Hello everyone, this is Ross at Teacher's Talk at the most influential blog on education in the UK today. I'm really excited to be joined by David Lowbridge Ellis. David is a school leader in the West Midlands. David, could I just get you to introduce yourself to our listeners and tell everybody what you do? Yeah, so until a few months ago, I was at Barbican School in Warsaw where I've been for many years. But in that time, I've been working across our trust, a small but perfectly formed trust called Matrix Academy Trust, which we set up here some years ago. And I've spent, I'm now formally working across the trust, working on school equipment. So that's what I do day to day. So I'll catch up on that in a second. But I guess just for listener context, we first connected, I suppose, when I discovered your, I think you sent it to me originally when I was doing my research for Just Great Teaching before the pandemic a couple of years back. And you had on your site at the time, 47 things that you do to support teacher workload. And I wrote about it and you kindly agreed. And I put it in my book and I actually came back to it last month and I thought, I just want to check, see how you're going. And I just like to unpick that for listeners because we know workload is just a thing that always drives teachers crazy. It's a constant burden. But I guess I want to just evaluate some of the things that you said you did.  Anything new that emerged? So I've got a big list here if you're happy for me to read them out. But could you just, you know, give me the background story to how it's happened? So as I wrote in the original article, I saw, I think it was John Thompson, who posted online that he had come up with a list of 27 things. And the last thing I ever want this to be is an arms race to try and outdo each other with the number of things, which is one of the reasons, actually, one of the changes I've made to it is I've taken the number off it. Right, interesting. Although it appears in your book with a number on it and it appears on the Department for Education website with your number on it. We did with that number on it. I've actually taken the number off because even though I didn't want it to be that we could be viewed as not work, if you were to amalgamate two issues into one and you go down, people might be, oh, it's not work to exactly because rather than progression and we'll get into the detail in a minute. But those things aren't necessarily equal, obviously. Some of them are going to have much more impact than others. So I just saw this list and I just to be perfectly honest, because I'm really sad, I just kind of sat there and made a list of the things that we we did as a school. And the more I wrote, the more I thought, actually, not necessarily some of the schools will be doing these things. Some schools will be doing different things. But I thought it would be I thought it'd be useful just to kind of make the list. And I was doing some work with the Department for Education at the time, which I've carried on doing recently, actually, on what eventually became the teacher workload reduction toolkit. Yes. And the more I kind of did that and did presentations across the country and talked about some of the things we did, the more I realised some of those things were quite special, not necessarily unique to us, but some of them were. But I came to realise that there were the worst things that I assumed everybody did, but I wanted to kind of get almost trying. You've got your trust lens going around different places. You've got a wider lens that actually it's not the case. People aren't doing all these things. But can I just part this for a moment? Let's what I do in my podcast is let's get a little synopsis of who you are. So describe your 16 year old self to everybody. Oh, gosh.  Always was still a goody two shoes. I wouldn't necessarily say teachers pet, but I used to find any excuse to try and avoid going outside at lunchtime because I was never being like a sporty. So, you know, if a teacher wanted me to help me with their displays and things, that would be I'm not creating a very pleasant picture. OK, so what happened after school then? Let's go up to kind of college university. Well, yeah, a part of this is unfortunately it's not it's not a bad thing that I'm gay, but at the same time I did and I've written on the articles on your website about this which which you kindly published to again to try and get those messages out there. But I didn't have a particularly happy time at school, if I'm brutally honest. And I was always quite an insular kind of introverted sort of person. So I didn't go very far away for university either. But I did kind of enjoy university and sort of find myself a little bit. I did a degree in English at the University of Birmingham. So that was half language, half literature.  So it was never anything I sat there and thought, you know, if I ever sat there and thought of, you know, I want to be this in the future. It was train driver, but, you know, like a lot of let's let's let's let's speak up teaching profession for a moment. You're still doing it. So what keeps you there? And I can't imagine doing anything else. And that's not from a lack of imagination. I just find it it's it's brilliant at giving you a sense of purpose. And I I can't imagine any of the job giving you that sense of purpose.  That seems really nice in terms of having a sense of purpose. You know, yeah, I'm sure there are lots and lots of jobs that break, give people purpose, but it's like it's like instant purpose. I think that actually is at the is at the heart of a lot of workload issue is actually with some teachers and that because they feel a sense of vocation and because it is one of those things, you almost when you start it, you feel there is nothing that that beats the heart, the natural high of imparting knowledge with your leadership, you know, juggling balls that you've got a wide range of skills now that far beyond the perception of just you're in a classroom with kids and whatever else. So we'll we'll come back to that. University, so where was your first job? Where was your first teaching job? It was well, I did I did teaching practice a school in the Central Wausel and then one not that much, not that far other away. In fact, pretty much the building I'm in now. So yeah, that was 18 years ago. So yeah, I've been there. I've been teaching my first lesson and trainee teachers that I do sessions with the lesson was on a chalkboard. Yes, there was still one there, but I was also the first teacher to ever use an interactive whiteboard. Well, there you go. I think it was that kind of that transition point really. So, yeah, I mean, what's your subject, David? I'm an English teacher at heart, although I've taught most I like many of us. I've taught many things over the years. I mean, teaching on the blackboards hard, but, you know, having to do technical drawings the night before and telling people not to rub it off as your kids came the next day was always a challenge on the blackboard, but there we go. We're in a we're in a technical era now. And so when did leadership first happen for you? I think I was five years into the profession, which, again, I'm never a fan of kind of competing, but at the same. I understand that was relatively soon. Yeah. And it was partly because of the circumstances of the school at the time. Yeah, probably, probably because this it was then for the first few years of my career was in an off-stead category. And I think the team that came in and I work with many of those people still, but the team that came in recognised the teachers who were kind of, you know, doing the business sort of thing. So in a sense, I think that was kind of advantageous because I got the opportunities because, you know, they were there to do things outside of my own classroom. So because I got those opportunities and I seized those opportunities, I think it was recognised that actually he can communicate to a broader or, you know, a teacher, an adult audience and can kind of drive things in terms of school improvement, which is what I'm doing today. Yeah. So now you should now you're a watch a specific title of the Matrix Trust. So it's Deputy Director of School Improvement, which sounds so what's your, you know, obviously pandemic and stuff, but what are you doing week to week, you know, visiting schools, working with certain individuals? So I'm trying to split my time evenly between our different schools. And I spent quite a lot of time this this term in the school that we took over earlier this year in the summer, which was in special measures. And we've we've we've taken several schools out of special measures. So we're kind of applying what works there, but obviously customising for context. So yeah, I spent a lot of time there, particularly in curriculum stuff, but also behaviour stuff, whatever needs doing, essentially. Yeah. OK, fantastic. And I guess, you know, some of the things that you're seeing and learning from, you know, visiting multiple different venues and working with a wider range of teachers has been an interesting learning curve. A really interesting learning curve, as I say, there are some things that we watch that Dylan William quote about nothing works. Nothing works everywhere, but it works somewhere. Yeah, that's the one. And that is so true. And I see I can see myself really fortunate because I get to see schools in different contexts across my week. It's never boring. Yeah. So it's about translating your best ideas and thinking, right, what what what can I take here? What can I try there? Yeah, it's always always a fascinating aspect. So let's come back to this workload thing. I've got the list up in front of me. If we start with the kind of teaching and learning part of your original forty seven ideas, I guess rather than going with kind of visionary things, for example, we trust teachers. Let me go to some specific ones. So number three on your original list was no lesson plans of any kind. So, yeah, you know, did that live out at Barbican? Is it something that can live out across the trust? Or in that special measure school case, is there a little nuance required? And it's something we that Barbican, we've never gone back on.  That doesn't mean you don't plan your lessons, but it means. Yes, of course. Lesson plans. There have been schools which we yeah, we have these schools we've taken over in special measures where the principles of planning weren't robust enough, but and we have kind of trial versions of lesson plans, like five minute lesson plans to try and embed those principles, but always with the aim of it's like it's like in a lesson when you model for the pupils and you include scaffolds. It was always there as a supportive measure. And yes, it does take a bit longer for practice teachers to fill in even a five minute lesson plan. But with the goal always of taking that away, which is what we stood by. OK, I've got another one for you. So there was another one you said no one covers more than one less and a half term. I suspect through the pandemic that's been a real challenge, doesn't it? It has been a challenge, to be perfectly honest. And I'm certainly at the school where I am physically right now. Staff have been amazing at pitching in where required. And yeah, it's it is one of those which we've managed to keep the school open without having to I know some school students lack of capacity to send. Obviously, before the pandemic, this was something that you could honor. So to speak, yeah, yeah, on paper. Yeah, so that's that's great. We still try to resist it as much as possible. And we do keep very close tabs on how many how many hours people have covered. Yeah. OK, let's move on to behavior. So we've got you've got two lines here, senior leadership provisible and all staff on the corridors and senior leadership run lunch duties so behavior doesn't bubble up. Yeah, so both still true. I must admit, I edited this recently just to kind of and I thought this is going to be a big job and only took me about 10 minutes because most of the things we've actually managed. And I think that's the crux of it really. Yeah, what we tried to do was tackle the things that really did make a big impact. So one of the things that I took out of the 50 things, 46, 47, 50, however many it's got to, I think it's 52 or something like that now. I've lost count. Yeah. But one of the things I took out was the thing about Zumba lessons. Because I was just like, we don't do that anymore. But also that was the only thing that I felt that was in the list was just kind of a bolt on some that you stick on for well being rather if you're going to tackle well being you need to do the stuff that's embedded. So if we go back to behavior, yeah, senior leadership are really, really visible. We spend very little time in offices, certainly while the pupils are in school and lunch duty. Yeah, we do. No one else. Yeah, it's already through a few things. No, no, I, you know, workload for me very passionate topic, as you know, it drives a lot of people crazy. And some schools that do quite the opposite. So it's an important issue, a couple more on assessment and reporting. So the one important one was give feedback, however you think best policy, which I love. So talk about that. And then the second one, no detailed reports to parents, no detailed written reports. So let's talk about the feedback policy first. OK, yeah, just be warned, I could talk forever. So I'll try to be succinct, because this is the thing I've worked most on with the DFA and across many of our schools, because I in most schools, it tends to be marking which teachers identify. If you do any form of survey or focus group tends to be to be high on the list. So the aim is to mark a set of books in under an hour or whatever it is.  They take about three and a half hours per class set. Awful. But yeah, we still we still stick to that. And that is the aim. And most people accomplish that. Funny enough, one of the schools that one of our other schools the other day, in fact, it was the it was the one in in special measures. They've got some as you always find with any school, whatever the off-stead rating, there are some amazing teachers at those schools. Of course, of course, there was one of the teachers I was talking to was saying, I set myself a goal of marking, you know, of being able to be able to do whole class feedback after reading through the books for 20 minutes. I was like, OK, that's is an ambitious goal. But then I actually saw what deal the kids were getting. And I went and talked to the pupils in his lesson and they were getting a fantastic deal. So I always it's one of those things like with most of the really serious workload issues that you you need to encourage staff to try doing it even better than they are already. I know that sounds really, really cheesy. But if you give staff the license to think of the more effective ways to feed back as long as it works and you check it's working by asking the children, you know, what do you need to do to improve? And, you know, what are you doing well already? And how can you build on these those sorts of questions? So a metacognitive approach, then then that's how that's how we approach it. I know we are nervous. Yeah, have we unpicked the special measures context, we don't need to go into details of school, but how do you see the feedback policy immersing from Barbican over to perhaps the good and the bad aspects of what could be used elsewhere? That's a really good question, because what you don't want to do is just transplant something that works at one school and the surface level features and you end up you end up transplanting it and it doesn't work because people do strategies, you know, a feedback approach. But unless you understand the principles of effective feedback, it's going to call for completely flat on its face. So what we've been doing is we've been doing before, you know, saying this is a strategy you could use, making sure that teachers understand the principles of effective feedback, such as, and I could promise I won't go on all day, but such as, you know, feedback is something that you don't just schedule at the end of a unit. Feedback is something that happens every single moment of every single lesson and making sure that staff understand that. Otherwise, whatever strategy you implement is not going to work. Oh, man. So what about the written reports? What does that look like today? And I guess a second question. What would be a device to schools that still push out three three page reports? Don't because they're usually not worth the paper that they're written on. What we again, what Bobby can have done for years and what are the other schools of now doing is we make sure that have regular updates and it usually is three updates through the year in terms of where their pupils are at. So case A3, we've done it lots of different ways over the years, to be honest, and it's something we always make sure we bring up with our parent forum because we want to make sure that we're giving them the information they need, but it tends to be the numerical information. So what teachers enter during data drops. Sometimes that can be translated into words. So they're working at above, below, etc. But if you if you do all the stuff around the numbers and you do so we've done explanatory videos over the years, a dedicated part of the website, there's the feedback approach which we take. So we say encourage your we educate the parents on asking your children about what they're learning and what they can do to improve. So it's not just, you know, taking something completely away, but it's putting all those other things in place, which actually do make a lot of sense so that you can take away the things that, you know, reports taking weeks to write and by the time they're published, they're completely out of date. Sure. Two more themes. We'll talk about lifestyle and professional developments, I guess, the big one. What does this see, you know, pandemics distracted all of this, but what was the general rhythm of CPD at Barbeek and before the pandemic? The general pattern is allowing a system that is responsive to need as it arises. And I think because we had that model already, I think it was it was something that we were set up quite well for during covid. So in terms of brass tacks, what we do is we do mostly disaggregated days and we do those as hour long twilight sessions, usually every couple of weeks, because it's too intense doing it every week. And then people have the training days off in lieu. We do sometimes have training days and we take advantage last September, 2020 of the extra training day we were allowed and, you know, that was that was really beneficial. But I've tend to find with training whole days, you don't have as much impact and you can't be as responsive to need. I do plan the CPD calendar in advance. But to be honest, it doesn't change all that much, usually. But as other priorities arise, you can kind of move things around. So you also got can I introduce you briefly there? So you also mentioned in your original list that, I guess, the NQTs also have a voice. So is that still the case? And we'll talk about the covid aspect, the CPD in a moment. But can your NQTs stand up confidently and present ideas? Absolutely. Yeah. I mean, we've got fun enough. We've just we've just literally this afternoon, we've had a CPD, which I partly led with another colleague and someone who's only been teaching for a couple of years, but has recently taken on their first position of responsibility and whole school. And she stood up there along along with us. And I have no perhaps it is my own experience of being that person who'd only been teaching for two to three years. I think I have my first position of responsibility, which was this is how insane the kind of school school was before it was taken over. I was given whole school literacy responsibility, I think, as an NQT. Right, crunchy. I know, I know. But at the same time, TLRs flying out all over the place. Yeah, totally. You find it everywhere, don't you? But as you know, there might be towards the end of this year, there might be some of our ECTs for year one ECTs who may be maybe starting to, you know, that they are those stars of the future. And so we just interact before you were talking about covid. Obviously, there's all the headaches that have associated. But let's just keep with the CPD thing. How has that shaped up from March last year all the way through to here where we are a year and a half later? To be honest, we sort of kept the same model. Now, obviously, quite a bit of it had to be moved online and obviously other priorities interceded, particularly around teacher assessed grades and the year before centre assessed grades. So we had to do we had to allocate a lot of CPD time to things which were absolutely necessary, rather than necessarily being the development priorities that we really wanted. But it was getting it was getting that balance. But the model essentially stayed the same. OK, well, that's a good sign that, you know, you got a lot of things that are an embedded part of your culture. Yeah. Now, the lifestyle one, you know, that headless chicken, there's no prizes for looking busy or staying late. Obviously, the pandemic and workload and teachers work in, you know, 50 plus hour school leaders, you'll know, work in 80 hours a week. How does that shape out?  And I just want to. Is it more than just words? It's it's not. I'm sorry to disappoint you, Ross. It isn't more than just words. Well, I would just caveat that with the senior leadership. And I know that we weren't alone on this, but senior leadership hours mostly due to things like contact tracing. I'm not I'm not kidding. There was I did I did a little poll on this on Twitter back in July, because I thought, are we alone on this? This is not getting mainstream media coverage. And I was getting I was getting fed up to be perfectly frank about that senior leaders. I mean, one week, I'm not kidding. We clocked up at least 40 hours. So what did you say, just out of interest? The. Of schools were spending about 40 hours a week doing contact tracing in the summer term crazy. And then the majority about I think it was about 60 percent were doing somewhere between 50 and 40, 15 and 40 hours. So we were sort of we weren't alone. There were a quarter of other schools that were like us, but we were being really diligent with the contact tracing. We were going through seating plans with a fine tooth code. Everyone took at least two hours. So we were we were we were we were. And as a result, we managed to keep the school more full of pupils than we than than many other schools. And that's not passing judgment on any other schools at all. Because like every other school, we were, you know, we were substantially reduced by the end of the summer term.   And there was a bit of a workload issue that you couldn't avoid regardless. We couldn't we. And it was it was just something we couldn't move. So some of the things that we did to adapt, for instance, is that I didn't want to stop doing any form of lesson droppings and giving feedback to teachers on how to improve. So we had to adapt our systems to be able to do that because we did have all this necessary Covid stuff. But we wanted to keep everything going that we wanted to have our cake and eat it, basically, I don't know, like it was a challenge. But we took the approach that actually if this is taking too much time, like we always do, we've got to find a more efficient way of doing it. Sure. Now, you've also let me pick up on where we started at the start of our conversation. You mentioned Zumba. So you've got in school health events, flu jab yoga. You've mentioned, you know, with the seasonal events, the less serious side staff get dressed up for World Book Day. And you've also got the international visits. Obviously, they perhaps haven't happened. I suspect, you know, Iceland, Martin and Greece. Well, we've fingers crossed for next year. All right, your fingers crossed. So what does the well being stuff look like at the moment for your staff? The I will just say in the interest of full disclosure, the yoga has also disappeared from the most recent version. Just, yeah, so. But, yeah, I mean, the series was is that a covid headache or a logistical or people won't see the member of staff who was doing it on maternity at the moment? But also, you know, it was it was, you know, something that that member of staff had to have to spend time doing. So it wasn't necessarily fair. And I know we did we did almost like a list of well being things. But I go back to what I said earlier to really impact the well being of stuff. You really need to tackle workload. And I know there are things you can you can do. We still do the flu jobs and all that. But we had another one this year as well. And and that sort of thing. But, you know, the panter, hopefully, you know, if we're allowed to do big gatherings, the panter, yeah, no, we don't know if we're a secondary, but no, no. So I guess, you know, lessons learned and where you are with your role now. How do you see your influence in workload being shifted to across the trust in with schools in different contexts? Is that something that's part of your brief or just a passion? No, absolutely. It's definitely part of my brief. So everything we implement, it's always try it. The most important thing to do is before you introduce anything new and I know this is there in the things as well. I passionately believe this. In fact, I think I put it right at the bottom just to kind of underscore it. But the if you're going to introduce anything new, you've got to take something away or make it more efficient. And that's the approach that we're taking. And a lot of the times I do feel like I'm going into schools at the moment and I'm just kind of hacking and slashing, kind of going, no, you're not not as kind of willingly as just hacking and slashing. But we've overcomplicated this. So, you know, you have. So, for instance, if we think about teaching and learning, people are told, put this in your lesson and it'll be a great lesson. It'll be an excellent lesson, whatever, whatever, whatever. And I'm just going in there and say, no, no, take it away. What you want to do is check what the kids know about this already, teach them some new stuff about it, check that they've understood it and then come back to it in future to make sure that it's going in their memories. That is it. That is it. And if you introduce any of this feedback, it's way too complicated. So that's a good point to kind of sum things up. So that and I guess the profession and, you know, I know you're active on Twitter. We're in a much better place. And we've still got plenty of things to do, but we're in a much better place, I guess, to when you and I first qualified. Yeah, I would say so, because I know a lot of it is being in evidence informed profession. I think I don't think we can really overestimate how important that is, even though still more evidence needs to be collected as the recent AF report pointed out, you know, some of the things that we we consider to be evidence informed still need some rigorous evaluation. Yeah. Sorry, David, I interrupted you again. I was just going to say we I was involved in a research project, a series of research project last year, projects last year, where we actually did we did proper research into proper studies into making sure that anything we were implementing in terms of workload wasn't having a negative impact on people attainment. So we need to do even more of that. Yeah. And I think also there's a real shift for teachers becoming research literate more than anything, you know, methodologies, whatever else. And even, you know, we find things that we don't like or necessarily can take and apply into our own school, you know, that going back to it works somewhere, but not everywhere. You know, there's the research informed, but being literate about research methods to be able to challenge them also, which, you know, some of the EEF things that we came out on retrieval practice still question that there's not enough robust evidence for absolutely, you know, keep pursuing it. And I think that that definitely put a cat among the pigeons for all the retrieval practice fans. And I know I'm one of them. Let's sum things up then, David. So you'll know in my podcast that I kind of throw a few kind of fast-paced questions at the end, kind of catch you off guard, little kind of summary of all the things that we've covered. But I guess just before I come to it, I'd like to ask you a big question, I suppose. And I know the answer is going to be challenging and difficult. But if we just put back on our head, you know, put a hat on in terms of the LG BQT agenda. Yeah. Well, and I know you've written about it on my site and it's an important topic, you know, and I've also researched, you know, if you are, if you want to come out, it's much more of a struggle for people in isolated communities rather than the big cities, they're saying. I'm not saying that it's difficult for people in cities, but there was an interesting piece of research I discovered as part of your blog. I guess the question I want to ask is, you know, where is the dialogue for not you, but, you know, teachers, and teachers who want to come out, people still ostracized, you know, etc., etc. You're the expert here. Give me some help. Where do you see this conversation of being gay openly in a school? Is it still a tough gig for some people or is it or in a better place? I guess the question I want to ask. We're in a better place than we were 18 years ago, the year I started teaching. You know, when Section 28 wasn't repealed, actually, even if I wanted to, in the first, you know, before I started teaching, I wouldn't have, you know, before 2003, I wouldn't have actually had the opportunity to do so. And I wouldn't necessarily have had the support. And I think that really, I think that nails it. I think it depends on the school. I'm part of the Askel LGBT group. And we meet usually about every month. And it's quite interesting, because obviously they're school leaders and obviously they're very on board and they're LGBTQ themselves. And I think that does make a real difference. But I am seeing an increasing number of allies. I've done quite a lot of work with some primary schools recently. Those headteachers are not LGBTQ themselves, but they really are passionate about it as, you know, lots of teachers are really passionate about tackling racism, prejudice against disability and so forth. But the appetite needs to be there from the senior leadership team, I think. So because I was, yeah, I think it's quite difficult if you go into a school and they've not done much work on that. And I sometimes think that I almost take it for granted that we've created a culture where it is absolutely, you know, absolutely. I mean, the point I raise it is because, you know, you're getting out to a few more schools, I see a lot of schools. And I know that dialogue isn't the case everywhere. It's not. And I always warn teachers to choose the school very carefully, totally, to your personal values and the school's vision and values. All right, so that that's, you know, it's a big topic. Maybe we can revisit that one in the future. So let me wrap things up then, I suppose. So we've covered your kind of role, your origins into the teaching profession, which was an interesting story. You're kind of role what you're doing today and then this big workload thing and how it all, you know, has shaped out throughout COVID. I guess one final question on this is what's still the workload key issue that you that you now perceive that still needs to be cracked? I think we really need to look at senior leadership workload. And I'm saying that obviously as a member of senior leadership. But as far as I'm aware, we haven't, you know, got. We haven't tackled the succession, you know, planning and I think that a lot of a lot of people might do. I'm not saying it for this school, but I've had conversations with people from other schools who are not senior leaders at the moment. But because of what we've gone through with COVID and because we've had to adapt to so many changes out of necessity. I think some people don't necessarily see senior leadership as something they want to join. Yeah. And actually, if again, apologies for interjecting, but the latest education support research, the teacher wellbeing index, I found not surprisingly supposed, but also disheartening that school leaders out of all the different roles in education, you know, teaching assistant support staff, et cetera, were the least likely to go and seek support.  So I guess, you know, going back to that top question, what are your hopes for senior leadership specifically then? And I wish I had the answer to be perfectly honest, Ross. I'm not sure what the solution is. And I have, as I say, I still work with the DFA and we've recently updated the workload reduction talk. It hasn't been published yet, but we were we were all of us who are working on that were pushing of more of an acknowledgement. I think that's a really good start. But an acknowledgement that, you know, the hours that senior leadership particularly have been putting in over the last couple of years and what he's really sustainable in the long term. So I don't have an easy answer. No, no, no. And, you know, when I when I did my deputy headship, you know, I love the classroom, I was only doing six hours a week. But even still, I was, you know, 60, 80 hours a week during term time easily. And that's without the normal workload you get if you were teaching 22, 25 lessons. So, yeah, I guess it's still a big nut for us all to crack unpicking succession planning, a good work in well being life as a school leader and having a bit of a life also and showing that evident in school. So I look forward to the toolkit being published. Any rough idea when the DFA might do that? No, I'm not sure, to be honest, it will be in the next couple of months. They're currently contacting everyone who's contributed items for it. Just to keep our eye on that. So let me wrap things up then. So I'll throw some whistle stop questions that you'd know. Let's see if we can catch you off guard. So let's start easy. What project are you working on at the moment? What's on your desk? You can see my desk. And then you say the gigantic piles of paper over there. I think, oh, God, I don't even know where to begin to be perfectly honest. But I suppose in terms of my own role, what's your next big deadline? Again, not sure where to go to be perfectly honest. I think I'm really enjoying getting to grips with the curriculum impact side of things. I think what lockdown did for a lot of us, even though we were incredibly busy during lockdown, I hate that myth that teachers were just sitting around drinking cups of tea in their bedrooms in their pajamas and whatever. That certainly wasn't the case. I don't know about any, you know, I'm sure like a lot of leaders. I was actually working longer hours outside the office than I was inside the office. But it sometimes also gave us a little bit more thinking space to do the curriculum intent side of things. Yeah. And what's really exciting now, although some people don't see it as as exciting, but I do, is seeing how that's then translated into the classroom. And one of the things that I'm really interested in is that tight looseness between this is the curriculum as planned and then how do teachers, how, what kind of latitude do we give teachers to implement this in their own way? It's in our list of things we do. We do encourage teachers to teach in their own way, but at the same time, we've all got to be teaching the same thing. Yeah. So that's the thing that I'm working on. That's the common thread. No offence. This is supposed to be quick fire. So let's let's let's finish this sentence. If you were Education Secretary of State, I would never miss an opportunity to acknowledge how hard senior leadership are working. Yeah, great. And what's the most useless thing you've bought online during the pandemic? A useless thing. My husband's the special is the expert on buying useless things. We've got so many remotes and pieces of technology in our language. I have no idea. None of them are working. OK, I'm going to say some of those things. Piece of advice for an early careers teacher who wants to become research literate. What would you advise? And follow the right people on Twitter because it's a great shortcut. Now, I'm assuming you've already said you're doing your best job ever. But if you had that off the wall, wacky career that you could choose, what would it be? This is going to sound really maudlin. I often think that if you're talking about purpose and that kind of thing, a funeral director. Right, OK, that's a that's a very, very interesting one. I think I think you can have a real impact on people's lives. Yeah, no, you definitely could. What's the last thing you experienced that made you laugh or cry? Um, I'm going to say the last James Bond movie. Right, I just cry thinking about it. Who would you recommend I interview next and why? Within education, I presume. Ideally, yeah, otherwise an education podcast. I try to have an education focus. I try my hardest. Yeah, otherwise, I go with Taylor Swift or someone like that. All right, well, I'll chase Taylor. But let's let's keep it real. Any any education recommendations? Oh, gosh. Yeah, I go for Claire Hollis, who does really great stuff with diversity in the curriculum. All right, I shall look clear up. Thank you. Where can listeners find out more about Barbican, your trust, maybe you on Twitter, et cetera. Will give us some hyperlinks. Yeah, so Matrix Academy Trust is who I work for. And the building I'm in right now is Barbican School. And yeah, you can find out information about those just by giving those or they're both dot code on UK's. And I'm on Twitter, David T. Lowbridge. Great. Thanks, David.  Don't put off things that you're passionate about. OK, and my final question, what do you hope to do your legacy? I hope that, well, we've got loads of people who I've taught who come back to this school or over the schools. So I kind of see that as quite flattering, to be perfectly honest. I didn't I didn't manage to put them off. Well, there you go. So thank you, David. There you go, listeners. David Lowbridge Ellis, a school improvement leader in the West Midlands. David, thank you for your time. Thank you, Ross. And it's been really good to see how the Barbican workloads moved on. I really look forward to the reduction toolkit being published. And, yeah, I think we should revisit the topic on the LBLGP for you and see what work needs to be done and see if we can support teachers out there. Thank you for joining me. All the best. It's a pleasure. Cheers, David. Bye now.


Welcome back. Before continuing our discussion on open systems, an interesting nomenclature must be mentioned. In literature, open systems are often labeled as control volumes. This fact stems from history. Historically, closed systems were called as control mass systems and by default, open systems have been called as control volume systems. For closed systems, such a nomenclature is reasonably apt in the sense that the mass in the system does not change. It is a fixed mass. It does not leave the boundaries of the closed system. But for open systems, the boundaries are not necessarily constant. That is, it is not really a constant volume system or a control volume system. For turbines or nozzles, such a nomenclature is okay and the boundaries do not change there. But for example, if you consider an open system such as a tire which you are filling up with air, then the boundaries actually are shifting and it is still an open system because mass is crossing the boundaries and entering the system. So, this nomenclature is not really apt for open systems. However, because it is used widely, we will continue to use control volume as a substitute for open system even in this course and often when we write a subscript for open systems, we will put a CV for representing control volume. Thank you.


A police of killing eight of its members during protests in Abuja. But the Nigerian police deny doing that. The plan's big for power generation. The Commissioner for Energy will be in the studio this morning to tell us all about the plans. And a foundation moves to get more girls in science and technology using boot camps. Glad to have you join us on the breakfast on plus to the Africa this very beautiful Wednesday morning. Thanks for joining us. I am Osau Ghee. And I am, and as a Felix, thank you very much for staying tuned to us on the breakfast on plus to the Africa. A very beautiful day today in the city of Lagos. But across the country, the top trending stories really don't give us a cost to be happy. Good morning to you Osau again. Good morning. Our first top trending story, the headlines say six dead orders injured as security forces opened fire on Shiite in Abuja. We know about the Shiites and their protests, usually their match that they usually come out. Once in a while to protest the release of their leader, it was exactly. Despite a court order for him to be released, he's still been held. But this time around, they didn't say the protest or match was for the release of their leader. They say it's an annual symbolic trek that they were observing in the city of Abuja when police officers fired open fire on them. And the days leading up to this particular annual match, security had been beefed up, you know, around the federal capital territory because of anticipation of violence or disruption or whatever the might occur. So I really don't know where they got this wrong for the police officers to eventually open fire leading to the loss of six lives. I mean, this occurred near Guarumpak gates in the capital. You know, they were singing songs, they were matching along the road. And this just happened.   And trust Nigerians to always string this together to say during the end-tasks protests, allegations of soldiers carrying bodies away during the raid on Ibu Ho's house. Allegations as well of law enforcement agencies carrying bodies away. And here now, we have no evidence to prove this, but that's what we have on record. And I witnessed telling Sahara reporters that six people were shot dead and the bodies of others were carried away. We really have no idea why that happened and why these raids in fact happened because, I mean, the last time I checked the constitution, we have freedom to assemble, you know. But we see this year and year out, week in, week out, month in, month out. So let's really see a clearer picture of what happened at Abuljah. We are finished. People were dispersing while the police and soldiers arrived. They started shooting tiagas, then later on the youth life ammunition on us, majorly female and children because most of the male have even left because they have already conducted the prayer for us to disperse. So this is what happens today. They just attack on innocent female and children. They have killed about eight people now. So many people have run into the bush, so many guns, gunshot injuries. All right. Just a short clip from the event yesterday or the incident yesterday in Abuljah. I was saying to myself yesterday that I personally don't think I am mentally or even emotionally ready to discuss this particular story and just really discuss how Nigeria breaks a person down and how Nigeria hurts because that's really how I can interpret this. Nigeria just really hurts and it's more reasons why you've seen thousands of people jetting out of the country to wherever it is that it takes them. It doesn't matter if they are going to Antarctica as long as they leave the country because the country currently really, really, really hurts. The reports of lives being lost to the reports of bodies being taken away to the fact that this was not even any way violent, it wasn't a protest or any way, it's a walk and the fact that I think it was someone who mentioned yesterday that the injustice that has been done to Ibrahim El-Zakzaki under no circumstance in the whole wide world will anyone look at that and just throw an ignore that it is the worst type of injustice that has been done to that particular person. And then Nigerian government and the Nigerian people just continue to look away. Yes, there's demands from Amnesty International, Sarah, and the rest but it has of course not had any effect. And of course we cannot see these things continue to happen because this is not the first time that we're seeing this. There's a more gruesome video that I actually saw and I shared it with the group of soldiers yesterday and what they were doing to these same shites and it makes you just start to, I mean it's a good point to just mention that when insurrections arise, nobody should act shocked or act surprised and say, oh where are these people coming from because this is not the first time that these shites have been killed in broad daylight. Multiple times, in fact it almost is on record that every time that the shites have a walk or a protest there is a loss of lives, it might be two, five, six, ten but every single time that there is a walk or a protest there is and to be honest and I think everyone should be honest with this that there's never been any time that has been on record that the shites went on a protest and were violent or they destroyed anybody or they cost a harm to anyone. It has always continued to be a repeat of the same thing where the police and the Nigerian army attacks them while they do their protest. There's a video I think I was still on radio back then where there were live videos of the army really just shooting live rounds at shites. Blank, I mean there was no provocation. They were really just walking, I think the video clips are still on YouTube where Nigerian army soldiers really just got on one knee and set it firing into a crowd of shites. So it's not the first time, it's happened many, many, many times and that is the Nigeria of today and that is a Nigeria that the Nigerian army has no respect no respect for the value of the Nigerian life. These are the people who are meant to protect Nigeria's integrity and Nigeria's territory and of course stand for a Nigerian but they are the ones instead that would kill without any fear or worry. And so I mean to be honest I'm just not there in a place where these things are easy to speak about because we're speaking about this today. Pretty much the same thing we did months ago and we will be talking about it in another couple of weeks or months when it happens again and I hate to be a part of a space that really just has these conversations and goes home to sleep and continue my life because it really, really hurts to see what Nigeria is today and there's no ignoring these things because if it doesn't affect you directly, it will affect you indirectly. Somehow, some way you will be affected by what Nigeria is today in 2021 and I made that statement when the policeman was killed in a Jawa state that Nigeria can happen to you at any time regardless of what space you are regardless of who you are, Nigeria can happen to you at any time. There are reports of unverified for now but I'm sure we'll make the news today of someone who was killed in the southeast. I don't want to call the name because it's still not verified but it's the husband of a very, very popular Nigerian who's also late who was reportedly also killed by a non-German in South East yesterday but when those reports are verified we'll talk about it. But well, good morning Nigeria. Six people dead in Abuja and when we just go further down into the northern part of the country, Buenos States, we hear stories of 20 more people who are mostly fishermen, also victims of Nigeria. What the news is saying is that an Air Force fighter jet fired into this crowd, this community in Buenos State and they basically killed these 20 people and like they would say, it's a glitch. We heard stories like this about two weeks ago also where in Buenos States an Air Force fighter jet also opened fire on a civilian community in Yobi killing some people. We saw the pictures on the front page of Daily Trust newspaper children badly injured, women and men as well and of course they denied this at first they will keep quiet but then later they will come up to say oh this happened, we'll investigate. Take us back to 2017, same thing happened in RAN still in this same bonus that we're talking about now in 2021 in 2017 an Air Force pilot dropped a bomb on a village in RAN killing dozens of civilians. The military apologised, promised a thorough investigation but they never made their findings public so we never really knew what happened in Buenos State 2017 what happened in Yobi a few weeks ago at least 12 people were killed and many others were wounded and just now we're getting news of this event that happened reportedly on Sunday, just a few days ago 20 people said to be killed on Sunday in Quatsa Daban Masara community in Buenos State How long more would we continue to hear stories about a technical glitch by the people who are supposed to be protecting us and firing bombs on us I really can't rationalise how this happens what sort of a mistake is it I didn't get training that's why people keep saying things like this has to be a deliberate attack by the army because we really want to question how people of such calibre I mean for you to get on a fighter jet you must have been thoroughly trained you must know your onion so how do you get on that plane with all the training necessary I don't know if it's a quality glitch I don't know if it glitches the right word to use and I think these things maybe happen when there is a mystic with the coordinates that are sent there's always reconnaissance there's people who are on ground I believe there's meant to be people who point out so who sent in the wrong coordinates because it's a mistake too many that's what would be the likely explanation for things like this and also to be fair about a month ago or less than a month ago the United States also had pretty much the same thing where they had fired a drone and on manned aircraft basically had fired what they thought was an ISIS camp or an ISIS member and so in their bid to diffuse that threat killed a man and seven of his kids who just had him driven back from work they had come to welcome him and the bomb exploded or the jet fired on manned aircraft fired and he was dead they had also initially denied it and said that it was actually a nice threat until investigations on ground by the Washington Post and a few others Do you really want to compare that U.S. situation to what happens in Nigeria really? Hold on they did investigations on ground and then the U.S. Army then owned up and said oh yes it was a mistake and they put out press statements speaking of compensations for his family his wife and other family members who didn't get affected but that's in the United States in Nigeria it happened in Iran like you mentioned in 2017 it happened two weeks ago it happened again on Sunday and that's where the difference is these things don't happen every four market days in a country that actually knows what it's doing and so once again Nigeria can happen to you at any time and it's embarrassing and how? and I said do we come here every morning and we're talking about 20 people dead 48 people were killed in Kaduna on Monday or Sunday or Monday 12 were killed two weeks ago in the same Nigerian Air Force was firing and now we're talking about another 20 if you remember not long ago there was also a story of a helicopter firing in the Niger Delta that also led to the loss of lives that to date has not been investigated there's still no explanation as to what happened there this really is just a very very clear picture of what the valley of the Nigerian life is to the Nigerian people and to the Nigerian government and that's exactly what it is because of the speed with which we move on from these things and I've accepted that we can wake up at once and hear 100 people died and we just move on like it's nothing it sounds like some Akara women's oil went bad that's how easy it is for Nigerians to move away from stories like this and nothing will happen the same with the Nigerian government itself has continued to and people would say murder its own citizens and really just move on like nothing happened there's no investigations, there's no sanctions there's no nothing, no checks and balances to be done to find out what happened and where it went wrong you would realize that in the coming days there would be no proper statement from the Nigerian Air Force to say this is where we got it wrong this is what happened and this is what we're doing to ensure it never happens again nothing we move on until we sit here again couple of weeks from now and report a similar story so Nigeria just really breaks your heart and I would say our condolences go to those families who have been affected in the Air Force, Miss Fire okay so we have another story moving away from security to politics right yeah so this is just a short video clip that we'll be sharing with you maybe on a lighter note and this is from River State where there was of course a meeting the chairman of the NDDC Gotsulakpabio was in River State for I'm not sure exactly what the program was but while they were there the governor of River State he had some wiki had a few things to say so let's play it for you and we'll be back there's no collaboration we have had with the NDC that they have completed one the mother and child in hospital we are supposed to have collaborated with the NDDC we brought our own part of the money NDDC didn't bring it down okay we found out it's our money that you are holding it was a walk thank god they know if they didn't pay what the problem would look like and they paid by that money now the headquarters where they are now Mr. Minister you are here you are in the NDDC you told me in government house that you are part of now the state government they are going to bring 2.5 billion the state government will bring 2.5 billion for the de-analyzation of the papers as I speak you have not got one now the road is only 35% if you don't pay I will make sure you use that road to your head because yes because I'm not there for our Christmas yes because you see I got the fact that you have built this one for police IG will not send police to support you that day because I'm going to be the one that will need to block that road because you must fulfill what you have promised hmm I've never said governor he has distinguished himself as the vocal governor almost like around Donald Trump in the sense that he would always bear his mind on issues and regarding the NDDC we know that he's always been calling them out whatever they do wrong whatever he feels this is not you know just doesn't go by the book he calls them out for it and I don't know people love him for it yeah and it's funny you know actually to see and maybe it's a good thing that we end up with that one because you know I watched it yesterday and I did have a good laugh at his you know the way he always expresses himself like you said you know he never holds his tongue on anything and so it's one of the things he's been known for and it's always very very interesting to see I like the part where he said you know it's a good thing that they refunded because you know they know what the problem would look like they didn't so it's funny you know and it's interesting and it also shows also that he knows exactly every every little tiny detail of what goes on in the state he knows about contracts he knows agreements he's you know on ground you know hands on he's not leaving some of these responsibilities for commissioners or house of assembly members or anything he gets involved with every single detail security infrastructure education all of it there's also a clip that we didn't get to play where he was you know in the gathering accusing the GOC in River State there of being involved in oil bunkering he said it to his face that he knows that he's you know involved in criminal activities of oil bunkering and he's a security threat to the state and you know he's maybe doing that for a reason of money to become Chief of Army staff at some point he said it to his face there's also a video clip that I married about a year ago where he was accusing a traditional ruler in River State there of being one of the troublemakers in the state it was very very funny but it shows that really he doesn't hold back his thoughts his views on anything you know and regardless of who you are how high and mighty you are he will tell you exactly what he thinks Do you think other politicians people would rather be politically correct and want to be more diplomatic more tactful regarding these things but we here would say no you're airing here and I'll call you off for it I think there's something that should be emulated so what's most important is to be aware first because a lot of people may not do it because they don't even know you know so what I am seeing here and the same thing with the Governor Yahya below there's also a clip where he was he went to see a hospital refurbishment and realized that it was below par and he called out the contractor who was right there I think was a Chinese contractor and told him that the work is written as zero so for me what's most important is the awareness of what exactly is going on in your state at every single level in every community that's what you as Governor should be yes you appoint people to handle you know MDAs here and there but doesn't mean that you should take your hands off you should know when their strict law is bad in every single corner you should know whoever it is let your security reports actually come to you and these things that you can verify so if he's accusing the GOC of being involved he has been properly briefed and he knows exactly what he's saying if he's accusing the traditional ruler of being a tout and you know being involved in the insecurity challenges in that region he knows what he's saying he's not just saying these things for humor and if he's accusing the NDDC of failing to play their own part you know when they had agreements with certain projects he knows exactly what he's saying and that's for me is the most important part not many Governors would have his humor or have his manner of expressing you know himself which a lot of people find interesting and funny but most importantly say what you want to say and most importantly rather be aware of what exactly is going on in your state and that's really what the answer is and I think that his personality that charisma really makes you know maybe humor that is not even deliberate it's just him it's just who he is and it makes people laugh but the point is he's driving home a message that somebody's failing to deliver on their job and definitely you should listen and take that seriously and sit up yes absolutely so yes kudos to him I mean that's the general view of Nigerians they say yes well done you are politically aware and you're not afraid to see what you think so yes that's across the papers on and off the press


So, I have four goals today with this talk. And my first goal is to introduce you to something called polyforms. Let's see if this thing works. So, polyforms are shapes that are made from, they're constructed by combining identical base shapes, like squares or triangles or cubes. And the most famous ones are tetrominoes. You've seen that before in Tetris, right? These are tetrominoes. These are all possible shapes that you can make with four squares joined together by the edges. But there are lots of other ones. These are polyominos. These are examples of the five polyominos up to order five. There's the monomino here, one square, and it's named after the domino. See, that's where the name comes from. A domino is two squares, right? So that's a monomino. There's a triomino, a tetromino, and a pentomino. And it goes up as high as you like. Practically speaking, it goes up to about heptominoes, seven, but then you get holes in the middle of the shapes and it gets messy and it gets really, really big. It's really interesting at the pentomino stage. And I brought some aids as well. Here's a set of pentominos that my wife brought back to me from Japan, which is pretty cool. Pass it around. Try not to get a greasy thing. So many sets of polyforms can combine to fill certain shapes. For example, in the pentominos, the five squares, there are 12 different pentominos, and they combine to form a 6 by 10, or here are the 12 pentominos. And these are their common names. So you can spell Filipino and then T through Z with the pentominos. And those are all 12 of them. So they're 12. Each of them is five squares. They can combine to make a 6 by 10 rectangle. All right? These are all 12 of them and they fit together perfectly. Now, what these are called polyform puzzles or dysentoric dissection puzzles. Different names for it. And wait a second. Oh, it pretty sure double-sided. I thought there were only four pages. Okay. So in the case of this puzzle, there are actually 2,339 different ways to solve it. Completely different ways to solve it. But the trick is try to find one. It's not so easy. There's a hang of it. It's not so bad, but it's not that easy. I first learned about pentominos from this book, Arthur C. Clarke's Imperial Earth. I read that when I was about 11 or 12 years old. And the main character has a set of those that he was given by his aunt or something, and it plays a part in the book. And, you know, a lot of people got into it because of this book. And I picked up a set of pentominos, like the one that's going around back when I was about 12 or 13, at Ted's hobby shop out in Point Clare. And I spent many an hour in my teenage years solving pentomino puzzles. So, yes, you know that I am a true geek.  These are all the polyominos of order one through five are in Blockus. And there are lots of other polyforms as well. These are heximons. They're named after the diamond. So, the purple is here, the diamond shape. Diamond is two triangles. So, this is a heximon, which is six triangles. And I think there are 12 of these shapes. So, this is one puzzle.  All polyimons have order one through six. And, yeah, these games are a lot of fun. You should try them. There's polyhexes made of hexagons, like a honeycomb. This is pentahex. So, there are five hexagons. And these are all 22 possible shapes. In this case, it makes a 10 by 11 hexagon lozenge kind of shape. And you can also get into three dimensions, like solid pentominos. Solid pentominos are the regular flat pentomino, but they're one unit thick. And they make a 3 by 4 by 5 solid. And I think there are over 3,000 different solutions for this. But I have yet to find one on my own. And I've got a set of pentaminos here, solid pentaminos. This one, I bought at the Valais de Coeur over on St. Denis. So, pass that around. You can see that they're one unit thick as well, so they go in sideways as well. A solution, meaning take those 12 shapes and put them together into this solid. You can do it over 3,000 different ways. So, these ones can go into that shape? Yes, they can. But try to find just one. This one, trying to do this, I get very frustrated, so I don't spend very long. The regular flat ones, it's not so bad. It's not so bad. But it's fun.  You've got a puzzle called soma cubes, which was invented by a gentleman named Piet Hein. I think he was a Danish architect, something like that. He also invented the super ellipse, if you've ever heard of that. No? Well, it's pretty cool. These are all of the non-convex shapes you can make with cubes up to three dimensions. It means that if you try to... It's up to four cubes. And if you try to go to five, then suddenly you can get into the fourth dimension and you didn't want to go there. Sorry? What do you mean by non-convex? Well, convex means that if you go around, it's always... You never have an inside... A convex one will always have outside corners. But non-convex has inside corners. So a convex shape would be like just two together as convex. So two doesn't exist in soma cubes. It's only three or four. You can put these together into a three by three by three cube, 240 different ways. And it's pretty easy to find one. You've got... This is pentacubes. This is if you take the pentaminos, but you extend it into three dimensions. They're not flat anymore. And you've got 29 different ones of these. You can make some very interesting shapes. And then there's another puzzle, which I've never even touched. These are called polysticks. And what these are, instead of putting squares together, you take line segments on a grid. So the little segments on your graph paper. And these are all the possible shapes from one up to four polysticks. And they fit together into this lattice. And I just look at that and I say, wow, that's really cool that they all fit together like that. Maybe that's just me. I hope you find it interesting. I hope you find it interesting, too. So this one I don't know. I don't know. At least I don't know offhand. I don't know if anybody actually knows this one. Some of the puzzles I've done, I've devised for this software, haven't been explored fully and I haven't let the computer run long enough to actually find all of them. Some of these puzzles can take days, weeks to find, especially because it's written in Python, which is not known for its speed. It's known for its speed of writing the code. That's what I'm interested in. My time is more valuable than the computer's time. So my second goal is to introduce you to some of the algorithms and some techniques. First I'm going to tell you about the first time I implemented this. It was back in Sajapur University. I didn't want to study, so I started writing this software. I was using Object Pascal, an object-oriented variant of Pascal. So the algorithm was using brute force and with some heuristics. The heuristics being things like the brute force would place every piece everywhere it possibly could and the heuristics would be the program would look at the remaining space and make sure that it's a multiple of five. So it wouldn't break up a space and three on one side and two on the other. Well that doesn't work. If it found a space that was exactly five squares it would try to figure out which piece fits in that space and if that piece was available it would put it there and if it wasn't it would backtrack. It would check for bottlenecks like a thin area where because of the thinness even though it wasn't exactly five squares still only one shape could possibly fit. So basically I made the computer solve the puzzle the way I was solving the puzzle and that should ring warning bells. It didn't with me but I was very naive and it never worked. And I gave up. So when I first learned Python in 1998 this was my this was my project to learn the language. It never well it had bugs I never got a you know what I think I might no no I shouldn't say it. I never got a solution out of it. It was a good learning experience when I wrote it in Pascal, object Pascal but I never got an actual solution out of the thing. So that's my definition of not work. I can't remember at this point whether it ever you know compiled I'm sure it compiled properly but I can't remember if I got all the bugs out of it or if it was just a time thing. Back in those days that would have been that would have been let's say Sage up I was in Sage up from 85 to 87 computers were really slow back then even if you're writing in Pascal it was slower than writing in Python today. So back to Python so I used it as a test bed to learn how to how to use this interesting language and I fixed it up I got it to work but it was still it was very very slow and so I sort of I gave up I even went so far as to register a project on source forage and it's a four-digit project which tells you something I was in the very early days of source forage before they had 10,000 projects and but it remained dormant for many years until 2006 so then I came across a very interesting paper by Donald Knuth who does not know who Donald Knuth is okay learn he's a professor or professor emeritus at Stanford and he wrote the art of computer programming he's still writing it is the series of books all about algorithms he's the father of the analysis of algorithms he wrote the tech computer typesetting program TEX it's actually it's Greek letter it's a chi it's not an X sorry? Tao Epsilon Chi a lot of people call it TEX but it's actually TECH and he also wrote the one of the first literate programming systems called web so he wrote this paper called Dancing Links it was published in 2000 I read it in 2006 and he discusses this algorithm called algorithm X and that's what I want to talk to you about and this algorithm finds all the solutions to the exact cover problem there's a lot of big words a lot of big concepts I'll explain them so here's the exact cover problem so what have I got here so this is the statement given a matrix of zeros and ones does the matrix contain a set of rows which together contain exactly one one in each column so it's a sparse matrix of zeros and ones you want to find a set of the rows when squished together have ones all across but no twos, no zeros and to find every solution we must find all such sets of rows so the trick is to construct a matrix that corresponds to the puzzle so the first thing you need to do is you name the columns and you name the columns after the names of the pieces and I showed you that pentaminos all have names and other puzzles do too with some of them I just made up names and then also the coordinates of your puzzle, your space that you're trying to fill so this is what a header could look like for a hypothetical puzzle it has three pieces A, B, and C and it fits into a three by three array so these are the I can try laser it's not working you've got oh, laser light, there you go the puzzle piece names and then the coordinates here and then you need a row for every possible position of every piece so you've got a piece and you can go here, here, here, here like that everywhere in the puzzle that it can go and it can also go here, here, here, here and then here, here, here, here like that and so every possible position you make a row and the rows would look like this there would be you put a one under the name of the piece that you're representing and a one under each coordinate that the piece exists in so this is in 0, 0, 0, 1, and 1, 1 and then you'd have a then you'd try to find solutions where you'd find a set of rows such that you add them all together and you get ones all across and one such solution might look like this so you see there's one piece A, one piece B, one piece C and every coordinate has one, one in it so there's a solution to this hypothetical puzzle so I'll give you a trivial example here so here's a puzzle of two pieces A and B into a space that's three squares big trivial, right? Very trivial and here's the puzzle matrix that results from that there are three possible positions for A here, here, and here and two possible positions for B here and here if you allow rotation which in this case we do and so if you look at this matrix you can see well okay you need one of A so let's choose this one this one doesn't work if you put A here you take this one there's no B row that matches but if you put A say up here on 0, 1 which is here then you try to find, so that's this one taken you try to find a B where it's the other two there it is, the bottom row so this row here and this row here combine to make a solution so that's the kind of thing we're dealing with was there a question? no? okay so the problem is that matrices for these kinds of puzzles can get really really big for the six by ten pentaminos puzzle the matrix is 72 columns wide there are 12 pieces and 60 coordinates and it is 2032 rows long which is pretty big and even that, that's not so big if you take a pentacubes puzzle which has 29 pieces it is there's 29 pieces there's 145 coordinates to fill so there's 174 columns and over 6,000 rows so it gets pretty big pretty quickly it's like square of the number or the cube of the number or something like that I haven't figured it out so that's the exact cover problem and then Knuth outlined this algorithm he called Algorithm X this is how you solve the problem how are we on time here? probably want to speed it up I won't bother going through all of this just believe me it works okay if you're interested in the details read the paper and then the other part of the paper is this concept called Dancing Links so in order to well I'll go back once one of the things you do in this algorithm is you cover columns cover means to remove a column from the matrix and remove all the rows that have a one in that column that you just removed so you end up removing a column and a bunch of rows as one operation and you do that here and then you do that here again so you end up messing with this matrix a lot so even though, okay 175 by 6000 doesn't seem that big when you got gigabytes when you have to do a backtracking recursive algorithm and you have to slice and dice this matrix all the time it gets you don't want to be copying this matrix a lot because it's pretty big so you need an efficient data structure so newt's algorithm uses doubly linked lists like this so every node has a left link and a right link his algorithm actually uses quadruple linked lists they actually also have an uplink and a downlink we'll just deal with doubly linked lists for now so say you've got a linked list like this and you want to remove node B you know what node B is you want to remove it from the list it's easy to remove it you just say okay say B dot left dot right equals B dot right what does that mean B dot left is A make its dot right the same as B's dot right so A now points to C you're the same with C C now points to A so this is what you get right now B is out of the list but this is a backtracking algorithm you've got to put them back again so how are you going to keep track of all this stuff well the really cool thing about this paper which was actually Knuth popularized it but somebody else came up with it was that there's something to remember B remembers who its neighbors are B knows B still points to A and C right A and C don't point to B anymore but B still points to A and C right so you can to reinsert B into the list you say B dot left right equals B and B dot right dot left equals B and suddenly it's back the way it was back to the original state so this is called dancing links because the links dance around they turn off and on and they dance so you call it dancing links and yeah it's very very useful for recursive backtracking so so then we have this algorithm he calls DLX which is dancing links algorithm X and it uses quadruple linked lists which have left right up and down as I said and it represents a two dimensional sparse matrix so you don't need nodes for all the zeros you only need the nodes for the ones actually if you only are representing the ones you don't even need ones you just need nodes right so it's an efficient use of of space and this algorithm when I read this it was so different from what I had done myself and so obviously superior that you know it sort of blew my mind what it does is it adapts the puzzles to the computers way of thinking not to my way of thinking computers think differently than people computers don't actually think right they're dumb stupid machines we have to tell them what to do well I couldn't teach it to think the way I do so this way it can do it's work the way it does it and it's a very efficient and flexible system answer the phone let's see and it's also applicable it's applicable to other other puzzle like problems like the eight queens problem you're familiar with that you've got eight queens on a chess board and you don't want any of them to be able to take any of the other ones and it also can be used for Sudoku by just very carefully arranging the columns and then after that you just let it run any kind of any kind of packing problem that kind of thing it'll work on so Sudoku works quite well as well and I've already written the module to do the solvings all you have to do is make the matrix and feed it to it and it'll do the work so after I read Knuth's paper my old itch resurfaced and polyform puzzler is the result and that's what my third goal is to talk to you about polyform puzzler so it's a set of tiny little front end applications which are two or three lines long and they call a bunch a Python package some libraries the exact cover algorithm coordinate systems polyforms themselves and the puzzles so they describe all this stuff and it's easy to it's easy to add new puzzles and even polyforms and it's not incredibly difficult to even add new coordinate systems to it that makes it easy okay where am I I'll use a puzzle to keep my place so we've got over 100 puzzles in the project made of 12 polyforms I showed you a few already and I'll show you some more but it's not an interactive program yet that would be really cool what it does have though is it has SVG scalable vector graphics and X3D rendering of all the solutions the pictures you've seen so far almost all of them have been drawn by my software and it's not that difficult SVG is just a XML so you just have templates and slice and dice and it works the project has a bunch of it has a gallery of puzzles and solutions so conclusion was anybody counting so my fourth and final goal was to show you some pretty pictures along the way I've shown you some here a couple more so here's Heptaim and Snowflake here's another Snowflake this is one my wife got me and I don't know about you but I look at this and I just think that's so beautiful it's like Snowflake's in real life it's amazing that nature works the way it does even mathematically that this could be possible it just blows my mind and then we've got this one here this is pentacubes corner crystal so you've got three walls here floor and two walls then you've got crystal staircase in the corner and this is interesting a gentleman in New Zealand had devised this puzzle something like 20 years ago and he's been working on it for 20 years so you have a single coordinate system is a coordinate system to actually build the matrix it goes into the exact number over the same yes as long as you make the coordinate system as long as you make a coordinate system you can make the matrix do we have like two algorithms now for 2G and 3G? no, just one algorithm creating the matrix is kind of the hard part that's the part where you have to really think hard and like when you go back to this one I'm assuming that you can show us that algorithm actually well that algorithm that one is per puzzle it is per puzzle or it's per polyform type so there's one for polyominoes it's a grid that's easy then when you get to polyomins which are triangles then it gets tricky and I actually use a pseudo 3D coordinate system for this if a triangle is pointing up it's a zero and if it's pointing down it's a one but other than that it's a skewed grid it's like a grid like this and I also use a 2D coordinate system for polyhexes the honeycomb shapes the polysticks which are the line segments that's also a pseudo 3D where I use zero for horizontal and one for vertical and then it's just XY after that but what you have to do is translate from some format that makes sense to you as a human to a format that makes sense to the computer and the computer in this case doesn't know anything about the underlying puzzle what the software does is it takes the puzzle description turns it into ones and zeros matrix the exact cover algorithm turns away and delivers the solutions and then the software has to translate it back into something that we can understand usually the output is ASCII text and then graphics like this Martin I have a few questions now so one part is creating the background from the part that shape you want into the matrix but the second part is also generating each of the possible variants of the pieces of the patient the translation should be trivial the rotation depends on the domain it's interesting do you do that with the computer or do you actually manually when I first implemented it I did it manually but now I've got the computer doing all that stuff and it makes me wish that I'd paid more attention back in linear algebra because all of that stuff comes into play matrices and multiplying matrices and groups and all that stuff it's all useful here and I wish I I'm sure I've done stuff in the software that has names that it's a recognized transformation in mathematics but I don't know what it's called because I forgot because it was 20 years ago that I learned it which goes to Google that you can say my problem is like this and like that and like that it's funny that it's a similar problem well it's probably all on math world or something but you know so my second question is more fundamental but maybe I missed that part I'm sure you must have mentioned it not necessarily and it seems clear to me that you don't have an infinite number of pieces to choose from because that would be a trigger problem of cutting out the domain well it's not a trivial problem but it's easier you have an inventory of shapes now given an inventory a specific inventory of shapes it's possible that there is no solution about the domain so what's the input of your program do you actually start from the domain generate the pieces without someone here's a puzzle what does it do exactly you start from a puzzle from somebody who created and then solve it I start from a puzzle somebody created or I created myself in idle moments at work I'll do it along graph paper you'll cut out the pieces like I said I've never actually done this physically even though I've got a set of these pieces I've never actually done this particular puzzle physically it's only in the computer that's actually done it you should generate the inventory of pieces yes the inventory of pieces all the combinations of in this case seven equilateral triangles that I have done manually and actually enumerating poly polyforms is a hard problem in and of itself there's different kinds of inventories you can say you can't have more than two pieces that are the same basic shape and when you get into that you get into some tricky areas I've done a couple of puzzles like that and it's one of those cases where I have to sit down and think hard how am I going to represent this as a matrix and I'll be happy to talk about it after but I don't think we can so when you start an inventory of pieces it turns away depending on how big the puzzle is for anywhere from milliseconds to weeks and then spits out zero solutions found it didn't find a row that had no links no I haven't found any bugs recently Francois this snowflake this picture this picture this picture this snowflake this picture my software did that yes well I designed the shape there's a website where you can make graph paper I don't know if you've ever seen this you can make graph paper in a regular grid or triangular or hexagonal and other ways as well and I printed out a bunch of triangular graph paper and I started doodling pictures just for fun just for fun basically what I do is I start with a hexagon say a hexagon like this and realize that okay this set of shapes doesn't fit in that hexagon I like to start with the simplest basic shapes first squares triangles, hexagons and then if it doesn't fit I'll play with it make holes add appendages I like symmetry so I would just play with it and pull it out until I could find one that fit or sometimes I couldn't find one that fit stuff like that so in this case I can't remember if I made this one up or if I found it on a website about these polyforms polyforms out there there are some websites that are just incredible the scope of these things the amount of work that's that would be a hard problem an NP hard or whatever you call it was there another question from over here this particular one I can tell you let's see puzzler solutions hep diamonds snowflake 2 dot text let's see how many have I got here I didn't solve them all I only got a couple of I only got one so far this is part of what the program gives me I did some ASCII art to print it out and I think that's the same is that the same one yeah it's the same solution and my software will also it'll generate the ASCII art and then you can feed it the ASCII art and it'll generate a graphic it doesn't actually parse the ASCII art although I've done that in the past it parses this data here so here at the end you've got the names of the pieces the coordinates they fill and it'll read out that block in and turn it into a piece of SVG graphics yes it can be parallelized well yes you'd have to duplicate the matrix you'd have to duplicate the matrix across each process would have to have its own copy but basically at the beginning of the algorithm there's a starting point deterministically you say well to keep the see what you try to do is you try to keep the search tree narrow and deep as opposed to broad and bushy right and so you choose the column in the matrix which has the fewest ones in it that'll give you the fewest that'll give you the narrowest search tree after that and so you choose the first one and then non-deterministically in other words one at a time you go through all of the rows in that column exhaustively you just do a for loop over them so you could feed each iteration to a different process a different computer whatever and if you had lots more computers level down and another level down I haven't done it but you know you could how long did it take which take this computation you know what it doesn't say usually I have it let's see I'll try to find one here let's see penta cubes corner crystal so this is the one I showed you a moment ago you can't even see it here darn some of them are if you take some like pentaminos the 6 by 10 pentaminos that took you can see here 2339 solutions it took 19 minutes in this case some of them take minutes some of them take microseconds some of them take weeks I've actually run it on my computer work left it on overnight nice down the the process so it didn't bother me when I was there during the day and left it running for weeks and also the software saves states so you can cancel it you can control C out of it and then resume it and pick it up later and it'll pick up from where it was you can write a C W named list structure I am using pythons that's a good point I'm glad you brought that up well no it sure you just have references to objects what's a real list well no I'm actually not using I'm not using python lists I'm using each one is an object with attributes left and right which point to other objects so if anybody is interested in writing a C extension module I've got a great project for you the hard work is all done already but my C is very rusty and I have no desire to polish it up okay well I haven't actually learned Pyrex so what I have done with it is I've used Psycho and that's spitted up like three times but yeah I could do that I just never got around to it to me it doesn't really matter how fast it runs I'm just interested in reaching the solutions and finding the solutions when there's 2,000 solutions it's cool to see them all when I reach 10,000 solutions I don't care anymore and if I get just one solution after a week that's enough for me hey there is a solution that's cool when you say city of state do you use pickle? yeah use pickle that's right just pickle objects that's all it is and there's that one there and there's this one and I can show you something do we have time? run out of time okay this is let's see let's see if I can zoom it out here and this is a program called Free WRL and so this my software also generates 3D data and so you can play with it in 3D so you can see behind it and see what the actual pieces are if you want to build it so I was saying about this puzzle here this was an interesting one this gentleman in New Zealand devised this puzzle like 20 years ago and he's been trying to solve it ever since for 20 years he's been trying to solve this puzzle he got as close as all but one piece fitting can you imagine? all the way he gets all excited it doesn't fit and the problem is with this puzzle is that the pieces go flat and then this way and so all of the 3D pieces have to be on the edges, on the corners or here in the middle the flat ones have to be here and so he found my project and he wrote to me and asked me if Polyform Puzzler could solve this puzzle and I said yeah I think so and I was busy that week so I wrote it up a week later and it took a few days I think for it to come up with a solution but it found a solution he was very happy I don't know I don't know I think there are a lot of solutions but I don't know how many and in the future I hope to explore some as yet unexplored polyforms that I've thought up in my head some 3D ones that don't seem to be explored very well and maybe even work on a GUI but if you'd like to help if you find this kind of thing interesting and why wouldn't you then I'd be happy to have your help you should build a really wicked one and send it to a guy and use it in pieces in pieces he also came up with the he also came up with another one which I the one back around slide 6 or so he came up with this one also this fortress kind of looks like a video game and I was able to help him solve that one too so it was pretty cool so your experience this guy spent 20 years trying to find a solution so you had the intuition that there was a solution how would you know you had the possibility how would you you generally have an intuition whether or not there is a solution well you can there was a solution there was a puzzle I came up with sort of similar to this you take three planes the x y plane the y z plane and the x z plane three intersecting planes and you make sort of an octahedron out of them it's like you take this one and duplicate it there and duplicate it there and smaller and I tried to come up with I tried that it wasn't working well and so I thought okay I'll think about this and one thing you can do is you can use you can use parity to see if you can solve a puzzle so for example if you color each of these cubes like a checkerboard so black black black and then white white white like that and if you can determine if there is an overabundance of one color over the other and there often is especially a puzzle like this this puzzle probably has an overabundance of about 10 of one color over the other and then you look at your pieces each individual piece and you color each piece and you see is there an overabundance on each piece and then you add up all the overabundances of the pieces and if they do not at least match the overabundance of the puzzle is not solvable at all there are some some kind of simple rules of thumb yeah there are there are some simple rules of thumbs and there are some very complex rules of thumb that people have come up with that are smarter than me but that's one of them so that that puzzle which was the crossed planes I figured out that I think the overabundance in the puzzle was about 25 so it was like 27 so it was not very likely that there would ever be a solution so it's left on the in the project it's left unsolved I haven't had time to run the computer long enough and that puzzle would one of these puzzles to run into completion under Python not Pyrex sorry, not yet anyway one of these puzzles would probably take weeks, months to run the solution space is so huge that it would just take a long time you should write one of those screen savers yeah it would be cool yeah and you know farm it out among the world it could be done the solution the solver the exact cover algorithm I wrote it as a generator so it could be done that way I wrote it as a generator so that I could monitor it as it went along and it's a re-entrant generator so that you can cancel the process and then go back into it stuff like that optimizing my own Python a little bit but not too much, I'm not really an optimizer I don't really care about speed too much that's true, I just wanted to check yeah look at docketills, it's dirt slow I don't care one of our participants sped it up by about 30% through some simple profiling and he likes doing that I'm not interested really parts of Python well the generator generators were useful it meant that I could isolate one part of the algorithm from the rest of it just Python's dynamicity itself the fact that you can have an attribute just point to anything Python fits my brain because I don't care about all the bookkeeping and all the little details so that certainly helped I mean the algorithm in code I can show you exact cover here's the here's the solving this this method here at the top from here to here that is the expression of the algorithm I showed you in pseudo code and it's only about half again as long as the pseudo code now of course there are dot uncover and dot cover and stuff like that which are methods elsewhere but if you can take an algorithm even if it's an 18-point type then you're doing pretty well exactly it's executable pseudo code as opposed to executable line noise that looks like an artifact of maybe the vertical line that was an artifact of I think that was anti-aliasing that's just an anti-aliasing artifact I didn't even notice that there's probably a mode you know Emacs there's a mode Emacs has everything everything I mean back when I used to use it on Unix workstations the icon was a kitchen sink has everything including the kitchen sink that's the end of my talk nobody's asleep I hope you found that interesting thanks for watching