Ni od border plenty. I welcome if you're joining us out. So I just give people a couple minutes to get in? OK so first of all a couple of caveats. Hello welcome. My name is Nigel De Naronna. I work for the UK Data Service at the moment, I suppose a lot of the material here really comes from my experience of teaching on the graduate Geography a news flynzers Da'수를 CHARPS which is going to have been through various incarnations and you'll get a chance to look at them afterwards, but they focus on using Excel. So it's a strange time really. I mean, we initially planned this workshop for November based on what we thought would be the availability of data. We moved it to now and we are still kind of relatively short of data, so in the examples I'm going to use, Yn y cwmhyslu, rym ni'n gweinio 2011 oedd yn ddaint. Byddwn i fod yn cynhyrchu a chyfnodd, byddwn i'r ddweud o gweithwyr ymddangosol ar gyfer 2021 neu ar ydych chi. Mae'n ddweud â'r ddweud a'n oes i ddweud eich cyfnodd a'u ddweud o'r ddweud o'r ddweud, ac yn ychydig i'r ddweud yw'r ddweud. Yn ymddangosol er mwyn i'n gweithio ar gweithio'r ddweud, sy'n gweithio'n deallu o'r ddataeth absiwys. A'i wneud i'n fath o'r dysgu faniwys arall a'r cymryd yn chweithio'r ddau. If you have questions, put them in to the Q&A and we can stop at a convenient point and talk about them. So, the aim is not for me to talk a massive amount, is to tell you some things to give you some time to have some practical application of using Excel for some exercises. Come back and talk a bit more, and then have a look at the ways you can access data, and then reflect, I think collectively on the ways that this might be useful in our future. And maybe inform some of the work we will do on developing materials to support more use of this. First of all, just the context. There are three statistical authorities, so there are three censuses. ac, ond mae wedi'i gael iawn, oherwydd sy'n gweithio'ch gweithio gyda'r pandemig, y twmfynol ar ein hirio ddechrau yng nghymru yn y Gweithreib yn Llywodraethol, yn ystod y byd 2021, ond mae'r Ysgrifffyr yng Nghymru yn y Llywodraeth. Mae hynny'n meddwl bod y ddefnyddio'r informatio yn ei ddysgu'r gweithreib yma, felly rydyn ni'n meddwl nid yma yn y Gweithreib yn y gweithreib yng nghymru, ond mae'r dyfnyddio'r panthoedd yn cyfrifiad. England and Wales have now nearly completed releasing all of the single variable tables, so the last one is due this week, and the next stage is to release some multivariate tables. Okay, so Jackie's asked the question about what tools we use. Maybe we could hold on to that one and come back to that later on because I think it does depend a bit on what we're doing. I suppose I've given this a kind of basic statistical literacy for students, which means using Excel as a common denominator, but there's no reason you couldn't use other things. I mean, the currency of the download data tends to be Excel, and it will be interesting to come back and see how other people might use this data, particularly when we get on to mapping, which is not part of the focus of this workshop, but clearly of interest to many of us. So once again, I suppose there's a debate about whether this is the last census and whether we're going to move to understanding our population from administrative data. Because of the pandemic, there was a significant amount of work done to validate the census estimates using other sources of data, and there is material from ONS on that for those who are interested in that. Okay, so what I'm going to cover is, first of all, the census outputs. Happy to be stopped here. I'm going to start with the obvious ones that are available, but as we move on, there are some kind of nuances to what's coming to explain the geographies that are available, to have a look at the kind of data that we're going to get. The tools, talk a little bit about tools we might use to understand it, and then move on to practical exercises, and finally some reflections on how you found that material. So in terms of census outputs, I've grouped them into four chunks. So there are different ways of cutting this, but one clear one is the geographical data. So the kind of boundaries and things we need in order to create maps of the data we're using. There's a set of univariate data summarised in topic summaries, which are currently being released and area profiles, and there's also multivariate data. So the first of those are due out next week, which will be the sexuality gender identity with sex and age, five-year age breakdowns, the same for race and the week after religion. So those are some of the predefined multivariate data. The other thing we're being promised now, which is new, is flexible tables. So this means we'll be going to cross-tabulate what we want, and the outcome that we get will be subject to statistical disclosure control, which I'll say a bit more about. Margaret's asked about the slides. The slides will be available on the event page. One thing I should have said is, because when we're discussing, we don't want to get tied up with asking new permission, we're going to stop the recording and discussion at that point. So recording, sorry, and transcription at that point. So the discussion is for our group, but the presentation and the practical exercises will be available, so all of the slides will be. And then the last parts are possibly the most complex, but I'll go over those a little bit more in the next slides. So first of all, the geographies. So we have a fairly standard set of administrative geographies, local authority, health bodies, and so on. And those do differ between the countries. Most of my examples do tend to focus on England and Wales, partly because that's where I've done my work. Then we also are due fairly soon to get the electoral data on constituency and ward. And finally, we've got a kind of, I suppose, a statistical area that was developed in 2001 to move, I suppose, away from the changes that arose from changes to boundaries. So if you looked at the census before 2001, there would be data at the lowest level collected on what was called in the new ration district, which was where the census collection team would operate in order to go and make sure the forms were completed. So they were fairly arbitrary geographies located around community hogs so that there was a base where people could work from. So in 2001, there was work on developing more homogenous areas, output areas that have similar types of characteristics. And that work developed a kind of definition of an output area and then building blocks, use those as building blocks to make two other areas. And that has been maintained for 2011 and 2021. Clearly, there have been some changes over that time, but the aim of that set of geographies was to try and minimise the change. And I think overall, the change in each year has been less than 5%. So thinking about teaching particularly, the examples I use here are focused on country, region and local authority as a kind of national geography that enables you to see kind of high level detail and to explore more detail. Other people might do work with constituencies or if you're working on a geography and some of our new materials will be focusing on this local authority geography within it, the neighbourhoods within it. An alternative geography that will emerge for some later on with the census releases is workplace geography, so that's the places where people work. So just to go through quickly, an output area has a threshold size, it has a minimum and a maximum and a target number of around 125 households. I said some of those. Those are then built up into lower-layer super-output areas, typically five or six, and mid-layer super-output areas, which are kind of akin towards size around them, 2,000 households to 6,000 households. And all of those output area geography boundaries are constrained within local authorities. So to give you an example of the way those work, and this does use 2021 data, I went on to talk about the different geographical data administered to the electoral and statistical, and then the ways that you might define the geographical scope. So most of the examples, the practical examples in Excel would use region, country region, local authority. You could also look at constituency, and if you're interested in the area you're in, you might want to use neighbourhood data around one of the statistical areas within a local authority. And later on, we will get workplace data. So I'm not going to go over all of this just to say there are three types. So the output areas, the basic building block, those are built up into lower-layer super-output areas, and mid-layer super-output areas. And just to give you an example now, these are the six London boroughs with 2021 data, and what these are showing is the proportion of households who have unrelated adults with no children. So this is more than two adults, so not couples or others, and it's a proxy for measure for houses under multiple occupation, and this is the highest level of geography, statistical geography, the mid-layer super-output, and you can see some concentration in parts of the boroughs in Tower Hamlets, Newham and Hackney. When we move down a level to the lower super-output area, you can see that the detail becomes more granular. We can begin to see patterns of concentration. The largest area has 33% of households of this type. And then finally, when we move down to output area, that granulation becomes very detailed, and the area with the largest proportion actually has more than half, 56% of people. So that's a kind of showing you demonstrating the geography, but I think in terms of looking at this, when we're looking at a single variable, in most cases, we can use output area once we move into two variables because the numbers are so alike to be small, it's quite likely that a number of data figures will be suppressed. So what happens with the tables that you get is, first of all, if there are small counts, they may be swapped between areas. And secondly, under the new statistical disclosure mechanism, if something is seen as disclosive of either individuals or a group, it will not be released, so you would get your requested table and it would say, this isn't available at this geography, or this is not available in these areas. So there's always going to be some kind of trade-off between the detail of the geography and the detail of the variables you're looking at. Okay, so let's move on to the data products. So the reason I've used 2021 data for East London was just to illustrate the point, really. It's an arbitrary choice, it could have been Manchester, it could have been Birmingham, it could have been anywhere, to do that on a national level, but let me look at the geography because you need to be concentrating on one or a few, not a small number of local authorities to demonstrate the difference. So there is 2021 data for the country across all of these indicators now, I think, apart from health, the health ones which are coming on Thursday. Hopefully that answers your question. Okay, so the topic summary is here, there's a set around demography and migration, so these are things like household composition, whether people are living in communal establishments, and a set of data around migration, particularly around those who, the year of arrival in the UK when age of arrival, etc. And those are the basis for future tables that will have relationships with those, but at the moment those are single tables. They are the ones that were used for the press releases around Albanians on the release of this data, which coincided with the events in an immigration centre as well. So from the other side of that, there's a lot of stuff about migration, but there's also quite a lot of stuff about the way people live, the kind of households people living in, living arrangements, which is where my previous example came from. The next release was actually veterans. Okay, can I hold on to that one Lawrence, can you come back with that question later on, because I think that's getting into quite a complex area of analysis. So I'll just focus on what we've got with the data now and then talk a bit about how we might use it with other fields a bit later on. So the veterans was tied up and released with, sorry, was released the day before Remembrance Sunday, I think, or the week before Remembrance Sunday, for some reason. There was a whole large group of questions around ethnicity, around national identity, that is what identity people feel they have, link perhaps to the migration ones which taught us about passports, language spoken and particularly kind of competence in English and Welsh and religion. I'm not going to go through these in the order they were released, we will have health disability and unpaid care questions. A whole set of stuff about housing which covered largely households at this stage in terms of tenure, the type of property and so on rather individuals and also provided some information on second homes, on cars and van availability, so some of those kind of semi-property related things. A whole set around the labour market and travel to work, at which point it's probably worth saying there is a kind of open question on that data because of the impact of COVID and the time the census was taken. So for those doing that kind of analysis, you may well be looking at alternative sources as well. Education has just come out and the last release that got quite a lot of coverage was around sexual orientation and gender identity and I think I'm not an analyst but I think it was quite, it's not an area for my study particularly but I think it was quite refreshing or quite welcome that the participation rate in these questions was pretty high. So one of the concerns I think in asking a new question that was volunteering was will people play, will people complete this or will it end up being not very valid because a lot of people haven't filled that in. And the result was it was quite well completed. Okay, so in terms of the multivariate data, so what we're beginning to get as I said that we get just before is some defined set of tables and my understanding is that those will become available over the next couple of months and that into March we will get what's going to be called deflectable table builder and this will dynamically calculate tables for you but it will apply a statistical disclosure control which will not therefore show things that are seen as disclosing. Also the variable categories are likely to vary between the univariate and multivariate and the point I made before about balancing geographical scan and the level of detail you are. So these other types of data are all going to come a bit later on but may well be interesting areas of studies that in terms of alternative population basis will have a picture of workplace populations, workday populations, out of term population and second address population. So if for example you were looking at the impact of students and where students came from to a university you were teaching in, you could use this data from the census, it's fairly contemporary and in the census as completed in 2021 students were asked to complete their term time address whether they were living there or not so it should be fairly reliable for at least UK born students, it might not be so reliable for those born overseas who hadn't registered the place already because they wouldn't obviously be completing the census. A small population so ethnic group, country of birth, religion and national identity again I mean I've looked at the ethnic group data and it is really quite confusing trying to unpick it at a local area level but it's basically a writing category so there is lots of detail there there's some data quality with dealing with it but lots of data there that might be of interest. Flow data is a new type of data for some so what it holds is an origin and destination is typically used for looking at migration flows, workplace flows and this time it'll be also be looking at second address flows and student flow so what it is based on is asking the question of where you live 12 months ago in terms of migration, in terms of workplace it's where do you live and where do you work, in terms of second address it's do you have a second address and if you spend more than 30 days there what's the purpose so is it a work second address are people going away to work somewhere is it a holiday address etc so you can get some picture of those kind of flows and students and largely focusing on on HE I suppose in terms of the volume so that data is quite interesting probably available from early summer onwards similarly the micro data for those of you who want to engage in more complex analysis it's a 5% sample of either regional or combined local authority geography or a 1% household sample so if for example you were teaching in a city and you wanted to look at a multivariate analysis of the population in terms of the data available within the census materials which is reasonably comprehensive so you can look at some reasonable descriptive reasonable dependent variables around deprivation you could do that one note though is that doing this is this is a safeguarded file so students using it would need to register with the data service and have permission to use it but this data file has the 2011 file had around 2.8 million records and if you cut that down to a city size you would you would get a reasonable sample of data so I was what teaching in Nottingham I had a sample around 15 000 to do an analysis so again a potentially interesting source if you want to come back to that later on as I said I'm focusing more on the kind of early outputs from the census so just to kind of summarize now what are the potential topics of interest so there's a whole set of things around demographics, population, migration, living arrangements, population, pyramids, age and sex distributions etc and if you're in a university town it maybe is quite interesting to compare the age profile of the population there with the age profile of the largest surrounding area so as I said I taught at Nottingham and the distinction between Nottingham as a city and Nottinghamshire as the surrounding area was was quite stark in terms of that kind of younger population who tend to move to study or to work a whole set of things around identity, around ethnicity, national identity, religion and language, work, education, housing and health there are other topics there but those are the ones that I kind of picked out as ones that have some resonance for teaching now what I'm going to do now is come back to to Lawrence's question I think the answer Lawrence is the other way around really so if you take data from understanding society and other sources there is a mechanism to link that to census data and there are two ways of thinking about that one is to link it at individual level which clearly requires kind of use of a safe environment approval so from the statistical authorities that was used quite a lot in the analysis of COVID cases, COVID mortality etc with pre-release census data so there are individual links to find out information about people's occupations etc that were part of the explanatory explanation from why particular things were happening in particular ways the other way to think about it is to link to an area base so you could take neighbourhood characteristics and it's not something we've talked about here but in essence we could build up a profile of a neighbourhood by taking variables associated with that neighbourhood and then say you know I think some work has just been published today by Queen's Belfast on diversity and increasing diversity in neighbourhood so if we could characterise neighbourhoods as diverse as lower class as having particular class profiles we could use that potential as an explanatory factor if we had geographical data in the survey data so the link is more from the individual survey data to either potentially the geography of census data or individual census data does that answer your question Lance let me know if that's okay so I mean I think if you do want to pursue that it's it's something you would need to talk to either the UK data service secure service or ONS secure service about that using that kind of linkage has clearly got issues and you would need to go through some approval process to do it and that's managed by both ourselves and ONS separately for for those projects okay so what we're going to do now is to have a look at some basic exercises using 2011 data this is also an opportunity for you to take a comfort break to get yourself a drink and whatever there are some materials that my colleague will provide a link to in the chat there are four sets of materials the first set are based on simple univariate data using regions so you can see the data on one side I'm not suggesting you have to go through all of this it's to give you an idea of the flavour of that the second gets more complex so it gets you to navigate a local authority set of data and then the third one moves into multivariate particularly picking up on pivot tables in excel and the last one is about text formatting so as I say they are quite detailed exercises you're free to take them away with you we will be upgrading them to our new accessible templates and 2021 data at some point in the future so if you want to wait for the more accessible versions that's fine if you want to take them with you I think you'll need to download them now and keep them and you're free to use them in any way they were paid for out of q-step monies initially and are kind of common okay so Margaret's asked about individual respondent level though there's nothing specific about primary or secondary schools attended so you can impute the area of attendance but there is nothing held at that detailed level if you had a primary school survey I'm not sure whether they would let you link you know that's an open question because the the individual educational data is quite secure as well I'm putting that together with census data um there might be nervousness but that would be the way to do it um to pull together the plastic data the whatever the pupil census data with the census data if you wanted those additional variables okay so um what I'm going to suggest is um we kind of give this maybe 20 25 minutes to see how you get on and I'll check in with you then to see what's happening meanwhile I'll keep watching questions and if you need support with anything then then just give us a shout hey um I'm going to um go through the different ways of getting 20 21 census data after this session of trying the materials so um if you hold on I'll go through those after this session just to show you the three different ways to get them hi Margaret that's an interesting question um I mean I suppose that the kind of work I've done with this has been um around skills development so it's around students answering similar questions and learning how to interpret data which is one way it can be used um I think the other way I've seen students use it and I would encourage them to is to paint some contextual information about broader areas of study so typically it's very powerful in a dissertation to be able to map some of these variables and show um what's happening with them in terms of detail work with the census um that's kind of complex I'm not sure it I'm not sure how easy it is for particularly undergraduate students to find something original um and I think if it forms part of postgraduate study it's like to form part of the methods used alongside other things um I hope that answers your question but happy for other people to kind of contribute what they think about that hi Tecwet um I'm I'm not sure what you mean by that if you're just saying is there an archive of projects um probably the short answer is no I mean this data is is is becoming available now um it's widely used and not just in um in the academy but also used significantly by policy makers um health professionals etc so there is a kind of a way that this data is very open data is used in all sorts of ways so when you look at briefings for parliament on the population when you look at um material used by local councils by local health bodies um by researchers etc there will be masses of work being being done a lot of it will be I suppose not original research but interpreting things within particular local context um you could search for census 2011 if you wanted to see what projects have been done using census 2011 data I think we're quite early on with the census 2021 released to see more advanced forms of academic work going on here hopefully that answers your question but but please come back to me if you want to clarify if anybody else wants to add to that um okay mark right hi um in terms of all of the tables and the flexible table builder I'd be pretty confident that will all be available by um by May 2023 I think the kind of the release of all the topics has finished I think all of the um predefined tables are likely to be available over the next few weeks and the flexible table builder will come as a big bang following on from that the other products and all the geography products are there and everything is being adapted to fit the additional geographies um I think the ones that might come later are what they are in ethical phase three which is the flow data the micro data and some of the alternative population things um that's for England and Wales clearly the Scottish data is likely to be a year behind that and if you want a combination of UK data that's going to be a further year behind there's some harmonisation work so the short answer is a lot of what we'd expect to see will be available by then but some of the more detailed products we might still be waiting a little bit for um okay sorry I've put off mac versions as well um there are no real differences in the mac versions three and four the big differences are in some of the keys you use and now those first two workbooks give you navigation keys which differ um with the mac in part three and four we're really looking at basically pivot tables and text formatting so we're much more into um not directly interacting key wise but building up formulas hi Liz um I think that what you'll find is the population um is for all ages and the qualifications figures are for working age groups so you'll you'll find there's a difference between those two um Margaret I think with the Scottish release Scottish release we're unlikely to see anything um by May 2023 I mean I think uh you could talk to national records of Scotland or you could put a call into our help desk and I'll refer it to my colleagues who liaise with them regularly to find out but I think they they thought there was a year from closing the census to getting to first release data um and we've seen with England that there've been problems with that data as they've released it we don't know that's going to be the same for Scotland but clearly they've got a kind of a significant estimating uh piece of work to do before they get the general population data so Scottish data won't be available and then I'd be pretty confident to say um but if you want to contact me outside of this I'll refer it to a colleague to get a kind of more detailed date yeah I would say so I would say that's a kind of reasonable plan to go with but like I say if you're if you're producing project proposals and thinking about what you're going to do in terms of that bit then I'm happy to kind of give you the information that my colleagues get from attending those liaison meetings with National Records Scotland um okay Payan you've asked about the methodology um I think that I will put a link in the chat just to show you um right so this is um an ONS page which has the original questionnaires um I'll put it into the chat rather than here so there are some differences between the countries as well um so the well uh particularly around language but there are some ordering differences around ethnicity as well and others but um and I think if you look at the Scottish questionnaire which is held by National Records Scotland um they ask a lot more details about health um hi it's a question from Nigel about multi-variant flexible table option um I'm not sure when that would be available because the workplace geographies are coming kind of later on as alternative population geographies but I would expect them to be available as um as that sounds like it's going to be the main interface now there are three ways of accessing the data and I think they are all in um a state of change so for those of you who have used 2011 data um you may have used Nomus or the UK data service um the ONS is new the ONS interface is has changed over time um I'm happy to go through it um on the screen but I'm going to try just with the slide and see how you get on and if you're struggling with it I will demonstrate it as well um because it's not the slickest of things to do um so first of all the ONS now one thing to say is that all of these interfaces don't yet allow for multi-variant tables uh multi-variant data and particularly when the flexible table builder comes along that's going to sit within the ONS website so the way that Nomus and the UK data service access that um is is not really clear so that's about ONS Nomus looks a bit like it did before and I presume it will get more like it uh if you look at the 2011 in space where you could pick variables um select your job of the etc um and the UK data service is a completely new interface it's under development so there are areas where um I've asked for changes based on using the material some are in there and some are on their way so let's start off with ONS so first of all from the front page you can go to the census and you'll get a page like that on the left and currently what's available are topic summaries and if you pick topic summaries you'll get the top screen which shows you a topic summary um you can pick any of those topic summaries so in this example I pick ethnic group an ethnic group and when you go down um to the variables you get into this get the data so you can select your area type um you can select your coverage and what the coverage does is it now allow you to reduce the geographical scope so for example if you wanted to look at um lower level super output lower layer super output areas in Manchester you could pick the area type as lower layer super output areas um and then pick the coverage as um an area you would be asked to type that in um it will search and come up and you select that and it will then restrict what you get back based on those two selections um so I'd suggest you have a go at the ONS one um if you're struggling with it I'm happy to demonstrate as I said but it's not the slickest of things to do um and I'd like to leave a bit more time for the discussion okay so um I mean again to explain if you go into NOMIS so the address is nomisweb.co.uk um and there are different ways of accessing census data there's a tab along the top that says census and you can pick 2021 um there's the census statistic data catalogue on the right um and there's also the query tool so whichever one you pick you arrive at uh topic summaries and data downloads and if you go into topic summaries you get each of the tables that are are available um within those you need to choose your geography um so you can just select from a list you can select areas within which would give you something analogous to the way we did the um the data for uh the ONS interface so we could pick the lower layer super output areas um so we select areas within we select select those lower layer super output areas and we say within um local authorities and then we navigate to the authority we're interested in. When you come to the ethnic group um the default is to have no categories so you need to decide on the categories you want so I would typically tick the top box on the third column that you might be able to see on the bottom right to select all the categories and then download that data so again we'll just have a five five ten minutes having a look at this um yes yeah the question about um geography because of it this is the first ONS access to census data so in 2011 they just provided to Nomys and the UK data service they don't specify um the different geographies so they implicitly means the 2021 version um I think if you took the um 2011 census question you would find that it would use the 2011 geography in Nomys as well um those the two I'm going to encourage you to use for the time being um and the reason is that the UK data service though it will get there doesn't have that geographic scoping so when you you run it it will pull down all the data um for the country depending on whatever geography you pick um so that's likely to come in a subsequent version but I'm not going to take you through that because it could um take quite a lot of time but broadly speaking what happens if you go in there is there's a lot more support material so within the learning hub from the front page of the UK data service there's information about the different censuses which you might find interesting there's some explainers about different variables that have been released so for example the new ones on gender identity the sexual orientation have some explainers about what what you're like to see and you have access to aggregate and and boundary data as well so the top side shows you the the aggregate data and the bottom side shows you the boundary data those at the moment are very much works in progress so rather than saying go and have a look at these I'm putting you off I'm going to suggest we skip that one and um we will publicize it once it's fully accessible and we'll be using it in courses in future but for now I would say it's not unless you're looking at national um tables um or national geography overall it's probably not the best


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Hello, good evening excuse us for the technical difficulties now. We are gonna have a talk about HPC in deviant the distribution for Clustering and Fabrizio Kanini is with us. So Fabrizio Hello everybody Since I came here in last Saturday, I was thinking of what I'm going to tell you I Not I'm not sure about it right now yet but What if what I know is that I've seen some problems when I'm was first when I'm beginning researching to change my the rocks Linux Installation of my company's cluster I noticed that there was some that it was pretty much documentation available but What I noticed that most of the times that the things that just don't work Like you had a lot of things that manually do You had to do you had to edit configuration files. You had to make templates or whatever sorts but There's a lot of manual work to do Things that I You didn't need to do like when using rocks for example And also it seems that people Doesn't seem to be aware people what I'm what I mean people is that Most common of people that use clusters like scientists engineers Especially for numerical simulation problems in weather forecast or Physics or chemistry or Geoscience is also so whatever whatever you need a huge amount of computing power Most of the people they don't they don't seem to to be aware that Debian's also a great distro for making this kind of For this kind of task so What I'm actually what I'm actually proposing right now We have the tools Have the tools you have a lot of Tools by this by this In this area MPI implementations libraries Task managers and You go on Compilers we have G for trying we have GCC. We have G Plus plus that now on G's now on version for three day F Open MP implementations which make for Which makes which makes them on the same level that commercial compilers let path scale like Intel like PGI I Think that we should Reach out these people see hey What do you think about using Debian this in the cluster situation or? Especially people there is already using be already using Debian on the situations Hey, what do you think about? What do you think about using Debian in the cluster situation? Was it hard to set up? Where where you hate to find any difficulties What could go what could be automatized what is the the boring tasks that could be automatized Also Yes, of course reaching out people that don't use that don't use of that have not have to choose to not use Debian for This kind of environment why? Why do we choose another another solution of? Why have you choose to go with Susie or redhead or rocks or? Sentos or Whatever see where you can where you can? Improve I think that You know most of the cases that Debian is successfully used in In a cluster environment. It usually takes what I call an inside champ For doing such a things something that somebody that is already on the organization and that Already knows Debian that is has been using it for quite some time and This guy knows knows how to do it and he wants to he wants you to do it But he wants it needs most of the times that he needs to convince his his workmates or his managers sorry His managers that Debian is indeed the right to the right thing to do the right district to use I think that we We had to Pick people from like Debian science mailing list which has a lot of HPC users I Think we had to like Like I said before we have to we have to reach out. We have to know what these people need so that we can so that we can Improve Debian so that we can Go on one step further to avoid domination I Think it also would be it Initially it would be great to have to to make a main list to discuss what is exactly this this this people need so What I'm proposing to do I'm going to well I'm going to to reach out these people and see what they want in a research like like of what Paul has done peps To But more specifically oriented to to this kind of situations I'm also I'm also going to Start working on Debian cluster components if you know it is It's a very nice Project it is You know have my lesson right do we have do we have oh right? Well links will be backed on on the on the lecture on the The session links and contents This guys I've been talking with I've been talking with the developers of Debian cluster components and They seem to they seem to really like Debian They really want to know they really want you to make this work. They I Think they share the same the same wheel that I am that you make Debian the distro for Cluster environments, so now I'd like to see I'd like to to know I'd like to know from you Who from you are using Debian in such environments? What to think about what it could be what is good what is bad and what is ugly and What can we do to improve it? Which packages would you like to see in Debian? Which packages do you use? One of the nice things about Distributions like Oscar and rocks is that typically you can have a single CD that you put in the system You boot it and then you can boot your different client nodes off of the supercomputer That type of a distribution would go a long way to helping people utilize Debian in say a high school or situation to Allow the students to practice using and programming supercomputers Yeah, there there are some there are some There are some projects like these there are some like Pelican like Pelican HPC That there's a it's a bit. It's a bootable CD There's also parallel gnomics that it does like it does something like this Debian cluster components. They also do They also have a city like this that you boot on a CD and that you They have already You have a host and three virtual Notes so that you can so that you can use it for Learning how to manage a cluster how to use MPI how to program with MPI and how to Not even this but you can do like learn wrapped in your Anything you like and it has a lot of and has a lot of The standard tools that you use it like LAM MPI on pay MPI Compilers Python and Java I Think it's what this is nice for this is nice for educational purposes Should it also it's something that we should take a look but What I'm what I'm What I'm trying to do right now is just to Choose to see to know what exactly what the point is at which point is we are right now and we have a lot of users and we have a lot of tools but What more do we need? to to to make it To go up and to to make things better to to the users which is which are Our final target and to enjoy answered and what's your personal background about clusters I Work in a weather forecast company in Porto Alegre Brazil So I've been in there in more than more than a year working working there. We have a six node clusters Six node cluster which he does The weather forecast for the whole Brazil twice twice a day Yeah It does the weather forecast for the whole Brazil twice a day it takes some Three and a half hours for the simulation to to to complete It takes also some 10 gigabytes per node of Generated data Yeah, that's what I'm trying to that's what I'm trying to have I've been researching and that's what I've been researching that right now. We're using a rocks Linux Installation that's what I'm trying to to put them out and to to put debium in And while researching this that's what I've I've come to to realize that What people were doing to What people were doing to to have Linux to have Debian running in a cluster environment So since since last year have been What can I do to make it To make it better. Why can I do to make it? things goes mother or Go just works so for people In the cluster environment Another question that you would have a marketing standpoint is What is the penetration of Debian in clusters as opposed to the other competitors? How many people are using the different versions of Linux in In that and you know if Debian is 2% well, then you might say that there's a lot to be done If Debian is 90% then you say well, you know, the other is just noise And so the question is how many you know what percentage of sites use Debian? I Guess you could say that Debian is not really the number one in the number one in In clusters usage At least if you if this looking by the top 500 Clusters of well top 500 dot org if you want to know There's a lot of there's a lot of Clusters that they just don't they just don't they just don't Don't release which version or which distro they are using They just don't they just say Linux But the most popular distros for cluster cluster environments, they are Susan 9 and 10 Redhead and the price three and four after that they come sent sent OS and Rocks and after that Debian There are some there are a few clusters running free BSD One or two running HP UX and a dozen running Half a dozen one and AI X and Solaris but Linux Linux as a general is is is the top dog in Cluster environments, but Debian specifically is not I think we should I think we have a long road to go to To go. I think we have a Lot of nodes to to get into if we wanted to be really representative in Cluster community to what answer Well again my only Comment on this is if you contact, you know So you've talked to some of the companies that produce cluster hardware and some of them Have Debian and do use Debian So the question I would ask them is why did you choose Debian over a different distribution and then to contact the people in the In the places that don't use Debian and say why did you choose this other one? I remember when red hat first started charging for their enterprise edition and Their charge was something like a thousand dollars a node and they came to the super computing conference in I forget where it was that year and I went up to them and asked them how much are you going to charge the cluster people for their clusters? And they said a thousand dollars a node and I said good luck So I mean obviously they've changed their licensing somewhat since then But I would imagine that people who run clusters who run red hat enterprise are still paying some amount of money To red hat and for something I hope So you know there must be a reason why they're doing that Again my understanding of rocks and an Oscar are basically that they are more or less You know they use a distribution as a basis But then they add their management software around it and it isn't it isn't a distribution like red hat is a distribution Or Debian is a distribution It's more of a wrapping around a some basic distribution Yeah rocks is based on on sent OS The version that we use that at at my company is rocks for to what One I think it's based on Santos and sent OS for It's a ghost At Sarge time I think So one thing one thing that might help convince them to go with Debian would be more of a liaison between Debian and themselves so that every time there was a new release of Debian that came out It would be easier for them to upgrade Then you know that it might be with sent OS if sent OS wasn't paying as much attention because sent OS is based off of red hat So there may be a Disconnect there that makes it difficult for them to keep up with releases of sent OS That Debian could help to solve with a little bit of communication back and forth I guess that because sent OS it it follows more or less the same releases schedule of red hat enterprise is just Cleaned up a red hat Cleaned up and recompiled red hat enterprise so they have the same reschedule and and Maintainance dates maintenance Periods like red hats enterprise I think one of the reasons that people People don't use Debian is sometimes is the lack of the inside champ Which I've which I've spoken That without this guy People they don't they don't really go after Quite a lot they just They just Take something that they know that somewhere else Did it and it just work it they they just installed it like Real scientists and engineers they don't Actually, they think about the same questions that we as developers think they don't they don't actually think about this Freedom and Open source they that we do praise to that we do praise very much so that's why I think that Debian has a long time to That has a long road to to walk to to it is a A big player in the cluster market We have we don't have Mindshare if we want to say so and Because people they don't act because especially because When installing Debian in a cluster some things that they just don't work. They don't just works people who gets afraid of using Debian because oh because Debian is hard to install that same old phantom that Debian is hard to install Well, I Work at SGI and I have had access to an ice box Which is what we sell as a cluster and it was my bounce box So I tried to install Debian on it and The Lenin installer at that point wouldn't boot on it So like I could debug it and spend time on it But at that point I just really need to work and I believe that when you get to deploy a cluster You just don't want to debug an installer. You just want it to work Actually, it looks like a few years ago as I was using Debian as the base OS for the operating system that was shipped on the clusters Again, that's I haven't been in the company for a long time. That's more cordial noises than anything else And I've been trying to look why we moved away to go to Susie Part of the things could be that Susie slays 10 is shipping a 2616 kernel With a lot of work that has been made to backport all the fixes to the kernel while maintaining a lot of ABI compatibility That in those machines you sometimes have a hardware for which the vendor will ship you a binary module that will work only on one Kernel and and that's really important to make it work and the kernel team is Not doing that in Debian because we don't have the manpower at the time to do it But that's things that you require to make it work properly I've been told about a network driver which had a free software implementation that was really really slow Compared to the binary one and absolutely unusable for people in that environment. So that's Some of the things yes, so Spedial there there really are sort of I think three categories of things that get in the way of Debian having a larger cluster market share right now And if this is something we want to work on we have to figure out How much of this we can address and then come up with a good plan for addressing it? The first one is that lots of clusters do run with interesting interconnect fabrics and things like this for which the Device drivers may not be fully integrated into a kernel or a kernel and therefore may not be in our default kernel packages that we're shipping and You know there's there's always device driver issues with different kinds of hardware But there's plenty of cluster hardware today available today that Debian runs very well on so There's certainly that class of cases that we can think about But I don't think we should get bogged down on that because there are two other classes of Things that we ought to think about one is that a lot of people Running clusters are running, you know commercial ISV provided applications on those clusters and when they do that they have the same Problem of the choice of underlying operating system that anybody with a dependency on a commercial Application does and that is that that application provider is going to choose the set of operating systems that they choose To certify that application for use on if you want to have support for it and today if that's Linux It's probably one of the commercial distributions for lots of you know good business reasons And there is a chicken and egg situation there where if there were lots of demand for those applications on Debian for Use on clusters they would probably port them, but you know How do you get there if the applications aren't available? How do you break that cycle? but the third thing is that for whatever reason the there are a number of Cluster oriented distributions that are out there. I mean rocks is one example. There are others And many of those seem to have been built on you know a de-branded Rebent branded red hat package base it may well be because they See some opportunity to be technically compatible with Some of these binary applications that are built and certified on red hat or Suzer or something I don't really know what the driving force or the history behind that is but it seems to me that one Opportunity would be to create some custom Debian distribution or other Lightly derived version of the distribution that specifically targeting the cluster community and includes You know some interesting management tools and related things that would make it attractive to them I don't know of such a Debian based distribution exists right now or not But if not then when someone goes and starts doing you know Google or whatever search is looking for Linux and clusters They may not see us as being an immediately obvious choice Yeah, one of the one of the other barriers that have seen to to Debian Adoption in clusters is exactly of proprietary applications like Floyd dynamics applications that are I don't remember them the application but It's lots of engineer and lots of engineer applications like wind tunnels wind tunnel simulations and that use a lot of dynamic fluids computations and They are very very expensive applications and they just and when you see when you go to the to the to the the software house web page it it only it only is It only says Red Hat Enterprise 3 4 Susie Susie 9 Susie 10 and that's it about Linux Another another operating systems may have HP UX or Solaris or AI X from IBM But that's that's it I think that's Another another thing is of as of drivers that like they said like mirrored There's no there's no free Mirinette drivers Available today only binary blobs That you just dump in your kernel edit. They they are made only for Susie and for Red Hat So this there's another barrier of Inclusion why on the other side? Most infinite band providers that I know they they have free drivers and Most of them are already on the main mainline kernel And that's a good thing Well actually but Dale says he doesn't know the history of it But I do and the thing is that back in the early days of the supercomputers Red Hat gave a lot of attention to it And they actually put out as a very early CD called the rocket science CD And it just had all of the software for clustering of that time on that CD And it got a lot of the people in the national labs who did a lot of the work on things like rock and oscar using Red Hat Which is why they were so upset when Red Hat changed their licensing of course sent OS got around that But when you say that yes, you know You know infinite band is available with some open Drivers but mirror that is not well, but that's the thing with Red Hat or Susie you can get both and you're not tied to just one See, I mean it's the whole ecology of it It's also the ecology that that a lot of the people that work on supercomputers are not computer scientists They're scientists or engineers and they're still programming with programming with Fortran and stuff like that Not to do anything wrong with Fortran Fortran 77 Was some sometime 90 but in any case in a case what they want is the same thing Running on their notebook so they can do their preliminary programming and everything and then take it over to you know the cluster and And these are all a group of things to do it my greatest my greatest suggestion would be to aim towards putting together a package that as before which would get in students Using Debian so as they went up and came out they would say hey Debian's a great distribution for doing this You know and that would be your inside person that you say you're champion To getting it spread out across a lot more of these areas Would have picked were to pick a side of suit of high-performance computing that a lot of the national labs For example, don't even think about for example financial Computing data mining, you know that type of supercomputing that you know, it would be a whole new marketplace That a lot of the Debian packages could actually utilize that Would it concentrate on things like the real multi-core type of programming so open? You know open MP To get that going and pardon me for saying so but from my experience the G Ccc compilers do not produce the same type of performance That you would see out of a really commercial compiler that is tuned to particular architecture You know you're gonna see a five or ten percent performance that over two thousand processors is like 200 processors that you got If you look at I 64 one of the architectures still used in HPC You see that last time I checked on half of the spec benchmarks actually the pro 64 compiler Which is the open source all this GI compiler is still the fast compiler much faster than a vendor compiler Well, I wouldn't use the itanic anyway, so But but as I said pro 64 is picking up a little bit of stuff Intel has some people working on it also for other platforms There is LLVM So it's not like easy sees the only compiler we still have Okay, but the thing is when you're seeing there with Your stopwatch trying to figure out how fast the compiler is because all you invested in is CPU As opposed to the portability I guess that I Guess that's not just there GCC is not that bad. I've seen tests made for by Brazilian University showing that with With the same level of optimization GCC for two has less than one percent of It was less than one percent slower than Intel nine compiler in C and C++ But it was it was much lower without optimizations But I think that I Think that GCC Why it has it's it's bad things and the law but GCC is Going Pretty strong on and it's getting better each release If we if we do the same the same test again, which is we we just see for three I'm sure that the difference between GCC and Intel compiler nine would be even even smaller and One of the things that you should be pushing with this is in the universities They're trying to teach computer science and trying to teach high-performance computing is the fact that you can see the source code For these compilers where you can't see the source code. That's a huge advantage for in an educational space Or if that you know, you should be leveraging the openness of the operating system and the openness of the compilers to the educational marketplace and then you'll build that that you know support as As the students come out of the college and go to work for different companies Yeah, I had a few words After you talk I personally work in a French aerospace lab We are big users of high firms performance computing supercomputers and alike. This is not really my field of expertise I'm very sorry for that. Oh Supercomputer supercomputers are as far as I know running commercial Linux distributions For only one reason because because this is why what we were supplied with and only for that The other reason probably is because as you said and I wanted to confirm what we said the the showstopper also has been probably the commercial libraries the commercial Fortran compiler. Yes, we are using Fortran. I confirmed that sometimes Fortran 90 and Actually, I think that the people were using our supercomputers and our cluster Don't care a lot about the C compiler It won't care at all, but they care a lot about the Fortran compiler That's on super computer And if this Fortran compiler is for instance provided by Intel and only works on one reddit Derived distribution there will be no choice. We will have to go with them Just to have an idea all the all the the weather forecast models that I use in my company They just they it is Almost How they've written in Fortran 90 Yeah, we actually use just the MPI part is written in C We use the very same kind of supercomputer than French Meteor Center And this is exactly the same culture and this culture is a very old culture And it takes a lot of time to change it and not only From through the students, but the through the infrastructure people and in the infrastructure people those will run these supercomputers to also get this idea that there are some Free distributions around Anybody else? Well, so I'd like to thank you everybody to come this come see me bebo this this stuff I Hope we can we can talk a lot more by mailing lists or by private mail or ear or whatever And I'm I'm personally going to pursue it. What I'm what I what I say here today And if if anybody wants to Anybody want have any idea or wants to talk me with me after that I'll be at the hack lab So thank you a lot for coming


Hi, I'm Zor. Welcome to a new Zor education. I would like to present to you a problem which, to tell you the truth, I was kind of surprised with the result of this problem. That was a long time ago and it kind of counterintuitive, if you wish. In any case, it's about electrostatics and this particular lecture is about this problem. It's presented as part of the course called Physics for Teens, presented on Unisor.com. Now, the whole subject is actually described also in writing as notes for this lecture. So, every lecture in this course has very detailed notes and I do suggest you to pay attention to these notes. All these notes are on Unisor.com. The lecture is basically, physically, as a recording. It's stored on YouTube and there are some descriptions on YouTube as well, but it's a short description. The real lengthy one is on Unisor.com. This course has a prerequisite which is Math for Teens. You do have to know math and in this particular problem I am using calculus, vector, algebra and stuff like this. So, you better brush up on your mathematics. And again, the course which is called Math for Teens is definitely sufficient to Physics for Teens. Okay, yes. And by the way, the site is completely free so no advertising, no financial strings. Okay, these are, it's kind of two problems but it's actually only one real problem. The second one is very trivial one. Here is what it says. Okay, let's consider you have an infinite plane, infinitesimally thin, so it's just the flat surface. Now, obviously you can tell that there are no infinite planes and no infinitesimally thin planes, etc. But again, we are talking about a model. Everything, whatever physics do, especially when it comes to a theory like this one, it's all about a particular model. Let's just bear with this from the mathematical standpoint. It's a plane, infinitesimally thin and it's charged with electricity. Well, it's infinite plane, right? So, the amount of electricity is infinite. However, we do have something which is called density of distribution of electricity. Which means that there is some kind of parameter which I call sigma, which is basically coulombs per square meter. That's how it is dimensioned. Which means that if you have any area on this plane, if you multiply the area by this sigma, you will get the amount of electricity in coulombs which this particular area contains. Now, what's necessary to do is to find out the characteristics of the electrostatic field around this plane produced by this particular distribution of electric charge. Now, in particular, let's just take some kind of a point P above this plane and let's find out the intensity of electric field at this particular point which this plane defines. So, how can I find out this particular intensity? Well, intensity is a vector, right? So, the vector must have first some kind of a direction. Now, for consideration of symmetry, this vector is supposed to be on a perpendicular from the point P to the plane. That's called the plane alpha. So, we have this plane and this is the perpendicular. Now, why is this the case? Well, it's very simple actually to explain why it's supposed to be on a perpendicular. Let's take any small domain here. Well, I didn't choose a point because point has no electricity. But any domain, however small, will have certain non-equal to zero amount of electricity. But let's consider that this particular domain is really very, very small. So, from every even smaller part of it, we can say that the vector of intensity is directed exactly on this line. Now, we know that vector of intensity, if you have two point objects, is always directed on a line which connects them. Because every charged point object has radial directions of the intensity vector. If this is the point object, then all the vectors of intensity at any point are always radial. So, we know that. Okay, so now we can consider that we have a probe object at, let's say, plus one cologne here at point P. And we have a very, very small area here. Well, this very, very small area has certain amount of electricity which is equal to sigma times the area, right? Now, this is the vector. I can always represent this vector as sum of two vectors. One is radial and another is perpendicular. Now, let's take the symmetrical relative to this. This is the perpendicular to the plane from the P, let's call it O. So, let's take symmetrical area here. Also, the same shape, the same area, just symmetrically positioned relatively to the point O. Well, obviously, since the area is exactly the same in size and because it's symmetry between these two segments are equal to each other, A, O and O would be. Now, A, P equal to B, P for obvious reasons because these are right triangles with the common catheters and the other two catheters equal to each other. So, the distance is the same, the charge is the same, so intensity should be the same in magnitude. But how about the direction? The direction will be this, right? Well, I put the arrow in this direction, it can be opposite direction. It depends on whether this is positive or negative, but it doesn't really matter. The matter is just the line along which the vector is stretched, right? And I can also represent this vector as a sum of this one and this one, all right? Now, it's the same magnitude, the same angle, right? Because the triangles are congruent, which means that my horizontal components of these two vectors are exactly the same. Because what is the horizontal component? It's length times cosine of this angle. So these are oppositely directed and equal in magnitude, so all horizontal components will cancel each other. Vertical components are the same, and they are along the same direction and the same magnitude. So my point is that all components of all the vectors of intensity from all the points, horizontal components will all nullify each other. Vertical components are always directed towards the same direction and they are parallel to each other, and that's why they will all be summed together. So that's basically a description of, this is a qualitative description of the fact that our resulting vector must be vertical perpendicular to the plane. Direction will be either from the plane to the point or point to the plane, depending on whether this charge is positive or negative. If it's negative, it will be attraction, because this is positive. If this is positive, it will be repelling. Okay, now this is kind of an explanation, not much of a mess actually here. So let's calculate this vertical component, which is the only thing which we are interested, from all the elements on this plane and then add them up together. Well, I used the word add, basically it's integration. So we have to choose some kind of a small component, find the vertical component of the intensity vector and integrate along the same plane. Well, you can do it in many different ways. For instance, you can arrange the Cartesian system of coordinates. This will be some kind of a x, y point. We will make an increment dx and dy, have a little square here, and then integrate by x and y from minus infinity to plus infinity by x and from minus infinity to plus infinity by y. Yes, we can do that, but there is a kind of a better, a little bit simpler approach. And here is what I'm suggesting actually to do. Let me just forget about this piece and this piece. We will do it slightly differently. Okay, this is my base of the perpendicular. What I'm going to do right now is I will introduce, instead of Cartesian system of coordinates, I will introduce cylindrical one. Now, this will be the z-axis, okay? And on the plane, I will use the polar system. Let's consider, for instance, this is an x direction, whatever it is. So any point here will be characterized by angle and radius. Now, I will do a little bit even more in this particular case.  I will use a ring. So the ring will have inner radius r, and outer radius r plus differential of r. So it's a very, very thin, infinitely thin ring. So it's very thin here. And obviously the whole plane is very thin as far as, as far as thin as in this direction, okay, infinitely thin. So what I would like to say that it's basically chosen for a purpose, this ring, y. For a very simple reason, because if you will take any small piece of it, it will have a certain amount of electricity and intensity vector would be directed from this piece toward this point p. Or this direction doesn't really matter. But anyway, it's along this line. So the length of this line is exactly the same for all pieces around this ring, right? Because it's the same radius. Here or here. So it's all right triangles with the common catatose, which is the distance from r to all. And the second catatose is the lower case r. So all these pieces will have exactly the same distance and the same angle here, which means that if they are all of the same area, infinitesimally small area, then the vertical component of the intensity vector will be exactly the same for all of these points. So when I will integrate them around the whole circle, the whole ring actually, they will basically be very simple result of this integration. I just have to take the whole area of this ring multiplied by sigma, which is the density of the electricity to get the amount of electricity. And knowing the amount of electricity, I will just use this formula for intensity, which we have learned before. So q would be the amount of electricity here. r would be the distance from any point on this ring to this point p. k is Coulomb's constant. And since the angle is exactly the same for all of them, I will just have to multiply by sine of this angle to get the vertical component. Okay, so how can we do it? Now this is actually a very simple thing. So the area of the ring is, well I have to take the area of a circle surrounded by r plus dr radius and subtract the area of a circle of the r radius, right? So it's pi r plus dr square minus pi r square, which is equal to pi r square plus 2 pi r dr plus dr pi dr square and minus pi r square. Now pi r square goes out. Now look at this. This is an infinitesimal variable of a higher order than this one. See, this is dr and this is dr square. And as we know from mathematics, whenever we will integrate, this will be a component which will be integrated and this will add an infinitesimal patch to the integration because we're integrating only once. So I can definitely get rid of this as well and say that my ring area is, area of the ring is 2 pi r times dr. Which is kind of obvious because 2 pi r is a circumference and dr is the thickness of this ring. And if dr is infinitesimally small, then the fact that it's curved instead of stretched doesn't really matter. The difference will be infinitesimals of higher order. So I have the area. If I have the area, I have the amount of electricity by multiplying by q. So my differential q at the radius r. Now why I'm using differential? Well, because the whole thing is infinitesimally small. It's differential only for this ring. It's 2 pi sigma r dr. Okay, now what's the distance from p to any point on this ring? Well, let's just take the distance from p to the plane alpha as h and then my r would be equal to the radius square. r square would be equal to radius square plus h square, right? This is the Pythagorean theorem. Okay, I've got that. And so my dE of r equals 2. This is my intensity according to this formula. It's the k times k times 2 pi k sigma r dr divided by square root distance which is r square plus h square, right? Now, I would like to know not just the intensity but the vertical component of the intensity because the horizontal components will all be canceling each other. However, only the vertical components will be calculated in the same direction, so I can just add them up. So instead of vector addition, because these are all vectors differently directed, I can't really add them up. But if I will represent each vector as sum of horizontal and vertical component, all horizontal will be wiping out each other but the vertical components will be adding to each other. Okay, so I have to multiply by sine of this angle, right? Sine of paO. So my vertical component which I will use ez as a suffix z. It's along the z coordinate. As a function of r, it will be equal to 2 pi k sigma r dr divided by r square plus h square. And I have to multiply by sine of this angle. What is the sine of this angle? It's h divided by the lengths. Now, we know this length. It's this one. Well, actually, it's the square root of this one. So I have to multiply it by h divided by the square root of r square plus h square. Okay, let me write it down slightly differently. 2 pi k sigma. These are all constants, right? h is also constant. What's not constant is r dr. r. dr I will put at the end. And this one is r square plus h square to the power of minus 3 second times dr. Right? Square root is power of 1 half. This is power of 1. So it's 1 and 1 half would be 3 seconds because it's in the denominator. And I will not use the denominator here. Everything will be in numerator. So this is my final amount of intensity vector, magnitude of vertical component of intensity vector of one ring. So the whole ring contributes that much to the magnitude of the entire intensity of the plane. Now, what I have to do is I have to integrate it for all the rings, obviously, concentric to each other. So which means I have to integrate it from 0 to intensity by r. Right? So it would be 2 pi k sigma h. And what I have here is r times r square plus h square to the power of minus 3 second dr. So this is basically the answer. This is the magnitude of the entire vector produced, entire intensity vector produced by the plane. Okay, so let's concentrate on doing something about this integral. Now it's, as we are saying, it's a pure technicality. That's why you have to know math before actually attempting any kind of a serious calculations in physics. So let me do it in two steps. I can do it in one step, but I can really prefer to do it in two steps. You see, I don't like that this is r square plus h square. I prefer to have something like 1 plus x square to some power which is more palatable from the integration standpoint. So what I will do is I will introduce a new variable called r divided by h. Now, what happens here now is my r would be equal to xh. So my integral, if r is from 0 to infinity, x also will be from 0 to infinity. Now my dr is equal to obviously h dx. I'm just differentiating, x is a variable, h is a constant. So differentiating just multiplier will be outside. Okay, in terms of x, the whole thing would look like this. But the integral also from 0 to infinity by x now. And I have this unpleasant multiplier in front of it. Which is 2 pi k sigma h.  And here I will have x square h square plus h square to the power of minus 3 second. I replaced r with xh. And dr would be h dx, right? Now that's equal to, obviously h square would be outside. So it's 2 pi k sigma h integral 0 to infinity xh. Now it would be h square times x square plus 1 and all of this in the power of minus 3 second, right? dx, no h, one more h, sorry. Well I can put h square here, or h square here. Actually I can put h cube. Okay, I put all h's together. Now equals to dx equals to 2 pi k sigma h cube integral from 0 to infinity x times. So h square times minus, to the power of minus 3 second would be what? H to the power of 2 times minus 3 second, right? Powers are multiplied. n times x square plus 1 minus 3 second dx. Now what is 2 times minus 3 second would be minus 3. And this is the plus 3, which means, and this is something which is again for me was absolutely remarkable. Look at this again. There is no h anymore. Let's take a graph from 0 to infinity x, x square plus 1 minus 3 second dx. There is no h here. So this is something which I think is the whole purpose of this lecture. What does it mean that there is no h in this formula? It means that the intensity of the field does not depend on the distance of the point to the plane. So no matter how far from the plane you are, intensity of the electric field will be exactly the same. This is a remarkable stuff. I mean, intensity, intuitively you feel that the further you are from the source of electricity, the weaker should be the field. So the forces should be weaker. But in this particular case, it looks like no matter how far we are from this infinite plane, the intensity of the force will be exactly the same. Well, why? Because it's an infinite plane. You see, it's infinite and all these infinite tails on all the sides are combining together, are making this intensity independent of the height. No matter how high you are above the plane, it will still reach you with the same strength. Strange, but the fact is the fact. Now, how can we find out what this particular integral x relative to x is? Well, that's kind of simple. Now the best thing is to say that we will have y is equal to x square, right? What does it mean? We have 2x dx would be dy, right? dy equals 2x dx. So the whole thing is equal to 2 pi k sigma. Now x is from 0 to infinity and that's why y will also be from 0 to infinity. Now we are using this 2 already, 2 and x. So we will have y square plus 1 to the power of minus 3 seconds dy. Now I'm sorry, not y square plus 1, y plus 1. x square is y, 2x dx is dy, right? So I have this. Now let me make it a little simpler. I will put x plus x minus 1, right? Then a plus 1 second, y is equal x square plus 1, plus 1. dy will be exactly the same thing, but now instead of y plus 1 I will have y here. But now integration should be not from 0 to infinity but from 1 to infinity, right? If x is equal to 0, y is equal to 1. If x goes to infinity, y goes to infinity. Now 2x dx is my dy and x square plus 1 is just y. Now this is just a plain power function and we can very easily integrate it. So what's the integral of this? You can wipe out this. Now you know that y to the power of n derivative is n y to the power n minus 1, right? You know that. That's the derivative from the power function. So if I will integrate, indefinite integral of y to the power of minus 1 dy, it will be equal to y to the n divided by n, right? Plus constant which we don't care about because we are talking about definite integrals. Alright, so my n minus 1 is minus 3 second. So n is equal to minus 3 second plus 1 which is minus 1 second. So this integral is equal to pi k sigma. So indefinite integral would be equal to y to the power of minus 1 second divided by minus 1 second, right? According to this. n is equal to minus 1 second. Okay, and now what should I do with this? I should really put it in limits from 1 to infinity. Okay, first we go to the... Well, let me just write it a little bit differently. Divided by minus 1 half is minus 2 pi k sigma and 1 over square root of y, right? If you don't mind. Now, if you substitute infinity, obviously we will have 0. So this is equal to 0 minus. And now you substitute 1 here. So minus and minus would be plus. Square root of 1 is 1 and this would be just plain 2 pi k sigma. So this is the intensity of the vector of electric field, electrostatic field produced by infinite plane where sigma is density of electricity which signifies how much electricity every unit of area will have. Well, this is the end of the first part of this. Which basically is 99% of the whole lecture. And another 1% is the question, how much work do we need to move any charge from one place above this plane to another? Well, that's obviously very simple thing to do. Look, we do have, this is the plane and I have 2 points. P1 and P2 and I have to take some kind of a charge q from this place to this place. Now, obviously I know this sigma is density. Now, look, this is projections onto this plane. Now, the intensity is exactly the same, here and there. And it's all directed vertically. Which means that my horizontal movement parallel to the plane needs no energy. And the only energy I need when I'm acting, when I'm moving against or along the vector of intensity. Since all vectors of intensity are directed vertically. And so the horizontal is perpendicular to the force. Perpendicular to the force requires no work, right? So only when I'm going along the force, with the force or against the force, I have to spend energy. I have to, my work will be positive or negative depending on the direction. So it's very simple. So first I move this horizontally to be on the same vertical. And then I'm moving along the vertical from whatever the height h1 to height h2. And my force is constant, because as we have seen, it does not depend on the h. So it's just the movement with a constant force, which is this one. From point which has height h1 to height h2. Which means my work would be the force times the distance, right? So the work would be equal to the force, which is 2 pi k sigma. By difference h2 minus h1. Now, obviously there is one more little thing about the direction of this force. We were just talking about magnitude. Direction depends obviously on what kind of charges, what kind of a charge q is. And what kind of a charge is in the plane. If they are of the same, then if h2 is greater than h1, it would be repelling. So it will be one sign of work. If it will be positive or negative, it would be another sign. So it all depends. So let's not talk about signs. Sign is easy, but the magnitude of the work is this one. And that basically completes this particular lecture. This is, as I was saying, 1% of the whole thing. Okay, I do suggest you to read the notes for this lecture. They are maybe in a little bit more detail than whatever I was just talking. And it's just a good reading anyway. It's like a textbook, as was probably every other lecture. So that's it. Thanks very much and good luck.


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