The Mathematical Life of Florence Nightingale

foreign the story of Florence Nightingale has gone down in Legend the lady with the lamp the ministering Angel of the Crimea she was already an idol in her own lifetime but a hundred years after her work in the Crimean War children were still reading books like this one which I had as a child the ladybird book of Florence Nightingale with the story of the lady with the lamp Who as a child had made hospitals for her dolls and then grew up to revolutionize nursing and reform public health and change the world so such stories are you know all very well as far as they go and they are true but they for me miss the most important question which is how did she manage to bring about those changes how did she do it and the answer is she did it with data with Statistics and particularly with the Innovative use of statistical diagrams like this one which probably the most famous of her statistical charts that tell a story in such a compelling way that it's impossible not to get the message and it's impossible not to act so today I want to explore with you the mathematical life of Florence Nightingale what she did how she did it how it fits in with the story of statistics and statistical diagrams um that goes through the 18th and 19th centuries to the present day and how her message about data is still relevant to us today and along the way we'll be counting all the animals in the zoo we'll be weighing a mountain and we'll be sabotaging the economy of France sorry France nothing I can do about it but to begin with who was Florence Nightingale well she was born on May the 12th 1820 to a wealthy family she had an older sister and they were both named for the city of their birth so Florence in Italy and her older sister was born in Naples now Naples isn't particularly a pretty name for a girl so instead they chose the ancient Greek name for Naples parthenapy so those are the two sisters and they were both very intelligent articulate girls Florence from the beginning love data loved numbers this is a picture of her as a young woman with the best pet in the world she had a pet owl which I love her for already and this picture was drawn by her Paul fenerby her sister now we've got some letters from from The Young Florence as a child that show her love of numbers and data right from the beginning and these are Charming things so one of the top I've put I've typed the words so she writes to her Grandmama the baby's pretty God not interested in the baby what she's interested in is listing every single animal how many there were when she went to the Zoological Society so she went to the zoo and she is saying I've got you know all of these things three of those four of these um the llamas get categorized into a brown one a white one and a small brown one and all of these other things so she's listening and she's remembered how many she saw and that is information to her that is important enough to tell grandma about the one underneath which very neat handwriting for Florence well done but she's writing to her older sister and she's saying we are sorting out the Larder and she's got a table of data in this letter she's sorted into vegetables and fruits she is categorizing the vegetables uh she's got little ones in that category goes potatoes and then long ones cucumbers go in that category and then peas they go into kind of dainties so okay maybe not an entirely professional taxonomy but the point is she's doing this because she's interested to sort things out put them into order and categorize her data so as she got older what what's Florence Nightingale going to do with her life well the expectation for a young lady of her social class and standing was you marry you have a family you you reign in the domestic sphere but she didn't want to do that she wanted to go beyond that and she decided she wanted to be a nurse her parents disproved because nursing was not considered an appropriate activity it wasn't a profession you know a young lady of her class would not typically become a nurse and they were against it but as we'll see in the course of this lecture when Florence Nightingale decided she wants to do something it quite often happens so she became a nurse and by 1853 we find her as superintendent of a nurse full of a hospital for gentle women in Harley Street in London but it was what happened soon after that the Crimean War that really was a pivotal point in her life so the war in the Crimea which was between Russia and then an alliance including the Turkish Empire the Ottoman Empire and Britain and France was perhaps the first conflict where reporting from the front line could get to the home countries and appear in the newspapers and actually cause changes in policy so reports came back and and there were newspaper reports of the awful appalling conditions Four soldiers at the military hospitals in the Crimea and this is a picture of one of them um you see Florence Nightingale in the middle there the lady with the lamp at scutari which was kind of the worst of these hospitals in terms of conditions um so when reports got back every you know that the conditions are awful loads and loads of soldiers are dying in these hospitals something had to be done there was pressure because of these newspaper reports on the government to do something to act quickly now Florence Nightingale happened to be a friend of the Secretary of War at that time Sydney Herbert and almost like their letters crossed almost she wrote to him saying let me go out there I can help and he wrote to her saying please will you go out there you can help so that's what happened she took a group of 38 women with her to the Crimea it was the first time women had been allowed to serve in any kind of official capacity they went out there and indeed things were really really awful beyond anything you know we could imagine I mean when I say that the hospitals were dirty there were rats running under the beds they were almost open sewers there was no drainage there was no sanitation no ventilation there were in the street outside and there were dead dogs and even dead horses that were just left to rot in the streets the conditions were terrible for this Hospital scutari which had about 2 000 soldiers in it usually in that entire hospital they there were no basins for washing and there were only 14 baths so it just was impossible to get clean to stay clean and Florence Nightingale and these 38 women kind of set too straight away to try and do something about this and they pressed for um kind of cleaning up better sanitation in general finally in March 1855 a sanitation committee came out to Crimea and they cleared up you know the problems with the with the drainage they fixed the overflowing sewers right this is how awful it was they've started to fix that and then things improved um it took some time but things improved when she came back from the Crimea uh Nightingale wanted to report on what had happened and what had changed and what had worked and she produced long long detailed reports full of facts data information here is what's happened here is the information here here is the detail but she also produced charts and pictures to illustrate the points that she wanted to make what she had seen from the data what was it telling her and at the time you know it's perhaps not what we might take from it because we all know that hygiene is important and that there are diseases that can be prevented with good hygiene and sanitation at the time this is before the germ theory of disease people didn't necessarily think there's anything we can do about certain kinds of disease you know you get cholera it's bad air oh no it's my asthma's so washing your hands in that situation is not going to help with bad air so the argument that had to be made really for that audience wasn't there's lots of disease they knew that there was lots of disease at home as well it was actually look when we cleaned up things really really improved dramatically so this was the argument she wanted to make and she did it by assembling a lot of data but also then by showing that data in brilliant visualizations so we're going to kind of go through I think the three things that make florist Nightingale a brilliant statistician and we can always have this message in our minds even today when we're thinking about what we do with data what the Florence Nightingale do with it and so there's three things the first thing is you've got to make sure your data is robust you've got to have the right numbers the right information gathered properly and consistently the second thing is when you've got your data you've got to know how to interpret it what do these numbers actually tell us and finally if I've got a message I want to get across what's the best way to do it and Florence Nightingale was brilliant at choosing great images that tell a wonderful story so we're going to look at these three things in turn but to put it in some context I want to just give you a couple of minutes on where statistics was at Florence nightingale's time and just before where do you even get that word statistics so the word statistics does not enter the English language I think until about 1791 with this chat John Sinclair looking very dashing there he wrote a statistical account of Scotland in 1791 he gathered lots of information and he'd written to sort of local worthies all around Scotland how many people are dying what are they dying of how you know what people what are people doing with their lives he wanted to measure the Quantum of Happiness as he put it of the Scottish people which is a lovely phrase I don't know what the answer came out as hopefully it's it's constantly improving but he was the first one to use the word statistics I believe in in English but earlier there was a word in German statistic spelled with a K that kind of means the science of the state and that gives a clue to its early use it's it's numbers and data to do with the state with the people living there with the money with the income outgoings exports Imports births and debts that kind of number and it was called in England beforehand a political arithmetic which is another interesting phrase um then you start to get this phrase vital statistics and this is things like what's our population what are people you know who's been born who's dying uh marriages things like this it was not state that was being routinely collected the first census in uh England and Wales was 1801 of course there's been the concept of a census goes back thousands of years I mean you know it's there in the Bible and and everywhere else but there was the official census in England Wales began in 1801 and has been running every 10 years since then there was opposition even to doing this census even to knowing what our population is because people said well what if the population turns out to be less than we've been telling people and then our enemies will be encouraged and think we're weaker than we are as a nation and so maybe they'll invade so this was felt by some to be a risky thing even to know your population happily those people did not win the argument and so we had the census but it wasn't until 1836 that there started to be a national record of even births and deaths um before them there were Parish records and things like this but it was sort of all over the country there was not a single place where this data could be gathered and so you know if you don't have the data you can't do anything so it was through the work of statisticians like William Farr who also worked with Florence Nightingale quite a bit uh that these kind of numbers started to even exist and we we knew them then over in France a sort of a same-ish kind of time you start to get moral statistics so here's a picture from a book by Andre Michelle Gary which came out in 1833 and this was the moral statistics of France so this had things like crime rates divorce illegitimacy and the one I've got here is um education so the literacy rates and and he's got kind of a chart of France divided into regions and he shaded them in according to the literacy rates in that particular region so these then kind of it's moving slightly beyond the sheer number of people you have and looking at qualities about about the population crime rates and things another thing that happened was that people like Adolf ketale here who was a Belgian astronomer statistician and sociologist started to get interested in characteristics of perhaps you know the human body so average heights average weights I came up with this concept of the average man and he also gave us which we may or may not be grateful for um what's now called the body mass index that your doctor will tell you off about uh for being too high or too low so we don't know how we feel about ketley preps um but this idea of averages then is coming from Sciences like astronomy where it's quite natural to take an average of several readings perhaps to then if you take the average you hope to get a more accurate answer because you're trying to eliminate random errors when uh people started to talk about averages in terms of figures like crime rates or deaths or uh even you know what people's body composition this was greeted again with suspicion and concern people really worried about these numbers that you're associating these moral statistics that you are so associating to a population how can you say that there is a you know a particular murder rate that you know is going to happen this year based on previous data this worried people and it was a topic of Fairly General discussion so you get um authors of the day engaging with these questions like Charles Dickens he was very worried by this he said if the number of people are killed so far this year is below the annual average he says is it not Dreadful it's a thing that before the last day of the year some 40 or 50 persons must be killed and killed they will be I think you should have picture this thing right you look you you and you the numbers are down a bit this year come with me so you know he was genuinely worried about and this sort of tension between individual choices made by millions of people versus what these tyrannical numbers are trying to tell us and make us do so he has a sort of Suspicion of data um someone who I think was much better at mathematics than Charles Dickens uh George Eliot had a completely different View and so this is this is a quote from uh her novel Daniel durander but I think it probably reflects her own feelings about data which is that they are not our enemy they can be our friend so she says it's no more wonder that quantities should remain the same then that qualities should remain the same for in relation to society numbers are qualities so the number of drunkards is equality in society it tells you something about the society the numbers are an index to the qualities and give us no instructions so it's you know they know they don't force our hands to behave in a particular way but they set us to consider the causes of the difference between social States and that's the key thing and that's the sort of thing that Florence Nightingale was doing if you spot that you know in this place uh mortality rates are higher than they are in this place that tells you it's not an immutable fact of life God has not decreed that so many people each year are going to die of typhus maybe there's something we can do about it and that's where the power of statistics and data can come in so I mentioned three things that frogs Nightingale did the first one or three qualities of her thinking the first is about are we measuring the right thing are we are we getting the right numbers getting good data and she several instances that we can look at where she would see data that was being presented or numbers that were being presented and they it was the wrong number to think about and I'll give you an example of this so uh I'm paraphrasing here but when she she was campaigning for the professionalization of nursing she wanted nurses to be trained and indeed that started to happen and there were training schools for nurses but some people who did not like changes to the status quo thought only doctors to be in charge of nurses shouldn't be doing anything um said wait a minute we've looked at the mortality rates um for patients uh being looked after by trained nurses and it turns out more people are dying as a higher mortality rate under the trained nurses then under the untrained ones so clearly training nurse is a terrible idea so again here's my paraphrase Florence Nightingale might reply to this and she did she engaged with this people genuinely said this and her response was uh you idiot she didn't say that in very polite Victorian way she said okay no this is wrong the quest the problem with this kind of thinking is you are not comparing like with like the underlying populations are not the same because who do you think we're going to give the sickest patients to to look after some confident they're incredibly ill do you give them to the one who is an expert and a trained nurse or do you give them to the you know the the untrained the the inexperienced nurse of course you're going to give the sickest patients the ones who need the most expert okay you're going to give those to the care of the nurses with the most experience in training so what that means is you're not comparing the the the less trained on untrained nurses are getting given a healthier population on average and so you know of course even if the trained nurses are improving outcomes considerably you might still expect that a higher proportion of those very sick patients might die so you do not have you cannot make that conclusion because you've got different populations that you're considering you're not comparing like with like so this kind of thing um you know nowadays when when we're doing medical statistics if you're comparing say the performances of surgeons of course we know this if you're looking at a heart surgeon who's doing very risky operations we do not expect them to have the same survival rates as someone who's doing routine tonsillectomies or something so we know this in medical statistics but they're all still unfortunately the the the age of the idiot is not over um and it can have severe important implications for policy like really important implications I'll give you an example uh in October 2020 the then prime minister was reported in newspapers that he'd he'd sent this WhatsApp message right and he was you know this is thousands of dying right and he's sending this flippant little thing about oh I've been rocked by the fatalities because um the median age of death is 82 and 81 for men 85 for women and that's above life expectancy so you live longer if you get covered right okay I've reduced the blood pressure so if Let's Pretend Florence Nightingale on this WhatsApp conversation what's she gonna say to this she might say something like you idiot you're not looking at the right numbers here right this life expectancy that he's talking about that's at Birth so if let's suppose that the men do have a life expectancy of 81 let's say um that would mean that half of the male babies born couldn't expect to live to 81 or over and half will die before then but if you make it to 81 then by definition you have not died you haven't you know died an accident or of a childhood disease you have made it to that point and so at that point your median life expectancy is not 81 like we don't all drop dead on the day of our 81st birthday your life expectancy is more than that right because you've made it that far so at 81 a man at 81 has a life expectancy of 89 and a woman at 85 has a life expectancy you know on average of 92. so it's actually been calculated or estimated that every death from covid um caused lost 10 years of life for that person so yeah what Boris Johnson said you know flippant and and wrong but it did affect the policy at the time because they've genuinely thought oh it's only the people who are just about to die anyway who died that affected their decision-making processes and to you know to do bad with bad results another thing that France Nightingale was really hot on was about consistency of data and um how often data was reported so this next uh fact again at the first glance it might not seem to be anything wrong with it so she was looking at information data from a particular Hospital actually noticed they were looking like sort of listing the patients in the hospital and what was wrong with them once a week so that's sort of taking a weekly snapshot now that might seem like okay fair enough you know that will give you a rough idea of what's Happening the problem with this is slightly more subtle and a good explanation of it or a similar issue um is illustrated by this you might have seen it's quite a popular meme that you see online periodically this picture will be shown so this picture is um based on in the second world war they were kind of looking at when planes had gone out on missions when they came back where had they been damaged so all these little blobs Mark damage to the to the plane and so there are various hot spots you can see so then the question is well what do we do with this information you know should we reinforce those parts of the plane these are where the most damage is happening what do we do and the really key observation here is to say okay what are we measuring what are we looking at here what is our sample so we're looking at the planes that have come back from missions and wait a minute we're looking at the planes that have come back from missions which come back we are not looking at the planes that have not come back why haven't they come back because the damage to them was so significant that they did not return so if this diagram tells us anything it tells us where it's okay to be hit you know and you'll still be all right so this diagram almost tells us the opposite of what it looks like at first glance now um something a little bit like that is happening with the once a week census it feels like just a you know a snapshot that will give you the general picture but there are two groups of patients who are going to be up underrepresented in in a weekly snapshot the one group is they basically find they've stubbed their toe you know they go away again after a few hours they're underrepresented in a weekly snapshot the other one at the Other Extreme is the very very sick patients who only live a day or two and so those ones that there'll be some of both of those groups in the in the you know Tuesday count but they will be underrepresented compared to the ones who are staying for a long time and so you're not getting a random sample of the data there okay so here are some of the ways in which we we can perhaps get the wrong numbers and get the wrong information and promised Nightingale was really really good at spotting those accidental errors once you've got numbers you have to interpret them so here's another thing that she was really great at and the others perhaps were less great at so here is I don't want to say A pompous ass that might be a bit mean but Brigadier General Lord William paulit writes to his boss from scutari in the you know the middle of the worst bit of the Crimean War and he has he's delighted to say how marvelous everything is um everything is progressing under my command is progressing as favorably as I could wish sickness is very much diminished so has mortality in January the number of death was this March in February it's going down everything's amazing I'm amazing give me another medal so let's let's paraphrase Florence nightingale's reaction to that you idiots um so here's what's happening yes the absolute numbers of deaths have decreased but that tells you absolutely nothing if you don't know how many people there were in the army or in the hospital at that time so what happened here from January to February um the number of deaths yes had come down in absolute terms but the number of patients had dropped even faster than that so mortality rates had actually increased they were increasing under the watch of this guy and he didn't even know like he probably genuinely oh good everything's great um but no mortality rates were increasing things were getting worse so and she you know spotted that so you cannot you cannot make this conclusion we don't know what the mortality rates are from this data we need we need to we cannot interpret it in the way you say and this is a kind of thing that I I call a what's the denominator problem we don't know what the mortality rate is from this information and you again you see this quite often and if you've got your Florence Nightingale like lenses on you can spot this kind of mistake in newspaper headlines there's two particular kinds of headline that we see that have similar kind of issues so this is the kind of headline a a new sport that you've never heard of and apparently everyone's now doing it and you read underwater darts is Britain's fastest growing sport now what that usually means is that Bob has invented underwater darts and is very excited about it so there's one player of underwater darts and then Bob gets his two friends to also become underwater adults players so now the headline can truthfully but misleadingly say numbers have tripled of underwater dance players and when you see that kind of headline almost always what it means is this is an extremely small sport played by heart anybody it's the only way numbers can triple so that's one example the other one is slightly slightly more kind of important sort of headline but we regularly see headlines the effect of some food is going to kill you bacon has been a recent one that's going to kill us all uh why will bacon kill us well there is an underlying nugget of Truth here there have been studies that shown that if you eat two rashes of bacon every single day for your whole life that your underlying risk of getting uh bowel cancer at some point increases by 18 percent and it's but the thing is it's your relative risk so the question is compared to what what's the actual overall risk of getting this this kind of cancer and the Baseline risk of getting bowel cancer at some point in your life is about six percent currently so this 18 rise it doesn't mean if you eat bacon every day that's going to be 24 it's a relative rise so it rises by 18 of 6 percent so what this and what this really means what the report uh the scientific data tells us currently seems to be that the increase of risk uh is it goes up to about seven percent if you eat bacon every single day so that's not nothing there is an increase but it's not you know the kind of headlines we see where every food is either going to kill us or curious of all diseases those are really not very helpful because they if we know that information we can then decide for ourselves are we can we cope with that risk maybe if we think okay I don't want to increase from six percent seven percent okay maybe you have a bacon roll once a week and not every single day but we with the data we can make an informed decision but the kind of oh 18 oh dear that's less helpful and it no to contextualize it smoking increases your risk of getting lung cancer by a factor of 2 000 not 18 2 000 you're 20 times more likely so you know smoking really will kill you bacon probably won't you see yeah that's absolutely good news um okay so so we've got our data we've made sure it's robust we've made sure we are interpreting the data um correctly the final piece in the puzzle is showing our conclusions to the world communicating that information in a compelling way and that is done quite often best through Visual uh means so I want to I'll show you some of Florence nightingale's brilliant data visualizations but I just want to give you a few instances historical instances and my favorite bits of data visualization um and the first one is to do with this guy Charles Hutton so he was a mathematician and in 1774 he went to this mountain uh ski halian in Scotland in perthshire and they were on a mission to measure they wanted to know the mass of the world they wanted to weigh planet Earth now we don't have scales big enough to do that so what do we how can we find the mass of planet Earth well we can find the volume of planet Earth because it's essentially a sphere we know the formula for the volume of a sphere a bit you know you can make it a bit more accurate but we could estimate the volume of the Earth so if you know density um density times volume equals mass so you can find the mass of the planet Earth if you know its volume which we do and if you know its density which we didn't know so how do you find the density well what you can do is you can take a little bit of planet Earth a mountain for example and you can find its density so that was the plan so how do you find the density of a mountain well you can find the mass and divide by the volume simple only we don't know either of those things so then what do you do well for the mass well they chose this mountain very carefully because it's not kind of in a in a mountain range it's sort of on its own in a relatively flat area so what they did was they took pendulums up to Scotland and if there's kind of if you're in a big flat expanse the gravity that pulls the pendulum down will go to the Center of the Earth and so it will hang vertically down if you've got a big mountain here and nothing much here then the pendulum will be just slightly deviated from vertical by the mass of this mountain that's pulling you know that has a gravitational traction and you can measure that deviation and with some calculations you can work out the mass of the mountain that is causing that tiny amount of deviation so they did that and they got the mass now they need the volume needs where Charles Hutton comes in so he decide the way to the way to find the volume of this mountain was to essentially imagine it is lots of slices and we're going to find the volume of each slice and then add them all up so what about all these slices so he walked all the way around the mountain lots of times and he took lots of measurements of of the heights at various points so that he got all these slices and when he wanted to get a visual for for these slices what he did was to have all these points that he had and he joined with lines the places of the same height and thus Contour lights now content wasn't the first time that a child had been drawn with uh joining things of the same value for some for some quantity but these we think are the first contour lines and you instantly it's such a great idea because we can instantly look at you know an Ordinance survey map or a kind of map with contour lines we know we can see instinctively you know the places where the lines are very close together that's the Steep bits once when the land is increasing in height most quickly so we can we can visualize from this map you can get a really good instant idea of the Topography of the landscape so that's a really great little idea that is instantly you can see fantastic way to visualize all that data about the different heights of the different pieces of land uh we get onto kind of what we might think of as common statistical charts they start to come in the end of the 18th century the start of the 19th century um and one of the key people in this story is a chat called William Playfair and this is a diagram from his commercial and political Atlas uh 1786 where he assembled loads and loads of data about kind of the economy Imports exports all these kind of things here is a bar chart so it's it's not the first bar chart ever drawn but it's an early bar chart and again you can see it's a really good way of representing the deity can instantly see look these guys have a lot of we're doing a lot of trade with the ones at the bottom and and you can see there's a huge trade deficit uh with with Ireland here you can just instantly see that in a way that a table of figures is not necessarily showing you but play fair was quite Innovative in his in his design so this is just an example but my favorite bar chart of his is this 1821 chart where he's measuring something we quite often to talk about now it's got this bar chart and over time and so the bars are representing the price of wheat and it's going up a lot so you might think oh no life's really hard wheat's really expensive but what he does this is quite Innovative he's got a line the red line that he's drawn which is also curving up points that's measuring the wages the weekly wages of a good mechanic says here so a sort of skilled worker and those are rising as well and they are rising faster than the price of Wheat and at the time he his graph finishes wheat prices have come down and the wages are still covered on going up so his mate wants to make the point here that wheat has never been more affordable this is like a discussion um of affordability really and that would be the next step you could combine these things but he's got these both these things on the same graph but what I like here is the explanatory text that he includes he feels the need to include this shows that people were not comfortable with charts like this yet because he has to say geometrical measurement right I know geometrical measurement has not any relation to money or time money and time are not spatial things but it's still okay to to represent them in terms of a picture so he's sort of trying to justify it's all right to do this we're making them represent making spatial things represent money and time and of course nowadays we don't we don't need to justify that we're all okay with it but this was the early days so one kind of chart that Playfair does seem to have invented um is the pie chart so here are two early well circular charts and what's interesting to me is so what's this is 1801 the one on the right this is uh proportions of the Turkish Empire that are in various uh consonants so you can see the typical slices of pie that we all know Africa Europe Asia so that's like a typical pie chart what I like here is that the conventions are not yet set right so this early examples when you're looking at Russia so this one Russia has some of Russia within Europe some is in Asia he hasn't got slices here he's got concentric circles now we don't tend to do that now with pie chart but this is this is the very early examples we're still deciding how we're going to play this one so yeah play for included these kind of diagrams and again it really helps you to see visually the information that's being presented this is quite innovative um now play fair things like pie charts and the statistical diagrams that he was using didn't catch on in England as quickly as they did in France one reason for that was that Playfair was a bit of a uh a wide boy I don't know he had some scandals uh there was some get rich quick schemes he may have been embroiled in various things he did spend some time in prison uh it wasn't a great look and so people may perhaps have uh not jumped to adopt his really brilliant ideas um as quickly as they may have done but in France where you know he hadn't I don't think he was in prison in front maybe they so they didn't were less aware of maybe the slight uh issues that in England he spent a lot of time in France he took part in the storming of the Bastille you know he was doing all the right things um the French may not it's possible it is his you can see there's some diagrams uh from a French book charminar in 1858 lots of lots of pie charts they may not have been quite so keen on Playfair had they known that he was uh spying for England and that he had had an idea which he executed to destabilize the French economy by faking loads and loads of French banknotes and then introducing them into the currency in order to make the real banknotes be worthless and this actually he did this and it worked and they had to abandon those kind of banknotes so he'd if the French had known that they may not have been so keen on the old pie charts um they nicknamed them Camembert by the way not pie charts in France for obvious reasons um but anyway they did catch on in France it took a longer while for them to get to England we'll get back to England um one one final since we've got a map here I want to show you another map that's a real Triumph of data visualization before we talk about Florence Nightingale some more um this one this is a very famous picture this was drawn by Jon Snow right at the same time as the Crimean War actually 1850s um and this is a map of Cholera cases in a particular area in London in SoHo and each of those little black lines represents a cholera case and he noticed that they were clustered around um sort of drawn this red dot here they were clustered around a particular point and that point was a water pump Broad Street water pump and he he this kind of gave uh evidence to his idea that cholera is not spread by bad air or in other things it's spread by polluted water and so they actually took off the handle of that water pump so that it couldn't be used and cholera cases came right down so this this drawing showing these these color cases it shows you immediately there's a cluster and that visualization is very powerful okay so let's talk about what Florence Nightingale did so we've established she didn't invent pie charts that's a myth about Florence Nightingale what did she do so here's this the picture that I showed you at the beginning I'm going to talk us through it this is the diagram of the causes of mortality in the Army in the East so in the Crimean War the Army uh is is out there it's fighting and there are lots and lots of deaths um the blue regions are showing the deaths from what we now know are preventable diseases and this was the case she was making we can prevent these diseases um what we've got here is a circular diagram and it's going through clockwise the months so every kind of wedge is is a month and that's a good choice of diagram because we're quite used to looking at time in the form of a circle you know every well it's a clock it's a circle divided into 12. so this is the months of the year so it starts in April 1854 and it got nothing much happened in the first three months the fighting kind of started um but then we go around and we get various deaths from from various causes and then on the left that's year two so that sort of dotted line leads us to April 1855 and then we go around again and we can see so the detail of this will will explain in a moment but that's the basic idea so let's talk through what she actually is putting in this diagram what's the information in there so as a just a toy example um you we know that we cannot just look at death in absolute numbers we have to look at mortality rates otherwise we otherwise we don't know if we're just seeing fewer patients in the hospital because they've already all been killed or whether it's a real Improvement in in treatment so the kind of let's imagine this is a sample month of the data she was gathering so for each month she she looked at What's the total size of the army at that point because that's very relevant let's say it's 40 000 at that point so in this month let's say so there are three categories she had so either you people dying from their wounds in fighting all of diseases which are actually preventable like like your choleras or typhus that kind of thing or everything else so you know if you have a heart attack not much they could do about that at the time so let's say 400 are dying from from wounds um 800 from preventable diseases and 200 from other causes so then she works out the mortality rate per thousand men so in the army of 40 000 if 400 dying in that month from wounds that's a mortality rate of 10 for every thousand men and the others similarly and then she worked out this annualized number so if that if that money if 10 people are dying per thousand in the single month then over the course of the whole year multiplied by 12 and you get 120 deaths per thousand men from in this case wounds so that's the the data then how do you plot that on your on your polar diagram so polar there's a pole in the middle and you're radiating out from it so you draw these wedges so so for each month that's one twelfth of the circle and you PL you're drawing a wedge for each of these numbers and the area of the wedge is proportional to the number you're representing so the area if you've got a circle of radius uh R the area of one of these twelfths of the circle will be pi r squared over 12. so that area is what you want to be proportional to the number okay so for that 120 there's your 120 deaths from wounds that's colored in uh shaded in red on her diagrams so then how are we going to get what what's the radius we want for the preventable deaths well we want to double the area so um the area depends on the square of the radius so instead of doubling the radius which will give us four times the area we want to multiply it by the square root of two so that's the kind of the shape we're going to get and imagine that the blue goes all the way to the center so we're looking at the total area not just the way we can see but the total and then for the other causes um well that's 60 so that's again half of the red area this time we divide by the square root of 2 and we get something like this now you might say uh this is a bit uh a bit extreme Sarah because look you're preventable diseases as 240 of every thousand Men You're these figures are a bit you know silly in this toy example because that would imply that like a quarter of the army would die every year from preventable diseases well the silliness of it is actually because it was way way way worse than that way worse so example the worst month January 1855 85 in that single month the mortality rate from preventable diseases was 85 in every thousand men which over the course of the year would actually correspond to 1023 for every a thousand would die preventable diseases which sounds ridiculous but that was that was you know if nothing was done right so luckily something was done but you could have something like that every month because of course you don't it's not necessarily the same the army of 40 000 is not the same 40 000 men you replace you replace and you bring in new people so you could you could have that and you know this this is true it's not a mistake in the figures um so these terrible terrible death rates and this is what's plotted on the diagram we can see there's January 1855 just an appalling number of people appalling mortality rate I should say of of these diseases so what happens between grav Circle one and circle two right at the end of March 1855 the sanitation commission arrives and they start cleaning up the sewers and fixing the drainage and sorting things out and from that you can see straight away there starts to be an improvement and by the time you get around to the the next year you know the blue areas which is preventable diseases have shrunk away so much that you couldn't barely see them so this is a huge success story but what Florence Nightingale needed to get across to people was this is the result of that cleanup operation so we know there are diseases diseases are always with us but we can change um we can change the outcomes we can change the mortality rate it's not just God's will that so many of these people will die so this was an incredibly powerful and successful diagram that made the case for sanitation reform not just in military hospitals not just in public hospitals but actually um in in society more generally so she pressed for um kind of Acts of Parliament that would require proper drainage um in in cities so that so that we can you know with this cleaning up places you can reduce these diseases um so I have to say she did not invent this kind of diagram she'd not invent polar area diagrams but let me show you what I think is the first kind of polar area diagram drawn so we mentioned this chap uh Andre Michelle Gary earlier with his moral statistics of France this was from an earlier publication of his 1829 and mostly it was about meteorology so these maybe the first polar area diagrams uh that appeared in print now they I mean they're all right yes he gets the credit for for perhaps being the first but they don't they're not sending a message they're not telling us a story in the way that Florence nightingale's pictures were um so the top ones are about the proportion of the time that the wind was blowing in a particular direction at a particular time of year okay and the bottom ones are about um numbers of people dying at particular times of day when that first question would be what's happening at midday and midnight these are particularly auspicious times or was that just the shift change at the hospital we all know if you're in any office until 8 PM or 8 A.M nothing happens for an hour so maybe this is that maybe this is just telling us when the shifts changes at French hospitals in 1829 I don't know but these diagrams they um they are not telling they're not a call to action in the way that France Nightingales were and they so I think her charts you know she's put them to amazingly good use I want to in the last few minutes give you just a few more examples of diagrams and charts that Florence Nightingale used and again she she didn't just no not all her diagrams of polar area down she wasn't a one-trick pony she would choose the right diagram for the right situation and get her message across so let's have a look so this one this is very strong diagram so this is what she called it batwing diagram um and you can literally see the shadow of death on this diagram it's very powerful imagery it's the same more or less the same kind of information that she was giving in the polar area graph here it's the annual rate of mortality per thousand but kind of from all uh causes and we can see it going around the circle so this at this time it looks slightly different because um she is the distance from the center so the radius how far out she's gone it's that that's proportional to the the number she's representing so it's now not areas it's kind of lengths distance from the center and so what she's done is she's plotted a point for each month and then she's joined them up to sort of a circular graph and you can really see very very vividly just the horror of this time period um with the number with the mortality rate that she's got there and on the left year two again you can see it's coming down almost feels like almost to nothing and indeed the worst month at scutari the mortality rate was 41 in that hospital I mean it's just unbelievable and by the time by the by the end it was down to two percent which is just an amazing transformation um in the middle there the small circle that you can see that is representing mortality in Manchester kind of a you know a a not a beacon of of Health right at that time it was a it was an industrial town there was lots of disease in poverty but you know even then the mortality rate was Tiny compared so that was one of the things she did she was very hot on looking at comparing mortality in the army with what's actually happening in you know the civilian population because surely the Army is supposed to be full of kind of fit healthy young men they should not be dying of preventable diseases more than than the general population so this next diagram this will appeal to you know the Victorian Patriot what have you got here says lines representing relative mortality of the army at home and the English male population so she is comparing as much as she can like with like men in the army of the same age look at the top one age 20 to 25 men who are in the Army and uh men who are soldiers and they're not even at War this is the Army at home so they're in their Barracks at home they're not fighting battles and you can see so it goes Englishmen and then English soldiers all the way down and so the line for the Englishman of that same age it's half as long right the the English soldiers and surely deliberate to have the English soldiers Be A Thin Red Line right it goes in with that kind of iconography the patriotism you're supposed to look at this and be appalled that the English Soldier The Thin Red Line you know they are dying even when they're at home this is shocking and this was a call to action and the action did indeed happen um why might this be the case so we've talked about sanitation overcrowding is also inimical to health and to show this and it's really brilliant diagram so these are kind of honeycomb diagrams hexagons showing how much space each person has in particular uh situations so I'll just zoom in on the right hand side of this so on the far left you've got how much space each Soldier has kind of amount of yards per person in an in an army encampment at home they're not at War this is at home then in the middle you've got the most dense District in England which is in East London where I live that feels about right and then and then on the right just London uh in general so the average for London you can see look at so much space that the londoners have on average compared to the soldiers and even compared to the most densely occupied you know poorest urban areas and so this is clear thing can really clearly see this with this clever choice this inspired choice of a honeycomb showing with hexagons how much space you have and of course yeah those guys are not going to be as healthy as these guys uh another so here's a little one that's almost like a tribute to her friend Sydney Herbert so here we've got three uh bars so the total area of of the rectangles in each case is the total uh deaths annually per 100 living from all causes and then it's divided up into what the causes are so the one at the top is the English male population so these are the best comparators to soldiers age 15 to 45. and you can see you know what various things dying of zymotic diseases these are the preventable diseases that we're talking about the next one is this is how Lord Herbert found the Army it's awful um twice as you know the mortality rate is twice as high for these preventable diseases and all other things can contribute to a large mortality rate and again I emphasize these are infantries serving at home they're not this is not them being killed in action they're serving at home but they are dying of these uh diseases that are preventable and then the bottom one is this is how Lord Herbert left the army so you know with with the input of improvements which campaign for by her and others working with statisticians like William Farr and then Sydney Herbert puts those things into action and you can see the huge huge Improvement um kind of after by the end of his tenure so Florence Nightingale her contributions she knew how to tell to argue for good data she spotted when the data wasn't good and argued for it to be improved she knew how to interpret that information and draw the correct conclusions of the the right conclusions valid conclusions and her particular genius showing those conclusions in diagrams that were so compelling that you could not ignore the conclusions and she she really believed this is a religious Duty you've got to make things better and how do you do it to understand God's thoughts we must study statistics for these are the measure of his purpose and she continued campaigning for the whole of her life for not only for improvements in nursing but for improvements in sanitation in hospitals and outside of hospitals her work was instrumental it saved thousands and thousands of lives and the legislation that was introduced following kind of kind of her campaigns around Public Health transformed life expectancies in the UK she was actually bed bound for most of her later life but she's still the picture of her she's got a rug on her she's sitting in a chair but she's got her correspondence she continued campaigning writing letters um right you know through her life she died in 1910 in August 1910 um she was the first woman fellow of the royal statistical Society she was the first woman to be awarded the order of Merit and as I say you know an icon in her lifetime and Beyond it um she's the second of three figures that I've been talking about in this part of the my series of Gresham lectures of unexpected mathematical lives so last time you can go and check this out online if you want I talked about Christopher Wren architect but also mathematician we've now talked about Florence Nightingale nurse but also mathematician so my next uh next month who I'm going to talk about well Alan Turing okay mathematician but also mathematician so we think of Alan Turing we think when we remember him we mostly think about his pioneering work in the mathematics of cryptography and early Computing but he also did pioneering research and thinking about mathematical biology so it's that thing I'm going to talk about next time on June the 6th and I hope to see you then thank you very much foreign [Applause] thank you so much Professor Hart I've got a couple of questions from online and then perhaps we can go to the room um first question is um who invented the bar chart so okay so I did have a picture from William Playfair up there in his uh in his political Atlas And I said it wasn't the first bar chart now there's some there's some discussion speculation about this you quite online you will often find it claimed that player Fair invented the bar chart and the pie chart but I don't think he did so there's some very very early things that look maybe look a bit like bar charts but I don't think they are um dating back a few hundred years but I think there is a good case for a particular um book that had a graph or a bar chart it looks like a bar chart to me of it's water levels in the sen so in Paris water levels the river high water mark low watermark over the course of the year and the bar chart covered kind of 30 years worth of data and I think that precedes what Playfair did by maybe a decade or so so there's a contender there but I would be delighted if anyone would be able to come up with an earlier bar chart so that's your homework if you want to attack it and a very quick follow-up on what's your favorite bar chart oh well how does one choose it's like choosing your favorite child I mean I do I do like play first one that I showed because it's giving this information but it's also superimposing this this graph and I think that was the first time I think that you get this time series sort of situation where you're following these two variables so I think that's that's got to be a contender how did Florence Nightingale acquire her mathematical and statistical education right yes great question so she she had some kind of education from her father who taught her a little bit about both both politics and some mathematics and statistics she also had a tutor and there's some speculation that that may have been a mathematician called Sylvester if I remember rightly um she I don't think this person necessarily taught her mathematics but she was friends with Ada Lovelace when they were children so you know who knows I would love to know what they talked about whether they did any exciting mathematical thinking together um but so she she picked things up a little bit along the way but then she did work as well with statisticians so I mentioned William Farr and there were others with whom she worked when she was putting together these these big lengthy reports so she wasn't absolutely isolated doing this stuff um but you know her see the impetus was was hers to communicate these things and actually William Farr I think it was I said to her at some point you know this this stuff is to statistics should be dry as dry as possible he said you know because it's sort of just the facts ma'am kind of thing you don't want to color it with any kind of you know emotions but that wasn't what she was trying to do you know she was saying we've got to get this information across so she was against it being dry thankfully for us yeah um Professor Hart think he's such a fascinating lecturer I'm sorry I don't even have time for any more questions today but thank you very much and don't forget to come to her next lecture um on the 6th of June [Applause]

Channel: Gresham College

Views: 3,680

Keywords: Gresham, Gresham College, Education, Lecture, Public, London, Debate, Academia, Knowledge, mathematics, florence nightingale, statistics, crimean war, zoology, military, scutari, data, statistik, political arithmetic, John Sinclair, census, Guerry, Quetelet, Charles Dickens, Daniel Deronda, George Eliot, Lord William Paulet, Lord Panmure, William Playfair, Charles Minard, polar area diagram

Id: Jyjv-dAYBjQ

Length: 59min 49sec (3589 seconds)

Published: Thu May 25 2023