Gresham College Lectures

The Mathematical Life of Florence Nightingale

May 25, 2023 Gresham College
Gresham College Lectures
The Mathematical Life of Florence Nightingale
Show Notes Transcript

Florence Nightingale is the founder of modern nursing and a pioneer of data science and medical statistics. Her innovative use of statistical diagrams helped people see just how many deaths were being caused by poor hygiene in military hospitals.

This lecture will look at the importance and legacy of Nightingale’s work, which led to her becoming, in 1858, the first woman elected to the Royal Statistical Society.

A lecture by Sarah Hart recorded on 16 May 2023 at David Game College, London.

The transcript and downloadable versions of the lecture are available from the Gresham College website:

Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation:


Support the show

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, um, 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 is 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 will be weighing a mountain and will 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, uh, 1820 to a wealthy family. Uh, 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 Pathe. So those were the two sisters, and they were both very intelligent, articulate girls. Florence from the beginning, loved data, loved numbers. Uh, this is a picture of her as a young woman, um, 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 enemy, her, 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 on the top, I've, I've put, uh, I've typed the words. So she writes to her grandma, ma, 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's 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 listing 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. Um, which very neat handwriting for Florence. Well done. But she's writing to her older sister, um, and she's saying that 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's categorizing the vegetables. Uh, she's got little ones in that categorized potatoes, and then long ones, cucumbers go in that category. And then peas, they go into kind of dainty. So, okay, maybe not an entirely professional taxonomy, but the point is, she's doing this cause she's interested to sort things out, put them into order, categorize her data. So as she got older, what was Florence Knight l 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, uh, typically become a nurse, and they were against it. But as we'll see in the course of this lecture, um, when Florence Nightingale decides she wants to do something, it quite often happens. So she became a nurse, and, uh, by 1853, we find her a superintendent of a nurse for, uh, of a hospital for gentle women, uh, 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, uh, the Turkish Empire, the Ottoman Empire, uh, and Britain and France was perhaps the first conflict where reporting from the frontline 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 for soldiers at the military, hospitals in the crime Crimea. And this is a picture, uh, of one of them. Um, you see Florence Nightingale in the middle there, the lady with the lamp at Scutari, which is 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, uh, 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. There were almost open sewers. There was no drainage, there was no sanitation, no ventilation. Um, there were, you know, 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, uh, for this hospital's Qatari, which had about 2000 soldiers in it. Uh, usually in that entire hospital, uh, there were no basins for washing, and there were only 14 baths. So it just was impossible to get clean and to stay clean. And Florence Nightingale and these, uh, 38 women kind of set two straightaway 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 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, it's perhaps, uh, 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 was 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, or you know, it's my asthmas. So washing your hands in that situation is not gonna 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 are gonna kind of go through, I think, the three things that make Florence Nightingale a brilliant statistician. Uh, and we, we can always have this message in our minds, even today when we are thinking about what we do with data, what will 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 France Nager was brilliant at choosing great images that tell a wonderful story. So we're gonna 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, uh, at Florence Nightingale's time, and, and just before, where do you even get that word? Statistics? So the, the word statistics does not enter the English language, I think until about 1791. Um, with this chap, John Sinclair looking very dashing there. He wrote a statistical account of Scotland in, uh, 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, uh, you know, what are 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. Uh, I don't know what the answer came out as, <laugh>, hopefully it's, it's constantly improving. Um, 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, smoke with a K, uh, 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 deaths, that kind of, uh, number. And it was called an England beforehand, uh, political arithmetic to that interesting phrase. Um, then you start to get this phrase, vital statistics. And this is things like, what's our population? Uh, what are, what are pe you know, who's been born, who's, 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 to thousands of years. I mean, you know, it's there in the Bible and, and everywhere else. But there was a, the official census in England, Wales began in 1801 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 are weaker than we are as a nation. And so maybe they'll, 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 then, 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 that we, we, we knew them then over, uh, in France, uh, it's sort of the same-ish kind of time you start to get moral statistics. So here's a picture from a book by, uh, Andre Michelle Garley, which came out in 1833. And this was the moral statistics of France. So this had things like crime rates, divorce, uh, illegitimacy. And the one I've got here is, um, education. So the literacy rates and, and the, he's got kind of a charter of France divided into regions, and he shaded them, yet 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, uh, people like Adolph Kek here, uh, 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. Uh, he 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 <laugh>, uh, for being too high or too low. So we dunno how we feel about keela preps. Um, but this idea of averages, then it's 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, uh, answer because you are 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're asso 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? Uh, 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 to think that before the last day of the year, some 40 or 50 persons must be killed and killed? They will be, I think you just pictured this thing, right? You look, you, you and you <laugh>, 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 Elliot had a completely different view. And so this is, this is a quote from, uh, her novel Daniel Geronda, but I think it probably reflects her own feelings about data, which is that they are not our enemy, <laugh>, they can be our friend. So she says, it's no more wonder that quantities should remain the same than that. Qualities should remain the same for in relation to society. Numbers are qualities. So the number of drunkards is a quality in society, tells you something about the society. The numbers are an index to the qualities and give us no instruction. So it's, you know, they, 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 gonna 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 Florence Natal 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, there's several instances that, that we can look at where she would see data that was being presented, or numbers that were being presented. And they were, it was the wrong number to think about. And I'll give you an example of this. So, uh, I, 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, uh, changes to the status quo for Tony doctors to be in charge and nurses shouldn't be doing anything. Um, said, wait a minute, we've looked at the mortality rate, um, for patients, uh, being looked after by trained nurses, and it turns out more people are dying the higher mortality rate under the trained nurses than under the untrained ones. So clearly training nurse is a terrible idea. So again, here's, here's my paraphrase of what nce Sni girl might reply to this. And she did. She engaged with this. People genuinely said this, and her response was, uh, you idiot, <laugh>, she didn't say that <laugh> in very polite, Victorian way. She said, okay, no, this is wrong. The, the que 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 gonna give the sickest patients to, to look after some comes in and they're incredibly ill. Do you give them to the one who is an expert, the trained nurse, or do you give them to the, you know, the, the, the untrained, the, the, the inexperienced nurse? Of course, you're gonna give the sickest patients the ones who need the most expert care, you're going to give those to the care of the nurses with the most experienced and training. So what that means is you are not comparing the, the, the less trained 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 the, you cannot make that conclusion because you've got different populations that you're considering. You're not comparing like with a, like, so this kind of thing. Um, you know, nowadays, when, when we are doing medical statistics, if you're comparing, say, the performances of surgeons, of course we know this. If you are 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 there are still, unfortunately, the, 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, uh, about, oh, I've been rocked by the, the fatalities because, um, the median age of of death is 82 and 81 for men, 85 for women. And that's above life expectancy. So you live longer if you get covid, ha ha ha ha ha, right? Okay, <laugh> reduced the blood pressure. So if, let's pretend Florence Knighting earlier on this WhatsApp conversation, what's she gonna say to this? She might say something like, you idiot, you are 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 there's a, the, the men do have, uh, life expectancy of 81, let's say, um, that would mean that half of the male babies born can 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, of a childhood disease. You have made it to that point. And so at that point, your median life expectancy is not 81. But we don't all drop dead on the day of our first birthday. Your life expectancy is more than that, right? Cause 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, this what Boris Johnson said, you know, flippant and and wrong, but it did affect the policy at the time. Cause 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 too, you know, too, too bad with bad results. Another thing that Fran Ingal was really hot on was about consistency of data and, um, how often data was reported. So this next, uh, fact, again, it the first glance, it might not seem to be anything wrong with it. So she was looking at information data from a particular hospital, and she noticed they were looking, 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, 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 this 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, uh, 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 hotspots 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, 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 are looking at the planes that have come back permissions, and wait a minute, we're looking at the planes that have come back from missions, come back, <laugh>, 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, it feels like just a, you know, a snapshot that that will give you the general picture. But there are two groups of patients who are gonna be up underrepresented in a, in a weekly snapshot. The one group is they basically find they've stopped 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 there, 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 are 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, and, uh, Al 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 wanna say a pompous ass, that might be a bit mean <laugh>, but brigadier general, uh, Lord William Paulette writes to his boss from Scutari, um, 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.<laugh>. Um, everything is progressing under my command. It's progressing as favorably as I could wish. Sickness has very much diminished. So has mortality in January, the number of deaths this much 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 idiot, <laugh>. 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 had 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. Um, and he didn't even know, like he probably genuinely like, oh good, everything's great. Um, but no mortality rates were increasing, things were getting worse. So, and she, you know, spotted that said, 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, 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 dart's, 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 darts players. So now the headline can truthfully but misleadingly say, numbers have tripled of underwater adults players. And when you see that kind of headline, almost always what it means is this is an extremely small sport played by hardly anybody <laugh>. 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 gonna kill you. Uh, bacon has been a recent one that's going to kill us all. Uh, why will bacon kill us? Well, there is an underlying negative truth here. There have been studies that shown that if you eat two rashes of bacon every single day for your whole life, the, that your underlying risk of getting uh, bowel cancer at some point increases by 18%. 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, um, the baseline risk of getting, uh, bowel cancer at some point in your life is about 6% currently. So this 18% rise, it doesn't mean if you eat bacon every day, that's gonna be 24%. It's a relative rise. So it rises by 18% of 6%. So what this, what this really means, what the report, uh, the scientific data tells us currently seems to be that the, the increase of risk, uh, is it goes up to about 7%, uh, 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 gonna kill us or cur us 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 6% to 7%. 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 2000. Not 18%, 2000%, but 20 times more likely. So, you know, smoking really will kill you. Bacon probably won't <laugh>. See, that sounds hopefully good news. Um, okay, so, so we've got our data. We've made sure it's robust. We've made sure we, 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 hallion in Scotland, in Persia. And they were on a mission to measure. They wanted to know, um, the, the mass of the world and want it 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 planet earth? Well, we can find the volume of planet earth cause it's essentially a sphere. We know the formula for the volume of the 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, uh, of the planet earth if you know it's volume, which we do. And if you know it's density, which we didn't know. So how do you find the density? What 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, uh, you can find the mass and divide by the volume simple only. We dunno 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, uh, the gravity that pulls the pendulum down will go kind of 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, 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. Here's where Charles Hutton comes in. So here side, the way to, the way to find the volume of this mountain was to essentially imagine it as, uh, lots of slices and we're gonna 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, 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 lines. Now cont wasn't the first time that that a, a chart 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, 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, start of the 19th century. Um, and one of the key people in this story is a chap called William Playfair. And this is a diagram from his commercial and political atlas, uh, 1786, um, where he assembled loads and loads of data about kind of the, 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 this really good way of representing the data you can instantly see. Look, these guys have a lot of, we're doing a lot of trade with the ones at the bottom. Uh, and, and you can see there's a huge trade deficit, uh, with, with Ireland. He, you can just instantly see that in a way that a table of figures is not necessarily showing you. But Playfair was quite innovative in his, in his designs. So this is just, uh, an an example, but my favorite bar chart of his is this 1821 chart where he's measuring something we quite often talk about now. And you've 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 week'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 it's sort of skilled worker and those are rising as well, and they're rising faster than the price of wheat. And at the time he, the, his graph finishes, wheat prices have come down and the wages are still count on going up. So he's, ma wants to make the point here that wheat has never been more affordable. So 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. Cause 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, a picture. So he is 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 play fair 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, continents. So you can see the typical slices of pie that we all know, um, 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 these early examples when he is looking at Russia, so this one, Russia has, some of Russia is in 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 gonna 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, which is quite innovative. Um, now playfair 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 dunno, 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, he 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 France, maybe they, so they didn't, were less aware of maybe the slight, uh, issues that in England he spent lots 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. His, his, you can see there's some diagrams, uh, from French book Sham in 1858. Lots of lots of, uh, 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 bank notes and then introducing them into the currency in order to make the the real bank notes be worthless. And this actually, he did this and it worked and they'd had to abandon those kind of bag notes. So he'd, if the French had known that they may not have <laugh> been so keen on the old pie charts. Um, they nicknamed them Canum bear, 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 wanna show you another map that's a real triumph of data visualization before we talk about Florence knighting some more. Um, this one is a very famous picture. This was drawn by John Snow, right at the same time as the crime Menan war, actually 1850s. Um, and this is a map of cholera cases, uh, 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 drawing this They were clustered around a particular point. And that point was a water pump, broad streete water pump. And he, he this kind of gave, uh, evidence to his idea that cholera is not spread by bad air or 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 horror cases, it shows you immediately there's a cluster and that visualization is very powerful. Okay, so let's talk about what Flo Nightingale did. So we've established she didn't invent pie charts, <laugh>, that's a myth about Flo Nightingale. What did she do? So here's this, the picture that I showed you at the beginning, I'm gonna talk us through it. This is the diagram, um, 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. And what we've got here is a, a circular diagram and it's going through clockwise the month. So every kind of wedge is, is a month. And that's a good choice of diagram because we are quite used to looking at time in the form of a circle. You know, every, what'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 go nothing much happening the first three months, the fighting kind of started, um, then we go round and we get various deaths from, from various causes. And then the left, that's year two. So that sort of dotted line leads us to, uh, April, 1855. And then we go round again and we can see, so the, 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 deaths in absolute numbers. We have to look at mortality rates. Otherwise we, otherwise we don't know if we are just seeing fewer patients in the hospital cause 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. Cause that's obviously very relevant. Let's say it's 40,000 at that point. So in this month, let's say, so there were three categories she had. So either you people dying from their wounds in fighting or of diseases which are actually preventable, like, like your cholera's 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 many of 10 people are dying per thousand in your 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 are radiating out from it. So you draw these wedges. So, so for each month, that's one 12th of the circle. And you plot, 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 of, if, if you've got a circle of radius, uh, ah, 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 gonna 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 full time is the area, we will not multiply it by the square root of two. So that's the kind of the shape we're gonna get. And imagine that the, the blue goes all the way to the center. So we're looking at the total area, not just the bit 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 of two and we get something like this. Now you might say, uh, this is a bit, uh, a bit extreme Sarah, cuz look, your preventable, uh, diseases, it's 240 of every thousand men. You are. These, these figures are a bit, you know, silly in this toy example because that would imply that like a quar 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, 1850 5, 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 1,023 for every a thousand would die preventable diseases, which sounds ridiculous. Uh, 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 no, 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 gra uh, circle one and circle two, right at the end of March, 1855, the sanitation commissioner arrives and they start cleaning up the sewers and flexing the drainage and sorting things out. And from that, you can see straightaway there starts to be an improvement. And by the time you get round 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 Naum 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, in society more generally. So she pressed for, um, kind of act 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 did not invent polar area diagrams. But let me show you what I think is the first kind of polar area diagram drawn. So we ch mentioned this chap, uh, on Jay, Michelle Garry earlier with his, uh, moral statistics of France. This was from an earlier, uh, publication of his 1829. And mostly it was about meteorology. So these may be the first polar area diagrams, uh, that, that appeared in print. Now they, I mean, they're all right, <laugh>, 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 knighting girls's pictures were. Um, so the top ones are about, um, 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. That first question would be, what's happening at midday and midnight, these particularly auspicious times, or is that just the shift change at the hospital?

We all know if you're in any hospital at 8:00 PM or 8:

00 AM 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're not telling, they're, they're not a call to action in the way that Lance 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, you know, not all her diagrams of polar area down, she, she wasn't the 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, uh, diagram. So this is what she called it, a bat wing 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, uh, 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 cause um, she is the, 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 length 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 could see it's coming down almost feels like almost to, 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 2%, 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, 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, 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 the, than the general population. So this next diagram, this will appeal to, you know, the Victorian patriot. What have you got here is lines representing relative mortality of the army at home in the English male population. So she's 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 Englishmen of that same age, uh, it's half as long, right? The, the, the English soldiers and surely deliberate to have the English soldiers be a thin red line, right? Goes in with that kind of iconography, the patriotism, you are 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 that action did indeed happen. Um, why might this be the case? So we talked about sanitation, overcrowding is also inimical to health and to show this and it's really brilliant diagrams. 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, on the right hand side of this. So on the far left you've got, um, how much space. Each soldier has kind of a amount of, uh, yards per person in a, 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 London 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, of a honeycomb showing with hexagons how much space you have. And of course, yeah, those guys are not gonna 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 a hundred 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 they're dying of. Zy, otic, diseases disease, 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 the mortality rate is twice as high for these preventable diseases. And all other things con 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 lots, bottom one is this is how Lord Herbert left the army. So, you know, with, with the input of, uh, improvements which campaign for by her and others working with Ians 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 Flores Nightingale, her contributions. She knew how to, how 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 those, 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 gotta 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, uh, for not only for improvements in nursing, but for improvements in sanitation in hospitals and and outside of hospitals. Her work was instrumental. It saved thousands and thousands of lives. Um, the legislation that was introduced following kind of, kind of her campaigns around public health, um, transformed life expectancies in the uk. She was actually bed bound for most of her later life, but she still has a picture of her. So got a rug on her. She's sitting in her 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, uh, my series of Gresham lectures of unexpected mathematical lives. So last time, you can go and check this out on nine if you want. I talked about Christopher Red Architect, but also mathematician. We've now talked about Florence Nightingale nurse, but also mathematician. So my next, uh, next month who I'm gonna talk about, well, Alan chewing Okay. Mathematician, but also mathematician. So we think of volunteering. 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, that I'm gonna talk about next time on June the sixth. And I hope to see you then. Thank you very much. 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 by bar chart? So, okay, so I did have, uh, 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'll often find it claimed that Player Farian rented 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, well, a bar chart, it looks like a bar chart to me of it's water levels in Theen. So in Paris water levels, the river high watermark, 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 were to be able to come up with an earlier bar chart. So that's your homework, <laugh>, if you want to attack it. Um, and a very quick follow up one, what's your favorite bar Chart? Oh, well, how does one choose? It's like choosing your favorite chart, <laugh>. I mean, I do, I do like play fairs. One that I showed because it's giving this information, but it's also superimposing this, this graph. And I can, that was the first time I think that you get this time series sort of situation where you are following these two variables. So I think that's, that's gotta 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, uh, 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 and whether they did any exciting, methodical 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, her, she, the impetus was, was hers to communicate these things. And actually William Farr, I think it was said to her at some point, you know, this, this stuff is too, statistics should be dry, as dry as possible.<laugh> you 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 <laugh>. Yeah. Um, professor Hart, thank you for such a fascinating lecture. I'm sorry I don't think we have time for any more questions today, but thank you very much. And, uh, don't forget to come to her next lecture, um, on the 6th of June. Thank you.