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BT 70.016 709.153 Td /F1 12.0 Tf [(Published on )] TJ ET
BT 142.724 709.153 Td /F2 12.0 Tf [(Up Close)] TJ ET
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BT 70.016 653.949 Td /F3 24.0 Tf [(#258: The world by numbers: How )] TJ ET
BT 70.016 624.645 Td /F3 24.0 Tf [(mathematics explains objects and )] TJ ET
BT 70.016 595.341 Td /F3 24.0 Tf [(events)] TJ ET
BT 70.016 549.679 Td /F1 12.0 Tf [(VOICEOVER)] TJ ET
BT 70.016 535.027 Td /F1 12.0 Tf [(Welcome to Up Close, the research talk show from the University of Melbourne, )] TJ ET
BT 70.016 520.375 Td /F1 12.0 Tf [(Australia.)] TJ ET
BT 70.016 491.323 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 476.671 Td /F1 12.0 Tf [(I'm Dr Shane Huntington. Thanks for joining us. Mathematical descriptions of )] TJ ET
BT 70.016 462.019 Td /F1 12.0 Tf [(physical and biological processes are often described as elegant. But they are rarely )] TJ ET
BT 70.016 447.367 Td /F1 12.0 Tf [(simple. Often equations that appear quite simple only hold true for very specific )] TJ ET
BT 70.016 432.715 Td /F1 12.0 Tf [(conditions. When we start to introduce the complexities of the real world, more )] TJ ET
BT 70.016 418.063 Td /F1 12.0 Tf [(complex mathematical approaches need to be applied ? approaches that are far )] TJ ET
BT 70.016 403.411 Td /F1 12.0 Tf [(from the equations the likes of Sir Isaac Newton would have been familiar with.Many )] TJ ET
BT 70.016 388.759 Td /F1 12.0 Tf [(of the problems tackled by mathematicians today involve multiple properties, multiple )] TJ ET
BT 70.016 374.107 Td /F1 12.0 Tf [(objects and multiple potential interactions between those objects. In some cases, )] TJ ET
BT 70.016 359.455 Td /F1 12.0 Tf [(subtle changes in approximations made by a mathematician can result in significant )] TJ ET
BT 70.016 344.803 Td /F1 12.0 Tf [(differences in predictions.To describe the approach taken by mathematicians in )] TJ ET
BT 70.016 330.151 Td /F1 12.0 Tf [(solving real world problems, and to explore some of the equations used, we are )] TJ ET
BT 70.016 315.499 Td /F1 12.0 Tf [(joined today on Up Close by Professor Chris Budd, Professor Applied Mathematics )] TJ ET
BT 70.016 300.847 Td /F1 12.0 Tf [(at the University of Bath and Professor of Mathematics at the Royal Institution of )] TJ ET
BT 70.016 286.195 Td /F1 12.0 Tf [(Great Britain. Professor Chris Budd is in Melbourne to speak at the Maths of Planet )] TJ ET
BT 70.016 271.543 Td /F1 12.0 Tf [(Earth Australia Conference, organised by the Australian Mathematical Sciences )] TJ ET
BT 70.016 256.891 Td /F1 12.0 Tf [(Institute along with the Academy of Science and the Australian Research Council. )] TJ ET
BT 70.016 242.239 Td /F1 12.0 Tf [(Welcome to Up Close, Chris.)] TJ ET
BT 70.016 213.187 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 198.535 Td /F1 12.0 Tf [(Hello.)] TJ ET
BT 70.016 169.483 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 154.831 Td /F1 12.0 Tf [(There are many types of equations used by scientists, engineers, economists and )] TJ ET
BT 70.016 140.179 Td /F1 12.0 Tf [(other specialists. Today we're talking about differential equations in particular. Can )] TJ ET
BT 70.016 125.527 Td /F1 12.0 Tf [(you define what these are for us?)] TJ ET
BT 70.016 96.475 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(Yes, a differential equation is a description about how something changes. So, if I )] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(have an object such as the velocity of the wind, for example, then that changes in )] TJ ET
BT 70.016 730.849 Td /F1 12.0 Tf [(time. It also changes from one place to another. What a differential equation does is )] TJ ET
BT 70.016 716.197 Td /F1 12.0 Tf [(it tells you how big the change is.)] TJ ET
BT 70.016 687.145 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 672.493 Td /F1 12.0 Tf [(Chris, there are many different types of equations that people will encounter. How do )] TJ ET
BT 70.016 657.841 Td /F1 12.0 Tf [(differential equations contrast themselves to those other equations we'd find in )] TJ ET
BT 70.016 643.189 Td /F1 12.0 Tf [(various areas of economics, the weather and so forth?)] TJ ET
BT 70.016 614.137 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 599.485 Td /F1 12.0 Tf [(Well, the key thing about a differential equation is it's explaining how something )] TJ ET
BT 70.016 584.833 Td /F1 12.0 Tf [(actually evolves and changes. So, if something is changing, you need a way of )] TJ ET
BT 70.016 570.181 Td /F1 12.0 Tf [(understanding that change and that's what a differential equation does. So it's )] TJ ET
BT 70.016 555.529 Td /F1 12.0 Tf [(different from, say, a quadratic equation which gives an exact description of how )] TJ ET
BT 70.016 540.877 Td /F1 12.0 Tf [(something is at a particular time. It's the change which is important. As change is all )] TJ ET
BT 70.016 526.225 Td /F1 12.0 Tf [(about us and everything we do involves change, this is why differential equations are )] TJ ET
BT 70.016 511.573 Td /F1 12.0 Tf [(so useful in understanding the world.)] TJ ET
BT 70.016 482.521 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 467.869 Td /F1 12.0 Tf [(Now, in physics one of the first problems that we would teach students is how to )] TJ ET
BT 70.016 453.217 Td /F1 12.0 Tf [(calculate an object's position and velocity?)] TJ ET
BT 70.016 424.165 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 409.513 Td /F1 12.0 Tf [(Yes.)] TJ ET
BT 70.016 380.461 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 365.809 Td /F1 12.0 Tf [(?at a particular time. Could you talk us through an example of this? Say, for )] TJ ET
BT 70.016 351.157 Td /F1 12.0 Tf [(example, an object falling in the Earth's atmosphere, how would we go about solving )] TJ ET
BT 70.016 336.505 Td /F1 12.0 Tf [(that problem.)] TJ ET
BT 70.016 307.453 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 292.801 Td /F1 12.0 Tf [(Yes. Well, a good example would be, for example, a rugby ball which you've kicked )] TJ ET
BT 70.016 278.149 Td /F1 12.0 Tf [(and it's moving through space. So its velocity is changing because it's being )] TJ ET
BT 70.016 263.497 Td /F1 12.0 Tf [(accelerated towards the Earth by the force of gravity. That gives you a differential )] TJ ET
BT 70.016 248.845 Td /F1 12.0 Tf [(equation for its vertical velocity. At the same time, the ball is probably moving )] TJ ET
BT 70.016 234.193 Td /F1 12.0 Tf [(horizontally as well. You have a separate differential equation describing that. The )] TJ ET
BT 70.016 219.541 Td /F1 12.0 Tf [(equations take into account a number of things. They take into account gravity but )] TJ ET
BT 70.016 204.889 Td /F1 12.0 Tf [(also the resistance on the rugby ball and maybe other factors such as the spin of the )] TJ ET
BT 70.016 190.237 Td /F1 12.0 Tf [(ball.)] TJ ET
BT 70.016 161.185 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 146.533 Td /F1 12.0 Tf [(Now, there are a number of things happening there that presumably are changing in )] TJ ET
BT 70.016 131.881 Td /F1 12.0 Tf [(time themselves, not only the ball's position but the way in which those other )] TJ ET
BT 70.016 117.229 Td /F1 12.0 Tf [(interactions are occurring on the ball. Do the differential equations take those )] TJ ET
BT 70.016 102.577 Td /F1 12.0 Tf [(changes into account as well?)] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(Well, they do. I mean, when you kick a rugby ball, the first thing that happens is you )] TJ ET
BT 70.016 730.849 Td /F1 12.0 Tf [(apply force to it and give it some initial velocity. As it moves, so its position and )] TJ ET
BT 70.016 716.197 Td /F1 12.0 Tf [(velocity themselves change. Also maybe there's wind blowing across the rugby field )] TJ ET
BT 70.016 701.545 Td /F1 12.0 Tf [(and that will also change and that will interact with the ball itself. So all of these )] TJ ET
BT 70.016 686.893 Td /F1 12.0 Tf [(factors need to be taken into account.)] TJ ET
BT 70.016 657.841 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 643.189 Td /F1 12.0 Tf [(How do we go about solving these particular equations? What sort of answers do )] TJ ET
BT 70.016 628.537 Td /F1 12.0 Tf [(they give us? Do they give us accurate answers or do we have a scenario where we )] TJ ET
BT 70.016 613.885 Td /F1 12.0 Tf [(essentially are getting probabilities?)] TJ ET
BT 70.016 584.833 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 570.181 Td /F1 12.0 Tf [(That's a really good question. It really depends on the system. Perhaps the first )] TJ ET
BT 70.016 555.529 Td /F1 12.0 Tf [(system to be properly understood and described in terms of differential equations )] TJ ET
BT 70.016 540.877 Td /F1 12.0 Tf [(was the motion of the planets around the Sun. In that case, you can write down very )] TJ ET
BT 70.016 526.225 Td /F1 12.0 Tf [(precise equations. In certain cases such as the Earth moving around the sun, you )] TJ ET
BT 70.016 511.573 Td /F1 12.0 Tf [(can solve them exactly in terms of mathematical formulae. Those formulae predict )] TJ ET
BT 70.016 496.921 Td /F1 12.0 Tf [(what you find, which is that the Earth goes around the Sun in an ellipse. Now, that's )] TJ ET
BT 70.016 482.269 Td /F1 12.0 Tf [(kind of unusual. More normally equations for something such as the weather are )] TJ ET
BT 70.016 467.617 Td /F1 12.0 Tf [(much, much more complicated. It's very hard to find an exact solution of them. As )] TJ ET
BT 70.016 452.965 Td /F1 12.0 Tf [(you said, there might even be a sort of probabilistic solution because of all the things )] TJ ET
BT 70.016 438.313 Td /F1 12.0 Tf [(that you don?t know and you have to estimate. What you then do is you put those )] TJ ET
BT 70.016 423.661 Td /F1 12.0 Tf [(equations into a computer and the computer helps you solve them.)] TJ ET
BT 70.016 394.609 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 379.957 Td /F1 12.0 Tf [(Now, I want to dive into this area of finding a solution a bit deeper. You referred to )] TJ ET
BT 70.016 365.305 Td /F1 12.0 Tf [(this a couple of times. Once we have the equation written down, the differential )] TJ ET
BT 70.016 350.653 Td /F1 12.0 Tf [(equation for the object in motion?)] TJ ET
BT 70.016 321.601 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 306.949 Td /F1 12.0 Tf [(Yes.)] TJ ET
BT 70.016 277.897 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 263.245 Td /F1 12.0 Tf [(?is that not the solution? What do we have to do that from point to make this useful?)] TJ ET
BT 70.016 234.193 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 219.541 Td /F1 12.0 Tf [(Well, again, that's a good question. To a physicist, you might say, ?well, I have a )] TJ ET
BT 70.016 204.889 Td /F1 12.0 Tf [(solution,? because the maths is completely describing what's going on. But, at the )] TJ ET
BT 70.016 190.237 Td /F1 12.0 Tf [(same time, you still need to work out what it's going to do. For example, if I had an )] TJ ET
BT 70.016 175.585 Td /F1 12.0 Tf [(equation like X + 2 = 5, I still need to find X. I subtract two from both sides and I find )] TJ ET
BT 70.016 160.933 Td /F1 12.0 Tf [(X = 3. With a differential equation, it's kind of like that. You might have an equation )] TJ ET
BT 70.016 146.281 Td /F1 12.0 Tf [(for some quantity such as X, which might be the position of the rugby ball, but you )] TJ ET
BT 70.016 131.629 Td /F1 12.0 Tf [(still have to kind of untangle that to find the actual solution so you know actually what )] TJ ET
BT 70.016 116.977 Td /F1 12.0 Tf [(it's doing. Really that's kind of hard.The first equations that were written down, which )] TJ ET
BT 70.016 102.325 Td /F1 12.0 Tf [(were the ones that Newton wrote down, he was incredibly lucky actually that he was )] TJ ET
BT 70.016 87.673 Td /F1 12.0 Tf [(looking at a system where the maths of that time could actually find a solution. Most )] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(of the equations that we look at, for even kind of very everyday things, such as the )] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(flow of water, are really too tough to find easy solutions for. This is why a computer is )] TJ ET
BT 70.016 730.849 Td /F1 12.0 Tf [(needed to actually make exact predictions.)] TJ ET
BT 70.016 701.797 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 687.145 Td /F1 12.0 Tf [(When we go into these areas of complexity, presumably there is some value in )] TJ ET
BT 70.016 672.493 Td /F1 12.0 Tf [(knowing what all the dependencies are to write down that first equation. Can we get )] TJ ET
BT 70.016 657.841 Td /F1 12.0 Tf [(much from that or do we have to solve the equation before it's of use?)] TJ ET
BT 70.016 628.789 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 614.137 Td /F1 12.0 Tf [(It's very important if you have lots of parameters in the system, for example, the )] TJ ET
BT 70.016 599.485 Td /F1 12.0 Tf [(temperature or the wind blowing on the ball, to know how that affects the actual )] TJ ET
BT 70.016 584.833 Td /F1 12.0 Tf [(behaviour. A lot of mathematics gives you answers to how things depend on these )] TJ ET
BT 70.016 570.181 Td /F1 12.0 Tf [(quantities even if you can't solve it exactly. One example would be the drag on a )] TJ ET
BT 70.016 555.529 Td /F1 12.0 Tf [(rugby ball is known to be proportional to the square of its speed. That gives you a lot )] TJ ET
BT 70.016 540.877 Td /F1 12.0 Tf [(of insight into how it then moves.)] TJ ET
BT 70.016 511.825 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 497.173 Td /F1 12.0 Tf [(Now, you mentioned some of these complex systems. How complex do these )] TJ ET
BT 70.016 482.521 Td /F1 12.0 Tf [(equations themselves get? How easy are they to solve? We start teaching students )] TJ ET
BT 70.016 467.869 Td /F1 12.0 Tf [(to solve these equations in late high school, first years of university. Are these the )] TJ ET
BT 70.016 453.217 Td /F1 12.0 Tf [(sorts of equations that students at that point would be able to solve or are they well )] TJ ET
BT 70.016 438.565 Td /F1 12.0 Tf [(beyond that?)] TJ ET
BT 70.016 409.513 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 394.861 Td /F1 12.0 Tf [(Well, let's give two examples. Going back to the example of the Earth going around )] TJ ET
BT 70.016 380.209 Td /F1 12.0 Tf [(the sun, you have two equations which completely describe it, an equation for its )] TJ ET
BT 70.016 365.557 Td /F1 12.0 Tf [(position and an equation for its velocity. Those two equations can be solved exactly )] TJ ET
BT 70.016 350.905 Td /F1 12.0 Tf [(and they can be solved by a high school student. They are solved by high school )] TJ ET
BT 70.016 336.253 Td /F1 12.0 Tf [(students. If you take something like the weather, in contrast, you have, we reckon, )] TJ ET
BT 70.016 321.601 Td /F1 12.0 Tf [(about a billion equations for the weather. Those billion equations couldn?t be solved )] TJ ET
BT 70.016 306.949 Td /F1 12.0 Tf [(by anyone. That's why we need something like a computer that can cope with the )] TJ ET
BT 70.016 292.297 Td /F1 12.0 Tf [(complexity of that system.)] TJ ET
BT 70.016 263.245 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 248.593 Td /F1 12.0 Tf [(Chris, some of our listeners may have heard the term partial differential equations.)] TJ ET
BT 70.016 219.541 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 204.889 Td /F1 12.0 Tf [(Right.)] TJ ET
BT 70.016 175.837 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 161.185 Td /F1 12.0 Tf [(Are these differential equations that aren?t playing ball? What does that mean?)] TJ ET
BT 70.016 132.133 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 117.481 Td /F1 12.0 Tf [(If you have a quantity like the wind, then the velocity of the wind depends, not just )] TJ ET
BT 70.016 102.829 Td /F1 12.0 Tf [(where you are in space, but also what the time is. It depends on two things, space )] TJ ET
BT 70.016 88.177 Td /F1 12.0 Tf [(and time. A partial differential equation is an equation about something which )] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(depends on space and on time.)] TJ ET
BT 70.016 731.101 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 716.449 Td /F1 12.0 Tf [(You're listening to Up Close. In this episode, we're talking about differential )] TJ ET
BT 70.016 701.797 Td /F1 12.0 Tf [(equations with mathematician, Chris Budd. I'm Shane Huntington. Chris, we've )] TJ ET
BT 70.016 687.145 Td /F1 12.0 Tf [(mentioned a number of the very simple scenarios. What about if we move towards )] TJ ET
BT 70.016 672.493 Td /F1 12.0 Tf [(something like a car accident or significant impacts where there is deformation and )] TJ ET
BT 70.016 657.841 Td /F1 12.0 Tf [(so forth? What sort of equations and how do we go about solving those equations for )] TJ ET
BT 70.016 643.189 Td /F1 12.0 Tf [(those particular areas of interest?)] TJ ET
BT 70.016 614.137 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 599.485 Td /F1 12.0 Tf [(Well, let's start with a bit of context, first of all. One of the most useful applications of )] TJ ET
BT 70.016 584.833 Td /F1 12.0 Tf [(what I'm talking about is the process of understanding what happens in a car )] TJ ET
BT 70.016 570.181 Td /F1 12.0 Tf [(accident as it allows the police and the forensic people to see what happens and )] TJ ET
BT 70.016 555.529 Td /F1 12.0 Tf [(what the causes and effects were. So this is really important mathematics. It's also )] TJ ET
BT 70.016 540.877 Td /F1 12.0 Tf [(used to make cars safer and to make the way that say, for example, seatbelts and )] TJ ET
BT 70.016 526.225 Td /F1 12.0 Tf [(collision stuff within the car is designed. So this really does make things safer for us. )] TJ ET
BT 70.016 511.573 Td /F1 12.0 Tf [(Now, the equations for cars impacting on each other are not too complex. Again, you )] TJ ET
BT 70.016 496.921 Td /F1 12.0 Tf [(need an equation for the speed and velocity of the car. When they come into contact, )] TJ ET
BT 70.016 482.269 Td /F1 12.0 Tf [(you have equations for the way the metal deforms under impact and other aspects of )] TJ ET
BT 70.016 467.617 Td /F1 12.0 Tf [(that such as the way that the human being might impact with the car itself and how )] TJ ET
BT 70.016 452.965 Td /F1 12.0 Tf [(unfortunately they deform on impact as well.So these systems are reasonably )] TJ ET
BT 70.016 438.313 Td /F1 12.0 Tf [(straightforward to study. The easiest example to have in mind would be, say, )] TJ ET
BT 70.016 423.661 Td /F1 12.0 Tf [(dropping a ball on the ground and letting it bounce back. That is a system where we )] TJ ET
BT 70.016 409.009 Td /F1 12.0 Tf [(can write down more or less what's going on. Again, in a kind of really complex )] TJ ET
BT 70.016 394.357 Td /F1 12.0 Tf [(scenario, you have to do quite a lot of work to see exactly what was happening. If )] TJ ET
BT 70.016 379.705 Td /F1 12.0 Tf [(you want to estimate something like the speed of the car just before impact, which is )] TJ ET
BT 70.016 365.053 Td /F1 12.0 Tf [(actually rather important in a criminal trial, then you can do that more or less by )] TJ ET
BT 70.016 350.401 Td /F1 12.0 Tf [(solving exact equations.)] TJ ET
BT 70.016 321.349 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 306.697 Td /F1 12.0 Tf [(Now, let's talk a bit about the impact because one of the things that many of our )] TJ ET
BT 70.016 292.045 Td /F1 12.0 Tf [(listeners would have noticed throughout their lives is there has been quite a change )] TJ ET
BT 70.016 277.393 Td /F1 12.0 Tf [(in the design of cars?)] TJ ET
BT 70.016 262.741 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 248.089 Td /F1 12.0 Tf [(Yes.)] TJ ET
BT 70.016 219.037 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 204.385 Td /F1 12.0 Tf [(?from cars that are very solid, often made of very hard materials, to cars that )] TJ ET
BT 70.016 189.733 Td /F1 12.0 Tf [(crumple.)] TJ ET
BT 70.016 160.681 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 146.029 Td /F1 12.0 Tf [(Yes.)] TJ ET
BT 70.016 116.977 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 102.325 Td /F1 12.0 Tf [(Mathematically, why is it important that a car has these crumple zones and is able to )] TJ ET
BT 70.016 87.673 Td /F1 12.0 Tf [(deform?)] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(Well, basically the effect of a collision on the body is proportional to the energy that )] TJ ET
BT 70.016 730.849 Td /F1 12.0 Tf [(you have in the system but also is inversely proportional to the time over which that )] TJ ET
BT 70.016 716.197 Td /F1 12.0 Tf [(energy is dissipated. So, if you dissipate the energy over a very short time, that has a )] TJ ET
BT 70.016 701.545 Td /F1 12.0 Tf [(very severe effect on you. If you spread that out over a much longer time, then it has )] TJ ET
BT 70.016 686.893 Td /F1 12.0 Tf [(much less effect. That's the advantage for having a crumple zone. But one thing )] TJ ET
BT 70.016 672.241 Td /F1 12.0 Tf [(that's worth noting is that the amount of energy in a collision is proportional to the )] TJ ET
BT 70.016 657.589 Td /F1 12.0 Tf [(square of your speed. So, if you double your speed, the actual energy goes up by a )] TJ ET
BT 70.016 642.937 Td /F1 12.0 Tf [(factor of four. If you triple it, it goes by a factor of nine. This is why high-speed )] TJ ET
BT 70.016 628.285 Td /F1 12.0 Tf [(collisions are much, much more dangerous than low speed ones.)] TJ ET
BT 70.016 599.233 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 584.581 Td /F1 12.0 Tf [(Mathematical predictions of the type you're speaking of, on paper seem relatively )] TJ ET
BT 70.016 569.929 Td /F1 12.0 Tf [(easy to put down. How useful are predictions when we move them into the real )] TJ ET
BT 70.016 555.277 Td /F1 12.0 Tf [(world? Do they start to very rapidly lose their voracity when we move into real )] TJ ET
BT 70.016 540.625 Td /F1 12.0 Tf [(situations where there are far more parameters to be concerned about? Or is the )] TJ ET
BT 70.016 525.973 Td /F1 12.0 Tf [(validity still there?)] TJ ET
BT 70.016 496.921 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 482.269 Td /F1 12.0 Tf [(The validity is still there. I'll give you an example. Modern aircraft are invariably )] TJ ET
BT 70.016 467.617 Td /F1 12.0 Tf [(designed not using wind tunnels but by doing calculations. So an aircraft will be )] TJ ET
BT 70.016 452.965 Td /F1 12.0 Tf [(designed by solving the equations for air flow over the fuselage in the wings. Those )] TJ ET
BT 70.016 438.313 Td /F1 12.0 Tf [(equations give you a huge amount of information as to how that aeroplane will )] TJ ET
BT 70.016 423.661 Td /F1 12.0 Tf [(behave. All the main calculations are now done by solving these equations. They )] TJ ET
BT 70.016 409.009 Td /F1 12.0 Tf [(may only do a wind tunnel test right at the very, very end of the process. So these )] TJ ET
BT 70.016 394.357 Td /F1 12.0 Tf [(are incredibly powerful and accurate calculations. The complexity doesn't mean you )] TJ ET
BT 70.016 379.705 Td /F1 12.0 Tf [(can't do it. It just means that you have to work a lot harder to do it.)] TJ ET
BT 70.016 350.653 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 336.001 Td /F1 12.0 Tf [(Chris, give us an idea into your sort of day when you take on a new problem. At what )] TJ ET
BT 70.016 321.349 Td /F1 12.0 Tf [(point does the scribbling on the page of equations get taken over by the computer )] TJ ET
BT 70.016 306.697 Td /F1 12.0 Tf [(modelling? When does that occur?)] TJ ET
BT 70.016 277.645 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 262.993 Td /F1 12.0 Tf [(It occurs right at the beginning. What I normally do is develop equations at the same )] TJ ET
BT 70.016 248.341 Td /F1 12.0 Tf [(time as I put them onto the computer. So the computer is used in the early stages to )] TJ ET
BT 70.016 233.689 Td /F1 12.0 Tf [(give me insight to make sure I'm heading in the right direction and at a later stage to )] TJ ET
BT 70.016 219.037 Td /F1 12.0 Tf [(really get to grips with the big calculations. So I will be scribbling on paper and on a )] TJ ET
BT 70.016 204.385 Td /F1 12.0 Tf [(computer almost at the same time simultaneously. Modern technology is so good )] TJ ET
BT 70.016 189.733 Td /F1 12.0 Tf [(that you can get equations onto computer very quickly and play with them almost )] TJ ET
BT 70.016 175.081 Td /F1 12.0 Tf [(immediately.)] TJ ET
BT 70.016 160.429 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 145.777 Td /F1 12.0 Tf [(When we look at particular problems where the outputs of the equations and the )] TJ ET
BT 70.016 131.125 Td /F1 12.0 Tf [(computer work are dictated very strongly by probabilities, by ideas of errors?)] TJ ET
BT 70.016 102.073 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 87.421 Td /F1 12.0 Tf [(Yes.)] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(?what is the distinguishing factor that makes these problems so difficult to nail down )] TJ ET
BT 70.016 730.849 Td /F1 12.0 Tf [(with the level of accuracy compared to other problems, as you mentioned before like )] TJ ET
BT 70.016 716.197 Td /F1 12.0 Tf [(the position of the planets where we can quite easily and quite readily predict?)] TJ ET
BT 70.016 687.145 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 672.493 Td /F1 12.0 Tf [(Well, with the planets, you've got a lot of precise information. You don?t have too )] TJ ET
BT 70.016 657.841 Td /F1 12.0 Tf [(many things going on. A problem like the weather is much, much harder. It's harder )] TJ ET
BT 70.016 643.189 Td /F1 12.0 Tf [(for two reasons. First, there's a lot more going on. Also, there's a lot less that we )] TJ ET
BT 70.016 628.537 Td /F1 12.0 Tf [(know. In particular, we don?t really know the initial state of the atmosphere very well. )] TJ ET
BT 70.016 613.885 Td /F1 12.0 Tf [(So what is often done in a subject like weather forecasting is you might, instead of )] TJ ET
BT 70.016 599.233 Td /F1 12.0 Tf [(starting the weather off from one configuration predicting what's going to happen in, )] TJ ET
BT 70.016 584.581 Td /F1 12.0 Tf [(say, three days' time, you might make multiple calculations where you take a whole )] TJ ET
BT 70.016 569.929 Td /F1 12.0 Tf [(load of different initial configurations, which will differ from each other by a small )] TJ ET
BT 70.016 555.277 Td /F1 12.0 Tf [(amount consistent with errors in measurements. Then you forecast what's called an )] TJ ET
BT 70.016 540.625 Td /F1 12.0 Tf [(ensemble of forecasts three days into the future.Now, if that ensemble of forecasts )] TJ ET
BT 70.016 525.973 Td /F1 12.0 Tf [(all basically agree with each other, then you say, yes, with high confidence that's )] TJ ET
BT 70.016 511.321 Td /F1 12.0 Tf [(what's going to go on. If one-third did one thing, two-thirds said another, you might )] TJ ET
BT 70.016 496.669 Td /F1 12.0 Tf [(then say, well, there's a two-thirds chance it's going to rain and a one-third chance )] TJ ET
BT 70.016 482.017 Td /F1 12.0 Tf [(that it doesn't. That's how you get probabilities. You often find in modern weather )] TJ ET
BT 70.016 467.365 Td /F1 12.0 Tf [(forecasts that you do get weather with certain probabilities attached. That's basically )] TJ ET
BT 70.016 452.713 Td /F1 12.0 Tf [(how it's done.)] TJ ET
BT 70.016 423.661 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 409.009 Td /F1 12.0 Tf [(Chris, let's now move into one of the more intriguing areas of mathematics which )] TJ ET
BT 70.016 394.357 Td /F1 12.0 Tf [(was first described by Edward Lorenz, namely chaos theory. Can you explain for us )] TJ ET
BT 70.016 379.705 Td /F1 12.0 Tf [(what the particular group of problems is that chaos theory describes?)] TJ ET
BT 70.016 350.653 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 336.001 Td /F1 12.0 Tf [(Chaos theory really is a description of systems which are what's called non-linear. So )] TJ ET
BT 70.016 321.349 Td /F1 12.0 Tf [(a non-linear system is where you have different things which interact very closely. )] TJ ET
BT 70.016 306.697 Td /F1 12.0 Tf [(What you get out isn?t the sum of those interactions. It's a much more complicated )] TJ ET
BT 70.016 292.045 Td /F1 12.0 Tf [(combination of them. A good example of a non-linear system would be the weather )] TJ ET
BT 70.016 277.393 Td /F1 12.0 Tf [(itself. Lorenz, who you referred to, was a meteorologist.)] TJ ET
BT 70.016 248.341 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 233.689 Td /F1 12.0 Tf [(When we take a chaos problem, how does it compare to the sorts of differential )] TJ ET
BT 70.016 219.037 Td /F1 12.0 Tf [(equation problems we were looking at earlier? What's different about the parameters )] TJ ET
BT 70.016 204.385 Td /F1 12.0 Tf [(that we're putting in and the outcomes that we will get?)] TJ ET
BT 70.016 175.333 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 160.681 Td /F1 12.0 Tf [(Well, if you take a system which is not chaotic, which is the Earth going around the )] TJ ET
BT 70.016 146.029 Td /F1 12.0 Tf [(Sun, then, if you make a small change to the Earth's position or a small change to its )] TJ ET
BT 70.016 131.377 Td /F1 12.0 Tf [(mass or something like that, then that actually doesn't affect the solution very much. )] TJ ET
BT 70.016 116.725 Td /F1 12.0 Tf [(A small change in the configuration leads to a small change in the solution. That's an )] TJ ET
BT 70.016 102.073 Td /F1 12.0 Tf [(example of a non-chaotic system. Now, we all know that the weather is rather )] TJ ET
BT 70.016 87.421 Td /F1 12.0 Tf [(unpredictable. One of the reasons it's unpredictable is that quite small changes to the )] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(initial states or to the parameters in the equations can, over quite a short time, lead )] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(to very large changes in the solution. That's the hallmark of a chaotic system. So )] TJ ET
BT 70.016 730.849 Td /F1 12.0 Tf [(chaos means really unpredictable behaviour largely arising because you get big )] TJ ET
BT 70.016 716.197 Td /F1 12.0 Tf [(changes due to small effects.)] TJ ET
BT 70.016 687.145 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 672.493 Td /F1 12.0 Tf [(When we consider something like the weather where there are so many )] TJ ET
BT 70.016 657.841 Td /F1 12.0 Tf [(measurements being made to go into these particular theories, and each of those )] TJ ET
BT 70.016 643.189 Td /F1 12.0 Tf [(measurements has errors associated with it, it is quite stunning that we can predict )] TJ ET
BT 70.016 628.537 Td /F1 12.0 Tf [(the weather to such accuracy, it would seem, in a chaotic system.)] TJ ET
BT 70.016 599.485 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 584.833 Td /F1 12.0 Tf [(Well, the reason for that is, over short times, the affects in errors in the )] TJ ET
BT 70.016 570.181 Td /F1 12.0 Tf [(measurements don?t have too much effect. The weather tomorrow is with a chance )] TJ ET
BT 70.016 555.529 Td /F1 12.0 Tf [(of about 70 per cent what the weather is today. The effects of errors accumulate. )] TJ ET
BT 70.016 540.877 Td /F1 12.0 Tf [(That accumulation means that, after about 10 days, you basically can't predict the )] TJ ET
BT 70.016 526.225 Td /F1 12.0 Tf [(weather at all. It is certainly true though that the weather is very sensitive to these )] TJ ET
BT 70.016 511.573 Td /F1 12.0 Tf [(things. It is still remarkable that we can get anywhere.)] TJ ET
BT 70.016 482.521 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 467.869 Td /F1 12.0 Tf [(I'm Shane Huntington. My guest today is mathematician, Chris Budd. We're talking )] TJ ET
BT 70.016 453.217 Td /F1 12.0 Tf [(about mathematical predictions here on Up Close. Chris, coming back to our initial )] TJ ET
BT 70.016 438.565 Td /F1 12.0 Tf [(discussion on types of equations?)] TJ ET
BT 70.016 409.513 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 394.861 Td /F1 12.0 Tf [(Yes.)] TJ ET
BT 70.016 365.809 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 351.157 Td /F1 12.0 Tf [(?you mentioned quadratic equations, differential equations. When we're dealing with )] TJ ET
BT 70.016 336.505 Td /F1 12.0 Tf [(something like chaos theory, what sort of equations are involved with those particular )] TJ ET
BT 70.016 321.853 Td /F1 12.0 Tf [(predictions?)] TJ ET
BT 70.016 292.801 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 278.149 Td /F1 12.0 Tf [(Well, there are two types of equations which are very popular in chaos theory. The )] TJ ET
BT 70.016 263.497 Td /F1 12.0 Tf [(first is the ones I've been describing which are differential equations. The other type )] TJ ET
BT 70.016 248.845 Td /F1 12.0 Tf [(of equation which comes up in a lot of cases are what are called maps. Now, I'll give )] TJ ET
BT 70.016 234.193 Td /F1 12.0 Tf [(you an example of a map. Let's suppose we know what the population of Melbourne )] TJ ET
BT 70.016 219.541 Td /F1 12.0 Tf [(is in this year, 2013. What's the population going to be in 2014? What's the )] TJ ET
BT 70.016 204.889 Td /F1 12.0 Tf [(population going to be in 2015? What's it going to be in 2030? Now, there might be a )] TJ ET
BT 70.016 190.237 Td /F1 12.0 Tf [(sort of relationship between the population this year and the population next year. )] TJ ET
BT 70.016 175.585 Td /F1 12.0 Tf [(That relationship is called a map. Maps are used quite a lot by biologists to )] TJ ET
BT 70.016 160.933 Td /F1 12.0 Tf [(understand the way populations of animals grow and evolve from one generation to )] TJ ET
BT 70.016 146.281 Td /F1 12.0 Tf [(the next. A very famous map is called the logistic map which was basically derived to )] TJ ET
BT 70.016 131.629 Td /F1 12.0 Tf [(look at the way populations change or how disease propagates. This map is known )] TJ ET
BT 70.016 116.977 Td /F1 12.0 Tf [(to be chaotic and to give somewhat unpredictable types of behaviour.)] TJ ET
BT 70.016 87.925 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(One of the areas that chaos theory would seem to bring into strong focus is the )] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(desire and need for extraordinary computing power. How has that changed the way )] TJ ET
BT 70.016 730.849 Td /F1 12.0 Tf [(we do chaos modelling over the last sort of decade as we've exploded our capacity )] TJ ET
BT 70.016 716.197 Td /F1 12.0 Tf [(in computing power?)] TJ ET
BT 70.016 687.145 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 672.493 Td /F1 12.0 Tf [(Well, I think it's fair to say that the discovery of chaos more or less coincided with the )] TJ ET
BT 70.016 657.841 Td /F1 12.0 Tf [(first use of computers to solve equations. So Lorenz wrote down his equations in )] TJ ET
BT 70.016 643.189 Td /F1 12.0 Tf [(about 1965. This was when computers were starting to be used to solve differential )] TJ ET
BT 70.016 628.537 Td /F1 12.0 Tf [(equations. It was because they applied computer-used equations and found things )] TJ ET
BT 70.016 613.885 Td /F1 12.0 Tf [(which they completely didn?t understand or predict that the whole subject erupted. )] TJ ET
BT 70.016 599.233 Td /F1 12.0 Tf [(Now, because computers are so powerful and so universally used, we kind of have )] TJ ET
BT 70.016 584.581 Td /F1 12.0 Tf [(chaos automatically built into a lot of the sort of problems that we work with.)] TJ ET
BT 70.016 555.529 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 540.877 Td /F1 12.0 Tf [(When we look at something as substantial in a social sense as climate change and )] TJ ET
BT 70.016 526.225 Td /F1 12.0 Tf [(we consider that this is based on chaos theory and based on many initial predictions )] TJ ET
BT 70.016 511.573 Td /F1 12.0 Tf [(and many initial measurements, how much can we rely on the outcomes given when )] TJ ET
BT 70.016 496.921 Td /F1 12.0 Tf [(you mentioned weather, you said, beyond 10 days things are difficult? Obviously )] TJ ET
BT 70.016 482.269 Td /F1 12.0 Tf [(these are different, larger systems. But where's the reliability there?)] TJ ET
BT 70.016 453.217 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 438.565 Td /F1 12.0 Tf [(Well, it's difficult to predict the weather 10 days ahead because of the effects of )] TJ ET
BT 70.016 423.913 Td /F1 12.0 Tf [(chaos. But climate's rather different. Climate is much more about the kind of slow )] TJ ET
BT 70.016 409.261 Td /F1 12.0 Tf [(evolution of average quantities rather than predicting what's going on from day to )] TJ ET
BT 70.016 394.609 Td /F1 12.0 Tf [(day. The equations for this are somewhat different and much, in a sense, more )] TJ ET
BT 70.016 379.957 Td /F1 12.0 Tf [(predictable. So we can understand how the Earth's temperature is going to arise )] TJ ET
BT 70.016 365.305 Td /F1 12.0 Tf [(year on year due to climate change even if I can't tell you whether it's going to rain or )] TJ ET
BT 70.016 350.653 Td /F1 12.0 Tf [(not on Christmas Day.)] TJ ET
BT 70.016 321.601 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 306.949 Td /F1 12.0 Tf [(With that, is the application of chaos theory still happening or is it back to the sort of )] TJ ET
BT 70.016 292.297 Td /F1 12.0 Tf [(more standard equations where those initial conditions aren?t as pertinent?)] TJ ET
BT 70.016 263.245 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 248.593 Td /F1 12.0 Tf [(Oh no, chaos theory is hugely important in many, many areas of science across the )] TJ ET
BT 70.016 233.941 Td /F1 12.0 Tf [(board, from physics through to biology. The reason for that is chaos is there. Chaos )] TJ ET
BT 70.016 219.289 Td /F1 12.0 Tf [(is a natural occurring physical phenomenon. The simplest system I know which is )] TJ ET
BT 70.016 204.637 Td /F1 12.0 Tf [(chaotic is what's called a double pendulum, which is one pendulum tied onto the )] TJ ET
BT 70.016 189.985 Td /F1 12.0 Tf [(bottom of another pendulum so they can oscillate together. That system behaves )] TJ ET
BT 70.016 175.333 Td /F1 12.0 Tf [(beautifully chaotically. It has completely unpredictable behaviour. It's there. It's there )] TJ ET
BT 70.016 160.681 Td /F1 12.0 Tf [(in the world about us. We cannot avoid it. What we do is we take it on board. It's just )] TJ ET
BT 70.016 146.029 Td /F1 12.0 Tf [(another aspect of science which we try to understand.)] TJ ET
BT 70.016 116.977 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 102.325 Td /F1 12.0 Tf [(When you refer to that as unpredictable, does chaos theory itself not give us an )] TJ ET
BT 70.016 87.673 Td /F1 12.0 Tf [(insight into what it will do? Or is it inherently non-predictable?)] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(What chaos theory does is it says there may be systems out there which look as )] TJ ET
BT 70.016 730.849 Td /F1 12.0 Tf [(though they are unpredictable. But what chaos theory does is say, let's look a bit )] TJ ET
BT 70.016 716.197 Td /F1 12.0 Tf [(deeper. Maybe underneath those seemingly unpredictable systems are equations )] TJ ET
BT 70.016 701.545 Td /F1 12.0 Tf [(which we can write down and, by solving them, get an insight into the system. That's )] TJ ET
BT 70.016 686.893 Td /F1 12.0 Tf [(really been the great breakthrough. So the things which we thought in the past were )] TJ ET
BT 70.016 672.241 Td /F1 12.0 Tf [(completely random we now know are not random. They are described by equations. )] TJ ET
BT 70.016 657.589 Td /F1 12.0 Tf [(It's just that the equations themselves have somewhat crazy behaviour.)] TJ ET
BT 70.016 628.537 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 613.885 Td /F1 12.0 Tf [(You mentioned the airline industry. What other industries are mathematicians at the )] TJ ET
BT 70.016 599.233 Td /F1 12.0 Tf [(moment getting heavily involved with, yourself, for example? Where are the )] TJ ET
BT 70.016 584.581 Td /F1 12.0 Tf [(outcomes from those particular projects?)] TJ ET
BT 70.016 555.529 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 540.877 Td /F1 12.0 Tf [(Well, I think it's fair to say that maths gets into just about every industry going. The )] TJ ET
BT 70.016 526.225 Td /F1 12.0 Tf [(biggest industry I am familiar with which uses maths is the information industry. So )] TJ ET
BT 70.016 511.573 Td /F1 12.0 Tf [(Google and the internet heavily rely on maths. Chaos itself is important in areas such )] TJ ET
BT 70.016 496.921 Td /F1 12.0 Tf [(as the electronics industry. The electronics industry uses an enormous amount of )] TJ ET
BT 70.016 482.269 Td /F1 12.0 Tf [(maths. But it comes into almost anything including, for example, the food industry is )] TJ ET
BT 70.016 467.617 Td /F1 12.0 Tf [(a big, big user of mathematics.)] TJ ET
BT 70.016 438.565 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 423.913 Td /F1 12.0 Tf [(Chris, is maths a science in itself or is it a service to other sciences?)] TJ ET
BT 70.016 394.861 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 380.209 Td /F1 12.0 Tf [(I like to think of maths as just something on its own. It's not a science. It's not an art. )] TJ ET
BT 70.016 365.557 Td /F1 12.0 Tf [(It's just mathematics.)] TJ ET
BT 70.016 336.505 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 321.853 Td /F1 12.0 Tf [(Chris, you mentioned Google, which is very much a human construct. That brings us )] TJ ET
BT 70.016 307.201 Td /F1 12.0 Tf [(to the issue of human behaviour.)] TJ ET
BT 70.016 278.149 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 263.497 Td /F1 12.0 Tf [(Yes.)] TJ ET
BT 70.016 234.445 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 219.793 Td /F1 12.0 Tf [(Is this something that chaos theory has a say in or are we very predictable?)] TJ ET
BT 70.016 190.741 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 176.089 Td /F1 12.0 Tf [(Well, I don?t think any human is particularly predictable. The brain is such an )] TJ ET
BT 70.016 161.437 Td /F1 12.0 Tf [(amazing thing and such a complex thing. I certainly couldn?t predict the behaviour of )] TJ ET
BT 70.016 146.785 Td /F1 12.0 Tf [(any one human being. I can't even predict the behaviour of my dog. One thing that )] TJ ET
BT 70.016 132.133 Td /F1 12.0 Tf [(we can use chaos theory for, and it is powerfully used actually, is to understand the )] TJ ET
BT 70.016 117.481 Td /F1 12.0 Tf [(behaviour of humans in large crowds and the way people interact in crowds can be )] TJ ET
BT 70.016 102.829 Td /F1 12.0 Tf [(described using differential equations. These equations are incredibly useful when )] TJ ET
BT 70.016 88.177 Td /F1 12.0 Tf [(designing things like sports stadia, railway stations or simply understanding how )] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(people might walk down the street.)] TJ ET
BT 70.016 731.101 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 716.449 Td /F1 12.0 Tf [(So, when you do look at something like a stadium, what sort of mathematics is )] TJ ET
BT 70.016 701.797 Td /F1 12.0 Tf [(involved there? What sort of things are you trying to predict, or determine or design?)] TJ ET
BT 70.016 672.745 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 658.093 Td /F1 12.0 Tf [(If you want to understand how a crowd moves, let's suppose you have a worst case )] TJ ET
BT 70.016 643.441 Td /F1 12.0 Tf [(scenario and there's a fire in the stadium. Then an individual will obviously want to )] TJ ET
BT 70.016 628.789 Td /F1 12.0 Tf [(leave the stadium through an exit. They will have some desire to move in a certain )] TJ ET
BT 70.016 614.137 Td /F1 12.0 Tf [(way towards that exit. They?ll also want to avoid other people so they don?t want to )] TJ ET
BT 70.016 599.485 Td /F1 12.0 Tf [(collide into those people. If you're there with family members then you will want to )] TJ ET
BT 70.016 584.833 Td /F1 12.0 Tf [(gather those members with you and walk together with them. The equations take into )] TJ ET
BT 70.016 570.181 Td /F1 12.0 Tf [(account this desire, where we want to go, our desire to avoid people, our desire to )] TJ ET
BT 70.016 555.529 Td /F1 12.0 Tf [(keep families with us and the fact that we can't walk through walls and stuff like that. )] TJ ET
BT 70.016 540.877 Td /F1 12.0 Tf [(Put all those together, you get a system of equations which you can kind of use to )] TJ ET
BT 70.016 526.225 Td /F1 12.0 Tf [(simulate the motion of the people. Then that is used by people designing sports )] TJ ET
BT 70.016 511.573 Td /F1 12.0 Tf [(stadia to work out where to locate the exits, how wide the exits should be and even )] TJ ET
BT 70.016 496.921 Td /F1 12.0 Tf [(what signage there should be towards the exits.)] TJ ET
BT 70.016 467.869 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 453.217 Td /F1 12.0 Tf [(Presumably, Chris, many of the equations and techniques we're talking about are )] TJ ET
BT 70.016 438.565 Td /F1 12.0 Tf [(also used in the gaming industry. By that I mean the online and non-online virtual )] TJ ET
BT 70.016 423.913 Td /F1 12.0 Tf [(environments that are used for entertainment and where virtual environments are )] TJ ET
BT 70.016 409.261 Td /F1 12.0 Tf [(designed that have to appear and interact with the users as though they are real and )] TJ ET
BT 70.016 394.609 Td /F1 12.0 Tf [(follow the same rules.)] TJ ET
BT 70.016 365.557 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 350.905 Td /F1 12.0 Tf [(Well, very much so. One of the things I love telling my students is one of the largest )] TJ ET
BT 70.016 336.253 Td /F1 12.0 Tf [(single employers of mathematicians is the gaming industry because of exactly what )] TJ ET
BT 70.016 321.601 Td /F1 12.0 Tf [(you say. They want to have reality, virtual reality things that look as close to reality as )] TJ ET
BT 70.016 306.949 Td /F1 12.0 Tf [(possible. That requires a lot of maths, both in understanding how things move, which )] TJ ET
BT 70.016 292.297 Td /F1 12.0 Tf [(is back to differential equations, or how light comes off them. Well, that's differential )] TJ ET
BT 70.016 277.645 Td /F1 12.0 Tf [(equations as well.)] TJ ET
BT 70.016 248.593 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 233.941 Td /F1 12.0 Tf [(Chris, when we consider some of the equations that we're talking about that cover )] TJ ET
BT 70.016 219.289 Td /F1 12.0 Tf [(aspects of the natural world we exist in, do these equations exist independent of us? )] TJ ET
BT 70.016 204.637 Td /F1 12.0 Tf [(Are they real things or are they just constructs of our own minds?)] TJ ET
BT 70.016 175.585 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 160.933 Td /F1 12.0 Tf [(This is one of the great philosophical debates in mathematics. Is mathematics an )] TJ ET
BT 70.016 146.281 Td /F1 12.0 Tf [(invention or is it a discovery? It's incredible that mathematics can be used in this way )] TJ ET
BT 70.016 131.629 Td /F1 12.0 Tf [(to describe the world. It's got an unreasonable effectiveness. It does very much )] TJ ET
BT 70.016 116.977 Td /F1 12.0 Tf [(seem as though differential equations are our best way of understanding the world )] TJ ET
BT 70.016 102.325 Td /F1 12.0 Tf [(and that the world's kind of, in a sense, is differential equations. A really good )] TJ ET
BT 70.016 87.673 Td /F1 12.0 Tf [(example of that is quantum theory, which is all based on a single equation called )] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(Schrdinger's equation which, at a very, very kind of fundamental level, does seem )] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(to describe the world that we're in. Whether there might be something deeper than )] TJ ET
BT 70.016 730.849 Td /F1 12.0 Tf [(that going on underneath, well, that's really a question for philosophers rather than )] TJ ET
BT 70.016 716.197 Td /F1 12.0 Tf [(mathematicians.)] TJ ET
BT 70.016 687.145 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 672.493 Td /F1 12.0 Tf [(We certainly have the perception that the number 10 is important to us in our )] TJ ET
BT 70.016 657.841 Td /F1 12.0 Tf [(counting systems and everything.)] TJ ET
BT 70.016 628.789 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 614.137 Td /F1 12.0 Tf [(Yes.)] TJ ET
BT 70.016 585.085 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 570.433 Td /F1 12.0 Tf [(But we can use other bases for counting that we don?t do, of course, because we )] TJ ET
BT 70.016 555.781 Td /F1 12.0 Tf [(have 10 finger and 10 toes.)] TJ ET
BT 70.016 526.729 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 512.077 Td /F1 12.0 Tf [(Yes.)] TJ ET
BT 70.016 483.025 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 468.373 Td /F1 12.0 Tf [(Under those sorts of constructs, things do start to look different, don?t they?)] TJ ET
BT 70.016 439.321 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 424.669 Td /F1 12.0 Tf [(Well, the number 10, yes. It's very much a human number, as it were, because of our )] TJ ET
BT 70.016 410.017 Td /F1 12.0 Tf [(fingers and toes. There are other numbers such as the number Pi which is a )] TJ ET
BT 70.016 395.365 Td /F1 12.0 Tf [(universal number. If I went anywhere in the universe and measured the ratio of the )] TJ ET
BT 70.016 380.713 Td /F1 12.0 Tf [(diameter of a circle to its circumference, I'd still get Pi. That is a universal number )] TJ ET
BT 70.016 366.061 Td /F1 12.0 Tf [(that, if I wanted to communicate with aliens that I knew knew mathematics, I'd )] TJ ET
BT 70.016 351.409 Td /F1 12.0 Tf [(communicate the number Pi.)] TJ ET
BT 70.016 322.357 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 307.705 Td /F1 12.0 Tf [(Professor Chris Budd, Professor of Applied Mathematics at the University of Bath )] TJ ET
BT 70.016 293.053 Td /F1 12.0 Tf [(and Professor of Mathematics at the Royal Institution of Great Britain. Thank you for )] TJ ET
BT 70.016 278.401 Td /F1 12.0 Tf [(being our guest on Up Close today and talking with us about differential equations.)] TJ ET
BT 70.016 249.349 Td /F1 12.0 Tf [(CHRIS BUDD)] TJ ET
BT 70.016 234.697 Td /F1 12.0 Tf [(Thank you.)] TJ ET
BT 70.016 205.645 Td /F1 12.0 Tf [(SHANE HUNTINGTON)] TJ ET
BT 70.016 190.993 Td /F1 12.0 Tf [(Relevant links, a full transcript and more info on this episode can be found on our )] TJ ET
BT 70.016 176.341 Td /F1 12.0 Tf [(website at upclose.unimelb.edu.au. Up Close is a production of the University of )] TJ ET
BT 70.016 161.689 Td /F1 12.0 Tf [(Melbourne, Australia. This episode was recorded on 11 July 2013. Producers for this )] TJ ET
BT 70.016 147.037 Td /F1 12.0 Tf [(episode were Kelvin Param, Eric Van Bemmel and Dr Dyani Lewis. Audio )] TJ ET
BT 70.016 132.385 Td /F1 12.0 Tf [(engineering by Gavin Nebauer. Up Close is created by Eric Van Bemmel and Kelvin )] TJ ET
BT 70.016 117.733 Td /F1 12.0 Tf [(Param. I'm Dr Shane Huntington. Until next time, goodbye.)] TJ ET
BT 70.016 88.681 Td /F1 12.0 Tf [(VOICEOVER)] TJ ET
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BT 70.016 760.153 Td /F1 12.0 Tf [(You've been listening to Up Close. We're also on Twitter and Facebook. For more )] TJ ET
BT 70.016 745.501 Td /F1 12.0 Tf [(info, visit upclose.unimelb.edu.au. Copyright 2013, the University of Melbourne.)] TJ ET
BT 70.016 706.849 Td /F1 12.0 Tf [( The University of Melbourne, 2013. All Rights Reserved.)] TJ ET
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BT 137.587 674.748 Td /F1 10.7 Tf [(http://www.upclose.unimelb.edu.au/episode/258-world-numbers-how-)] TJ ET
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