way we hear and the way we see is just it's simply a it's simply a way for us to understand something of how absolute hearing and absolute power and absolute seeing works and so Allah reveals all His attributes to us in some way or another that when we see something a natural disaster that's a revelation of that's a manifestation of Allah's جلال His majesty is absolute His absolute ability to do whatever He likes and then when we see something beautiful that's a manifestation of His جلال so that we understand something of beauty and understand that Allah is even more beautiful than that that when Allah gives us when Allah gives us the beautiful trees and the flowers that we look at that we think to ourselves ربنا مالخلق تهدى about Allah that Allah didn't create this for nothing but you created this so that we can understand something about this and then we can understand that Allah put this here so that we know something of beauty so that we can appreciate beauty and then appreciate the absolutely beautiful which is Allah and so Allah He is He's expressed some of Himself in this Surah He's given us some qualities of Himself that if we knew these qualities we wouldn't have these problems of of what to believe and what not to believe that we have if we truly understood this Surah that we would be able to that we would be able to know that what our limit isn't asking of what is Allah and what isn't Allah and that we know that we can never truly understand Him and because we can never truly understand Him that we can never truly worship Him the way He should be worshiped but it's still a promise to try and which is one of the reasons why we make this default after a prayer after the prayer after the prayer what do you say أصدفت الله أصدفت الله we ask forgiveness right after we've done after we've done an act of worship because Allah has Allah has shown us that in this in this prayer you haven't done enough and you should make this default that because you haven't done enough and then you wish that you can do more and so insha'Allah during the next part the clip I'll get into it أقول القودي هالا أصدفت الله نري ولكم نسائل المسلمين أصدفت إنه هو الغفور الرحيم اسمي الله ورحمده لله والسلام على رسول الله وعلى آله وصحبه وموالا and so now that we have this knowledge that Allah has given us in this beautiful surah this just this magnet surah this surah that hasn't been the likes of it hasn't been given to any other woman before us we have to do something with it if you know something knowing something is not the same as knowledge knowing something is like data in fact and knowledge is actually applying those data in facts and so that's what true knowledge is and so with this knowledge what we do is we worship Allah as he should be worshiped as he should be worshiped we know in the hadith جبري that after the section on imam what we should what belief is and what we should believe that Allah gives us the next step which is إحسان to apply apply that to apply that we believe into ourselves and that we worship Allah as he should as we see him and we know that we can't see Allah in the dunya so that that we recognize that Allah sees us because he's the all-powerful and he is the one that the only one that sees us sees us in all our states and the only one that knows our intentions that he knows us better than we know ourselves and because he knows us better than we know ourselves it's our responsibility to appreciate that and worship him and so that that when we when we know this that when we do our prayers we do it in perfection and when we make when we make that we do it in perfection and we do it to the absolute best of our ability and what's really interesting that is that after this Surah we have the next we have the next we have the next we have the next and these two Surahs is where we're asking something from Allah because now that you understand and understand now you can ask something from Allah because you understand that Allah is the one that can give you and there wasn't and so that we now that we've understood we should be grateful for the blessings that we've been given and we should be grateful for the fact that Allah has sent down His Messenger صلى الله عليه وسلم with His miracle which is the Qur'an and with that pearl of the Qur'an which is so that we can know something of the one who created the Messenger of Allah the one who gave us the Qur'an and the one who created us and the one who created the situations that we're in and the one who created the difficulties and the hardships and the one who created the ease that we are in and that we are we are responsible to praise Allah for that and also that we are responsible to thank Allah for the blessings that we've been giving and that we've been given the blessing of the Prophet صلى الله عليه وسلم and that we know that Allah says in the Qur'an إِنَ اللَّهُ مَلَا مِكَتَهُ يُصَلُّونَ عَلَى النَّبِينِ indeed Allah and His Angels sent the blessings and greetings of the Prophet صلى الله عليه وسلم this is an action that Allah does and then He commands us to do the same يَا أَيُّهَا الَّذِينَ آمَنُ صَلُّوا عَلَيْهِ وَسَلِّمُوا تَسْمِيمَا اللهم صني على سيدنا ومولانا محمد وعلى آل سيدنا ومولانا محمد وبارك وبارك وصني صني عليه اللهم هنت السلام ومنك السلام تبارك هذا الجنال والهكرام حيلنا واذخلنا دار السلام حيلنا واذخلنا دار السلام حيلنا اوئ داخلنا دار السلام اللهم عز الزب اسلام والم dólares وأدر نشمتاصلا وفي الآخرة حسنة وقنا عذاب النار ربنا هبنا من أزواجيا وذبلياتنا قلوة عيني وجعلنا لمتقنا إماما ربنا تقبى مننا إن كانت السمير علين وتب علينا إن كانت التغاب الرحيم برحمتك يا رحم الواحيم إن الله يأمر بالعدل والإمسان وإتارذ القرمات وينهى علي فحشاء والمنكر والبضي يعيدكم نعلكم تذكرون اذكروا الله يذكركم ودعوه يستجب لكم ولذكروا الله يأتبروا الله يعلم ما تصنعون وقتني صلاه