Babbage: The language of the universe
When it comes to the COVID. Nineteen a modeling. It can be a little bit confusing. You have likely heard the phrase flatten the curve used. When talking about reducing number of grown a virus cases the horizontal line is the key one whether health systems have the capacity to cope with the numbers of infections. Nineteen pandemic has dominated every part of life since the beginning of the year. Some countries have done better than others. That holding back a disease but everyone has used the same tool to guide their response. Mathematics science correspond detail economist Mats. And I go a long way back a very long time ago. I was a physicist. Mathematics was the language of the world's that I used to explode. Today's baggage from economists. Radio looks at how mathematics can reuse to tackle some of life's most pressing problems. Predicting Pandemics guided health policy to spotting bias in politics. I'll also speak to physicist grandfather about the way mathematics reveals the true nature of the very building blocks. If you're the sort of person who has very raw interests I think mathematics is something for you. I think that's often forgotten like people. Think of mathematics is a very narrow subject. That's David Sumter. A professor of applied mathematics at Uppsala University in Sweden. He's also data scientists for football club in Stockholm goodies. Coming book the Ten equations that ruled the world. And how you can use them to. David lays out how a small set of mathematical formula could help. Everyone make better decisions about their lives if you learn some basic mathematical skills if you learn the ten equations you can go around applying these things to all different types of problems and get involved in in lots of interesting projects. And that's how I sort of ended up working directly with players inside a football club. Now which is just an incredible thing for somebody who can't kick a ball to end up doing but That's the sort of possibilities. You have as a mathematician. Okay so give me an example. The one that interested me was. How do I get rich? That's actually why it started with the book because I'm the type of applied mathematician who loves to apply things. So as I've mentioned I work with the football club but I've also been interested in how gamblers work and how they make money. The first equation in the book is called vetting equation and the idea is you want to find biases in the odds. I think a lot of people when they get into gambling. They think Oh. I know this team's GonNa win. I really think this team's going to win and it's not about that at all. What about is finding where the odds are in your favor so the first thing to do is you plot the odds. You compare this to the betting equation and you can see way. You have an edge. And that's what professional gamblers do. They didn't think about if they're going to win. Any particular maps. They don't even watch football matches they bet on or watch the Horse Races. They look for biases in the odds. Where all of the rest of us have made a mistake and they can win these equations that you talk about in the way that she come from. I mean essentially there. If I understand correctly that formulas for statistics in Peru ability in some sense they actually come from the last two hundred and fifty years of mathematical development. An in the book I outlined my theory actually about how this is kind of a secret society living amongst US and these secret society they publish openly. How you solve this. How you win money betting for example how you can have confidence in your decisions and to give you an example. The Algorithm now that Youtube use in order to decide. What video to show you next. They increase the amount of people watching youtube video all the time watching Youtube video by twenty times and this made an incredible amount of money for Youtube and it was basically three guys applying a minimization mathematical algorithms. So they were just doing differentiation. Something you learn. In opposite country school they were just doing differentiation to find a minimum and then they could solve this problem and they could get us all addicted to youtube so this society is kind of living amongst US solving these problems and making a lot of money along the way. Okay so we've got a situation where mathematics is used in many facets of life from gambling to youtube algorithms to become models. What is it about mathematics that allows us to access and manipulate the world? In this way thing the main thing is that it simplifies problems. There's just no way of getting round the if you can use this you can sort of get shortcuts to answering questions. You can get edges in anything and probably sciences. The is the one that is most useful for so. I don't think mathematics is fundamental in science in the sense that the science is written in the language of mathematics. But I do think it's fundamental as a tool. If you didn't have mathematics it would be like not being able to write. Things actually wouldn't be able to be not being able to write a text or not been able to take. Videos of things is an essential tool to understanding science. Mathematics weren't just held. Make you richer more successful. It also has a key influence on the policy. The shapes our lives mathematics drive the computer models. For example that scientists have been using to understand how covid nineteen is spreading and how different interventions such as lockdowns and social distancing might slow that. Spread down what you can use mathematics for is to describe the processes that are driving epidemiology. Crystal Donnelly is an epidemiologist. She works at the University of Oxford and Imperial College London so in the case of infectious disease. That's people coming into contact with each other so you have some people who are infectious and they come into contact with some people who are susceptible and then you can have transmission. So what are the ways that you can reduce that we could show this by equations? What sort of reduction you'd get. Will you can vaccinate the susceptible people so that their immune and they never even got the disease or you can reduce contacts. And that's what we've been forced to do in this setting with covid. Nineteen is reduced the rate at which the infectious people can come into contact with susceptible. People calculations in these models are playing a huge role in decisions by governments on how to implement monitor and eventually ease the drastic lockdowns across the world. Here's a member of the American government's. Coronavirus VIRUS TASKFORCE DOCKED. Deborah books. I just want to thank the five or six international and domestic model ours. Who helped US tremendously? It was their models that created the ability to see with these mitigations could do how steeply they could depress the curve book how to these. Models Work Crystal Donnelly again epidemiological modelling in the sense of transmission modeling. So that's sometimes those are called dynamical model because you're writing down equations to describe the dynamics the processes that happened underneath that that's what's often referred to now when people are talking about modeling and that allows you to answer quantitatively what might happen now. That's still what might happen based on a set of assumptions. But would I really like about that sort of modeling is that you can write them down and by writing them down you allow yourself not just to help think through the process and make sure that you've done it logically but it allows other people to see you're working so you talk about building these models with assumptions? What kind of assumptions? My you have which leads me onto will. How accurate can these models actually be? They have assumptions about how we mix for example so the simplest model is a random mixing model where you assume that whatever population you're modeling people are equally likely to come into contact with each other any two people now. That's clearly not going to be the case. Even in a household you have a household of size five. You don't randomly mixed with those five people because some of them be adult. Some will be kids so even on that scale. It's not absolutely true. And it certainly not the case that even in a village or small city that people randomly encounter each other. You will have places that you tend to go and you will see a lot of the same people even when we don't count work where of course most people see the same group of colleagues a lot of the time it will always be the case that there's more complexity than can be included in any one dynamical model but that doesn't mean that models can't be useful and that's where we have to focus. The question is an are they absolutely right in the Senate have. They described every single bit of the process. That's going on but have they explained the key processes the ones that are driving most of the behavior so that we can. What's happened so far and make useful predictions on what might happen under certain conditions and those can inform decisions. They won't say these are the individuals are going to be infected but they made a good job of predicting on average how many people might get infected within the model each of these variables you talk about is represented mathematically as part of equation. Not Right. What's actually? The computation is going on within the models. So we talk about in the simple case sl our model so we divide people into three types s is for susceptible is infected and infectious and ours for recovered and so everybody in a population can be divided into one of those three types and then we can write down equations for how the numbers of susceptible 's infected and recovered changes over time. Now not only. Does that often assume that those individuals are randomly mixing and whatever scale? We're talking about. But also that every one of those susceptible people is equally susceptible and every one of those infectious people is equally infectious. That's not going to be absolutely true. There will be very ation. We're all different. But it's trying to get the average behavior right and understand enough of the variability to give you something useful out at the end you worked on many infectious disease outbreaks Saws Bowler to name a few do each of these different models or can you start using the same models with different tweaks go alone. Oh there are some things that are fundamental when you look at it directly transmitted disease for example so respiratory disease goes directly from person to person if you're looking at Zeka That's different because it goes from person to mosquito to person and so then you're in a very different regime completely and as we've gone on over the years we've made tools available. One of them for example is called. Epi estim- and that's for epidemiological estimation and that uses a case data. So that's the number of cases or the number of deaths observed per day and uses that data to estimate this reproduction number over time. Now that can be used in lots of different settings and we've used it in several different diseases but for a lot of the models that particular questions and the particular aspects of transmission will be such that even if we have starting blocks that we need to adapt and tune them to the particular situation. Matic's is not only useful for setting policy but because it's an objective tool it can also be useful for settling parties anticipates in America. Scientists are using mass to help with what has become a divisive political issue gerrymandering. This is the practice of manipulating the boundaries. Around congressional in such a way as to create unfair advantages for one political side. You have so many did analytic about who the people are where they are vote. Whether they're likely to vote that you can draw designer districts to get an outcome you might prefer moon do chin is a mathematician from Tufts University in Boston Massachusetts. Her work involves using mathematical models to identify areas. Where gerrymandering taken place? So sometimes people say that. Democrats people of color pack themselves into cities and because they're so dense in the cities. They tend to be concentrated in a few districts with very high proportions. And since we have first past the post voting. In each of these districts it's really to your disadvantage to have extremely high percentages. If what you need fifty percent plus one vote and what you have is ninety percent we could think about that as as vote wasting and what you can see is how the clustering of various kinds of demographic groups or party preferences how does that clustering lead district to divide up the population when you're not trying to extract extra advantage so something that my group does and several. Other teams of mathematicians have started to do to great effect. I think is map sampling. So I'm going to now get an algorithm to draw not ten not a hundred but maybe thousands or millions of maps at random just according to the stated rules and by construction those algorithms are just taking into account what they've been told to take into account that's how computers work for better and worse and then we can see if all the summary statistics that you can observe from districts are they huge out liars among a comparative batch of maps that were made without seeking advantage. Moon hopes that this map sampling can lead to something a bit more reasonable. I'm working pretty hard with different collaborators to take some of these ideas from the math space into the policy space. But what might that look like? Maybe you have a state and it has a certain suite of rules and criteria that are stated what you might imagine is that the line drives propose him up an analyst compares it to neutral draws that use the same rules and says you know you're doing a better job of these criteria than those and that's the thing when you're doing complicated problem like this typically there will be trade-offs if you WANNA get better at not splitting counties. Maybe you'll get a little worse at population balance and so on with an eye to that. What model or sometimes called Pareto frontier? That is sort of. What are the maps that do well on some measures and that aren't dominated by other maps? That are better. In all the measures I envisioned actually. The potential for collaboration between quantitative analysts. And the line drawers that can iterating towards a better fairer maps want is any of his matter so you can have states and we do where the vote between the major parties is about half and half but there's dominance by one party in the seats and that definitely Piques People's intuitions of unfairness feels. It feels wrong and one consequence of that is reduced trust in the system. Maybe decreased likelihood to vote decreased engagement more cynicism so sometimes that disproportionate that you observe will be the result of Gerrymandering. No question one thing that I hope for these tools is that they can restore faith in the system by showing you by measuring the consequences of political geography in order to show you what a expected reasonable outcome that just has to do with communities where they lie and what on the other hand is agenda driven line dry so I think you know in a lot of cases you might find that the effects of self interested line drawing aren't as great as you thought and in other cases like some of the cases I've been involved with finding just as great as he thought and that even though the playing field may be tilted one way or the other. The line drawing goes even farther than that so. I think being able to pull those apart. That's a big advantage of the math modeling coming up after the break. How MASS CAN HELP? Ac- The truth not only about a world but about the entire universe. Come back to badge. Mathematics plays an important role in understanding shaping everyday life science though the connections. Go even deeper. It was Isaac Newton who gave us the idea that physics as we now call. It is about setting out law's written in mathematical terms that make predictions you check. It against experiment don't work. You have to go back to the drawing board and pretty what everyone knows that. That's the way physicists. Work Grandfather is physicist and author in his most recent book. The universe speaks in numbers. Graham explores how mathmatics has helped physicists to rethink key ideas such as gravity space and even time Einstein was one of the people started this and he wrote near the end of his life that the miracle declared to his friends was that we can understand the universe because it is fundamentally ordered. And it's that older that enabled US understand through mathematical patterns. Feinstein was working at the start of the twentieth century in the past Hundred Years. Though the love affair between physics and mathematics has only become stronger. What's really new? I think is that we're in a very unusual situation at the frontiers of physics. Because there's very little exciting new data coming through safe from the large Hadron collider about the goings on inside atoms but theory so having to do their work despite that. I'm what is turning out. He's that physicists. By looking at their theories a driven tools exactly the same territory as Pew. Let's get back to Weinstein for obviously use mathematics to do most of his work because he didn't do it. He experiments so wooded mathematics allow him to discover just using paper and a pencil. Okay well Einstein is a great case when he was in his twenties and he had he did that fantastic work on timothy where he gave was a new understanding of space and time he really did believe. I was quite aggressive about it. That physicist only need old fashioned mathematics. They did back in the stuff that you learn in your basic classes and anything more than that indulgence as he a pure luxury. That's the word he used. And he believed that until nineteen twelve at it was then he was developing his new theory of gravity and he found. He couldn't do that without mathematics that was in effect unknown to him and Gals and remote and people like this good again. Not Having I thought about gravity had set out the perfect tools for Einstein to import into his theory of gravity. That you mathematicians actually. They did both actually but yes. They were mainly mathematicians and that's what convinced Einstein. The advanced mathematics was something that he other needed. And so the idea is then. Einstein comes up with those that you need an advanced mathematics. Pops aren't necessarily related to physics ideas but then kind of in discover new physics. It's sort of flowers really isn't doesn't take us through those sorts of heady years of multiple Nobel Prize winning scientists. How long have you go? We just Stein? He events arguably his great piece of work at the twenty sixth grade using which was that new theory of gravity based on that new mathematics. Shortly after that came the most revolution redevelopment in science the whole of signs in the twentieth century which was quantum mechanics. The theory of motion on atomic scale turned out to be if you like a complete break or so it seemed from the theory of motion that Newton dot hundreds of years before a gain. Those pioneers found that they had to use new mathematics that it only being out in some cases you know five ten years and this mathematics was what you needed to look matter on the microscopic scale. Now the real puzzle and it's still there as we speak. This puzzle is still here. You have to great theories. You have the classical theory of relativity of gravity and you have quantum mechanics. Gravity has its own mathematics and quantum mechanics is actually rather different. The mathematics look very different. And also it's got probabilities in it. Which Einstein abominated in the sense that he really believed that you should we had to predict. Is Paul Wrist? He's not that they've randomness in nature which called mechanic says areas now the big challenge for physics and said it's endured right to this day. It's still problem is how to jam those theories together to get something that will enable us to understand all of nature of the general-level to the the mathematician if I can say of physics has achieved great things and will continue to do so but is mathematics always real. Mathematician comes up with ideas for some new mathematics. Is it always the case? That's going to be something physical. Most of the really top notch appeal mathematicians. Don't give a tinkers cuss about physics right. They do it because they are working in wizardry. Eight hardy on patterns of ideas that interests them just for the sake of it right. They are not thinking. What does this got to do with nature? The key thing is. We're now finding that the two frontiers of overlapping even mathematicians who deal with stuff that looks to be completely irrelevant to anything to do with. The real world is actually relevant to the real world and by the same token physicists when they look at your colts and you glue on his side every atom in your body and everywhere else right you look at those subjects deeply enough and you'll take it into the world of mathematics that cross either has pushed scientists fat opening up new avenues discovery. The biggest milch cow so to speak at this field is being string. Theory string theory basically says instead of thinking of things like electrons and photons or what have you point particles rather there's an elementary string and the mental particles exi- -tations of that so called string very very short pieces of string in space time that subject as consistent with quantum mechanics and relativity. That's the first thing to say. And the reason why people love that theory you have so much facing it to quote the Great Edward Witten. Who is the of that field that subject showed why gravity must exist? You're Georgia drop. When you hear that. Gravity is just brought in right. It must exist as a result of relativity and quantum mechanics. Absolutely amazing thing. Now if you look at that theory which is has to be said is very difficult to test an issue very very high energies but in the expiration of its consequences we find ourselves take into all sorts of things to do with combinations of Algebra geometry things to do with curvature fields many many subjects that mathematicians are looking for their own reasons but the physicists need in order to discuss how those strings could make up the real world so the mathematical physics is just way ahead of the experimental right now a mighty conversations with people doing these things sometimes say they might take hundreds of years to develop the technology to test the things that are coming out now because mathematics. You don't need anything more than a paper and Pencil. Ibm Software on these things. But what did you think is sees the big promise? The mathematics has for visits. We've talked about how it can really shoot Ford and you think about different things and CD investor friendly. What kinds of promise is there in the future for this? Then physics is GonNa have to get used to long periods when we won't be teeming with experimental results because they're getting more and more expensive to produce from the telescopes from the expensive collider's they'll be these gaps. We have to fill now because I think mathematics see so thick on the field it will enable us to do creative work wall there those gaps. That's what I suggest in the epilogues on my book so I think mathematics is proving its worth and value even when we haven't got the experimental input. Matic's not only lets us see the future physics unseen parts of a unit as we'd had it describes the hidden Hatton's around and gives us the ability to control and predict. That's all for this episode of Bob. Thanks coach David. Sometimes Crystal Donnelly Moon Do Chin and grandfather for more great stories about science and technology subscribe to the economist comments dot com slash radio to get twelve issues. The twelve dollars. Twelve pounds jaw and in London. This is the congress.