High Anxieties- The Mathematics of Chaos (2008)

what has ultimately always stood behind our conviction that the world is unknowable and therefore controllable place is that the mathematics which governs the world said so but what happens when that assurance is taken away when the mathematics begins to tell us that perhaps the world isn't as predictable and controllable as we once thought that our old assurances might be wrong markets across the globe are in turmoil this afternoon as another fruit Bank your lap and when the disasters of today begin to fuel fears for tomorrow there is a growing awareness of the fact that the world in which we live is incredible chaotic powerful hurricanes on record hits forgotten now wow you thought we could control everything now we feel we can control nothing and and that comes out of this notion that there is chaos in the world that you can never know enough to be able to really predict it let alone control it from simple models and the mathematics which control them is coming a challenge to our old world of you there's a simple human need to have a forecast about the future as a deep desire if you lie to better control the future and a very very deep reluctance to accept the really modern advances in mathematics which suggests that there are high levels of fundamental unpredictability America's mortgage crisis foods for the future of two huge companies of their shows and reels from the impact of the latest oricon hundreds of it used to be that our dreams of the future of a bright and open place what happened to us that our vision of the future is no longer bright but dark people are really really hitting they're really impressive there's nowhere to turn where did it all begin you know what's the answer it's like it was a big design global type of effect well you have anxiety attacks you have nightmares who can we blame this on anybody can anybody tell me that the key kind of psychological experience of anxiety is a fear that something is also as something awful is going to happen the kind of dread and uncertainty this film is a history of that anxiety and the mathematics which created it we are in the midst of a huge cultural change only fifty years ago experts had a whole vocabulary for describing the world which already sounds very foreign to us they talked about a command-and-control economy of engineering the weather of central planning no one today thinks the world can be described in such terms today we're much more likely to talk about disorder instability turbulence tipping points the butterfly effect this is the vocabulary which has come to us from the mathematics of the last fifty years and it is this mathematics which is in the process of completely altering our understanding of the fundamental nature of the world we live in and I believe is giving us a whole new vocabulary we're talking about our anxieties about that world looking back we can see what was not obvious then those mathematical discoveries which would eventually undermine the optimistic view of the world and set us on our way to the anxieties of today the mathematical roots of our modern anxiety have their beginnings here in Paris in 1885 the city was preparing to celebrate the optimistic worldview of science and reason there was to be a grand exhibition to celebrate progress in democracy it was the centenary of the Republic and towering over it all was to be the world's tallest building a symbol of everything that they believed in a perfect him in iron to the rational and ordered worldview of Newtonian science Newtonian mathematics describes a place that follows clear rules of cause and effect which make it predictable and therefore ultimately controllable in the hands of one of Newton's greatest foes the French atheist and mathematician pierre-simon Laplace it became a set of beliefs about the nature of everything an almost religious belief that the world could be understood as a machine there was this strong notion that the world should be mechanistic and deterministic David rhew well is a theoretical physicist and one of the principal discoverers of chaos mathematics and Newton and Laplace saw the world as a machine and everybody did to the extent that they were scientists they wanted to have determinism in a mechanistic world nothing happens without cold nothing is unexplainable in this world if you understood the mathematical rules you understood the world everything was predictable science could guarantee safety and progress so that you could have this laplacian what was sometimes called as a clockwork view of the universe where you know if enough people did enough sums then everything would be understood because they thought they knew how how things how systems behaved they thought everything did in the end behave nicely they knew disasters happened they were perfectly well aware of that but actually they thought there was the mathematics would be able to explain it completely and this was ultimately what underpinned their optimism and ours and made the future seem so open but beneath the surface of optimism that the world was conquerable and controllable was an undercurrent of worry that perhaps the world was not as tame safe as they wished to believe right at the heart of Newtonian mechanics was a problem which if it couldn't be solved endangered the whole belief that ultimately everything was mathematically predictable because it was to do with the one thing Newton was supposed to have absolutely solved the obits of the solar system see the genius of Newton's equations is that if you have two bodies one orbiting the other like the earth going around the Sun the equations of motion allow you to tell the exact nature of their orbits and to predict precisely where both bodies will be anytime in the future the claim of Newton and Laplace is that you simply scale that up and you can predict everything about the universe once you've got a solution you you can say to me well I'd like to know where that body is going to be at such-and-such a time and that could be at any time in the future or any time in the past I can just plug in the numbers the time that you want and out will come the answer and it'll give me essentially the coordinates and and velocity of where that body will be the same mathematics that govern the orbits of the planets also govern the motion here on earth it was the bedrock of Newtonian science that if two objects began in almost identical orbits they would continue in almost identical always the difference between them never go so if you knew the orbit of one you could predict the orbit of the other and in theory that's fine in practice what happens is that as soon as you add just one more body just three suddenly you cannot solve the equations and you cannot predict anything every major mathematician from Newton onwards had hoped that one day what they call the three-body problem would be solved but then in 1889 a French mathematician called re Poincare he discovered there was no way of predicting the orbits in some cases no matter how similar the paths were at the start if there was any difference at all eventually one would fly off on a different and totally unexpected and unpredictable path prediction banker elementadd becomes impossible he saw something behaving in a way that he didn't expect and he realized it was to do with the initial conditions and what we now call sensitivity to initial conditions and that's what was unexpected that if you just tweaked something a very little bit you could get a huge difference in outcomes that was where he actually discovered what we now call mathematical chaos Poincare had glimpsed a profound truth about the planets and their orbits what disturbed him was that he realized this unpredictable behavior might be present throughout nature he realized a small disturbance no more than the flapping of a butterfly's wings might be enough to create a storm when known was predicted this was a very different world to Newton's and I think the interesting thing is is the fact that he was so himself even FUNKER a sort of greatest mathematician around at the time was still immersed in that view of thinking that things would all work out nicely everything in the end behaved properly and he was horrified when he discovered the way these solutions worked out and you could get this what we now call chaotic behavior it was quite shocking to him Branka rays discovered struck at the root of a view of the world which neither he nor his contemporaries were yet willing to give up the world in which he was living and moving was still very much one that was embedded in that laplacian view this very strange behavior that he discovered was sort of glossed over by the commentators people were just not ready to hear that their world was not as orderly as they'd always believed then in 1940 in Sarajevo a tiny disturbance did push the whole world system from its course this was the tiny disturbance at starting contrast in hindsight we can see how appalling Li prescient when Kara's discovery had been but at the time the rest of the world was just not ready to listen they were still determined to believe that they lived in a Newtonian world but even the complexities of human affairs could be predicted and the war would be over by Christmas when World War one broke out they all wheeled out their artillery confident reality could be made to follow their plans after all the same mathematics which predicted the orbits of the planets also governed the firing of artillery the mathematics of ballistics told them exactly where the shells would land of course at the beginning of the 20th century ballistics was essentially firing at a stationary object and you might have to fire over something so you might not be able to see what you were firing at so the mathematicians had had sort of sorted it out they had range tables and so on the magic of science this predictability of things who mathematics science is not just proving theorems it's to give us some power over nature about what happens predicting and eclipses this kind of power building steam engines is also power and science was built in part about that the tragedy of the war was that no matter what carnage unfolded they believed there was not only a science of ballistics but a science of war a way of predicting how many men per mile of front would win the objective they thought if they understood the science of war they could control its outcome they could simply overpower the chaos in the end they weren't fighting each other both sides were fighting the chaos of reality in the end the chaos defeated them all and ten million men died fran莽a raised notion that a small unnoticed disturbance could eventually cause an unstoppable storm was the first discovery to tell us the world is less predictable and controllable than we'd like it to be one of the mathematical roots of modern anxiety ii was uncovered in russia by alexander lyapunov he was studying the transition from stability to instability in fluids but doing so during the great upheavals of World War one and the Russian Revolution the a panov was studying the way a fluid or gas becomes turbulent it was one of the most intractable problems in all of physics and he was trying to put a number on that transition from order to chaos he was trying to understand how our systems seem to maintain their order almost resisting change but then reach a critical point at which they seem to flip suddenly from smooth to turbulent from order to chaos what we now call tipping points this move away from the idea that the world is ultimately predictable to one where is unpredictable is mostly associated at least in the climate and environmental world with this idea of a tipping point so this idea that you push the system and it goes basically how far it moves how far it changes professor peter Cox is one of the UK's top climate change experts and an adviser to the government in that case you imagine a system so you're rolling a ball up a hill you know if you roll the ball up a hill here and you let it go it's going to go back down this way but say there's a there's a peak on the hill you roll up so far away at this point it can go either way and then of course if you're at the top of a hill you can push it a infinitesimal amount and you'll be off and there's no relationship between the ultimate displacement and how hard you push it so it's essentially an unstable system the apple of work had begun to put a number on this moment of instability the moment when the ball at the top of the hill is pushed over when the orderly boom of smoke suddenly becomes turbulent most people when you ask them what is dangerous is is falling off a cliff right I mean and that's the equivalent of a tipping point right it's where the system changes and you can't go back but while the a panov was still trying to understand instability his life was approaching its own tipping point when the chaos of the Russian Revolution and World War one overwhelmed him personally tens of thousands of War wounded had been pouring back from the front and brought with them an epidemic of tuberculosis when his wife became infected the a panov tried desperately to save her but on October the 31st 1917 she died in his arms hours later the same day he put a bullet through his brain when Caray had discovered that our world might not be as predictable and controllable as we have thought the upon Ava's work had put a number on the moment of transition from order to chaos and opened the door to the modern idea of the tipping point between them they had discovered what could have been the beginnings of a new and profound understanding of the world that chaos it a part of the system of justice breakdown but Lyapunov was dead anchor a never took his work any further and the rest of us we wanted only to believe that chaos and unpredictability were just a nightmare from which we could wake we stood at the place where a clearer understanding branched off we did not take it the war had shaken our old faith somehow it had to be renewed and to do that a new icon belief had to be found Henry Ford's assembly line walls that icon it became both the symbol and the means by which we believed we could engineer a world of stability predictability and prosperity we began to see the world particularly the human world the economy in its image no longer a world which might veer out of control but one perfectly balanced stable at equilibrium which had the dependable and changeless nature of a machine they fell back to classical physics so equilibrium systems where if you like there is a fixed amount to spread professor Paul or Broad was for a decade director of economics at a henley center for forecasting and is today a respected author and consultant and they use the mathematics of that to try to explain an account for a very elaborate theory of how economies would actually allocate resources a most efficient way but it was a fixed set of resources they were concentrating on and an equilibrium concept which they borrowed from classical physics before Poincare a made his discoveries once we had imagined the economy as a machine it was a small step to believe we could engineer it maybe even control it the idea of an equilibrium system became required embedded in economics as a description not merely of the market economies of the West but also of an idealized centrally planned economy running like a machine in complete equilibrium and for a while it worked in the Roaring Twenties the cars rolled from the assembly lines and the tractors plowed the land again and the Pioneer aimed the plane a wave of optimism flowed from the factories and fields of the new world the world and we seemed to be back in control but only for a while we may have wanted to see the world and the economy as a machine stable unchanging at equilibrium but how we wish the world to be and how it actually is are not the same this is the massive fissure carbody factory in detroit once it was part of the seemingly indestructible US auto industry part of the good times which we thought would never end but in 1929 they did Adaline still blow when the Sun still bakes the land he does practice control and conservation without warning the world reached not one but two tipping points the climate and the economy both merged without warning without obvious cause an equilibrium to Keynes the nightmares of the Great Depression in the Dust Bowl were upon the Great Depression of the 30s was a major problem for equilibria economics the labor market for labor for hiring and firing people wasn't an equi Librium because morning for people didn't have jobs and yet even this was not enough to get us to give up our faith in the world of order equilibrium and control according to the equilibrium view of the world they couldn't be anything inherently wrong or unstable with the economy people themselves as to caused the breakdown but the basic argument it still remains the same today is that people where a sense weren't really involvement they were they weren't unemployed because they'd been sacked they were choosing to take it's incredible this is true they were choosing to take leisure and be unemployed rather than work that was the core of the explanation that people were making a rational choice between consumption and leisure so essentially the Great Depression was essentially an extended holiday for tens of millions of Americans but certainly many in a major academic economists including some Nobel Prize winners subscribe to this theory the experts at the time found it impossible to imagine that the Dust Bowl or the depression were in part caused by inherent instability or tipping points in the system's themselves another decade of reckless use the grasslands will truly be the great American desert there were no tipping points the cause we decided was reassuringly simple mechanical I think when we were thinking in a more linear way about the world we tended to look for causes that fitted outcomes actually if you're talking about instability of course I mean say you've got a pencil balanced on its end doesn't really matter which breeze blew over something was going to blow it over so you could say well that particular eddy caused this thing to tip but really the only thing that matters is is going to tip anyway it was unstable and so when you get to the view of the world having these bifurcations tipping points then you in a sense the causality is less critical it's just that the system is going to change but while we were adapting to changes in environment we paid the price of feeling insecure despite all the chaos and turbulence of the 30s despite the blighted lives and misery economists and scientists continued to see the world as they always had believing that the uncontrolled would one day be brought within our grasp it was the invention of the computer at the end of the war which suddenly seemed to promise a level of understanding and control we had never had the assembly line had been the icon of the 20s here was the new icon of power prediction and control same 64 take 2 in the 40s and 50s we got our first glimpse of that icon at work when the military unveiled the top-secret technology that had helped win the war this machine is as McCarron as it looks ENIAC was the first all-electronic high-speed computer which was ever built in the whole world the only difference between a human being and the ENIAC is that the ENIAC is much faster the very first job the technology of tomorrow had been given was the old military task of calculating angles elevations and velocities of the firing tables but it was soon essential to a new and frightening power you are firing tables for the army and all bombing tables for the Air Force my gun is pointed towards an enemy we have done some computations to tell the artilleryman how to direct this gun in order to help a certain target when compared with God not only was the computer calculating the aiming and launching of the bomb it was also the only way of doing the vast calculations necessary to understand the explosion ourself yield 15 kilotons unlike the situation with an implosive weapon Messiah you're able to observe fireballs growth from a body of fissionable material sighs it's not just return proving theorems myths give us some power over nature the old Newtonian magic ballistics was married to the godlike power of the nuclear age if we could control such pal was there anything you couldn't predict and control it's hard for us to imagine I think what the effect of the of the atomic bomb must have must have been at the time and that something seemingly so small actually could have such a devastating truly horrifying and devastating effect and we could control it so that you know we had control over it the nuclear age brought with it fields but also a feeling of tremendous power and possibility I think there was a kind of an optimistic peak if you like in terms of what we thought technology and science could do probably in the middle part of the 20th century in the 50s say and I suspect I was associated with all sorts of technological developments but also with a sort of cultural autism that came probably after the Second World War the idea that technology was going to solve a lot of the problems that we had previously in the 1950s the future was going to be a planned utopia of wide boulevards shining skyscrapers where we'd all be happy and prosperous and the engine of this new prosperity uncertainty was to be the computer justice the telescope had let us see the heavens and the microscope the building blocks of life so the computer promised a letter C into and maybe even control another dimension the future James Lovelock remembers those heady times there was that wonderful sense of certainty in those days about everything look where we've got this you know the future is terrific we can do all these things and it was wonderful everything was so simple and so possible the sky was the limit suddenly we could do computations the unaided mind never could solve problems we had never solved just build a bigger computer and even the unpredictable would be predicted no more dust balls now we would predict and control the weather no more economic crashes with the calculating power of the computer policymakers believed they could now predict and control the economy affecting the lives of millions they believe that they finally now got the theory got the statistical tools with the power of the computer to once and for all understand how the economy really did operate policymakers believed that these were if you like laws of economics in the same way that there are laws of physics come after the traumas of the 30s and the war of the earlier in the 40s the West economies perform spectacularly well for a very long period of time I was totally unprecedented prosperity very low unemployment and in everybody exude confidence turning in the direction of a new world that symbolizes man's dreams prophecies hopes and aspirations in the distance we see a government and corporate films confidently portrayed a future of equilibrium stability progress and prosperity but at the same time that scientists were competently predicting this floorless future a meteorologist called ed Lorenz discovered something in 1962 radically at odds but while the military were focused on trying to predict the weather day to day using vast computers to do it Lorenz using an early desk computer built a simplified model to look at the underlying mathematics to see if the weather had hidden patterns the reigns's discovery came when he ran his model first with one set of numbers and then again with what he thought were the same numbers but which the computer had rounded off making them minutely different he put in what he thought were identical numbers but the the the starting number were different by just a tiny tiny amount so there was no reason of him to think that it would actually end up being very different what Lorenz found was that the tiny differences in his starting numbers instead of having no effect dramatically changed his results things look like they're all carrying on very nicely and then they suddenly all behave in a very odd way and the numbers don't do what you think they're going to do you know you imagine these two parts going along just and there they're just nudging each other and it becomes a sudden point where suddenly one of them goes off but actually that happened the fact that that was going to happen was right back here it wasn't where it happened one of the most fundamental assumptions which every scientist from Newton onwards had made was that a small error in a large system just disappears it has no consequence like a small imperfection in a single part on the long assembly line but make no significant difference to the final out it is this critical assumption which edy Lawrence's work turned on its head Lorenz is accidental discovery had tremendous implications for the real world he could suddenly see that when assistant changed it needn't be because at that moment something had caused it to change it could be that the seeds of its destruction had been slowly growing hidden in the mathematics all along the moment the system diverged was the end result of a tiny unnoticeable change a long time ago Lorenz had rediscovered what Poincare a had merely glimpsed he called it the butterfly effect so if you have a butterfly flag flapping its wings the effect will be very tiny at the beginning you will see nothing and then after a while it will change some fluctuations in the air some fluctuations in turbulence and then if you wait long enough like six month it may have a tremendous effect the computer which had been heralded as the engine of stability and certainty have become the engine of instability and uncertainty so computers allowed us to explore things that we used to throw these terms away you know mathematician said well that's too hard or just assume it's not important we can't do that bit so let's assume it's not important and you end up with a linear system which reinforces your view that the world is this kind of quiet place generally speaking where we're nothing really surprising happens and we'll be fine and we just need to know how it works and we can work everything out to something where you the computer allows you to put back in these terms or Lorentz was basically putting in terms of previously would have thrown away and it turns out they change the system altogether into certain ease predictability it's just a brilliant demonstration accidental demonstration of chaos really in the system it is the function of the United States weather bureau to gather information untouched condition the question was how much chaos was there in the system and to give advance warning when human life and property are threatened by high water how many aspects of nature did this new mathematics apply to was the unstable turbulence of natural phenomenon simply because they were complicated in which case one day we would sort them out or were they governed by the sensitivity to initial conditions of the butterfly effect believe the smoke the fire will continue to move unchecked through the night just how chaotic should we expect the world to be and by the late 60s these suddenly seemed very pertinent questions in these turbulent times just as Lyapunov had been drawn to study instability during the Russian Revolution mathematician David rule was drawn to study the onset of turbulence we proposed that hydrodynamic turbulence was associated where there is this sensitive dependence on initial condition but it happens almost everywhere that it happens all the time turbulence was thought to arise because of the sheer complexity of the phenomenon ruel through a combination of experiments in mathematics proved the turbulence was not the result of complexity but was caused by the mathematics of sensitivity to initial conditions the butterfly effect and turbines were everywhere this is not completely a coincidence that I got invested in this program in 1968 these were the may 68 events this was an atmosphere where questions were asked that would not normally be asked the times became wrong because the mathematics was there because the computers were there and suddenly there was this enormous ly interesting experience of interacting with people in different disciplines mathematically turbulence and chaos were established and psychologically were making it harder to pretend the world was still Newtonian the language of chaos was beginning to enter our vocabulary the notion of chaos has been around since the early part of the 20th century and before that actually it wasn't called chaos until later I guess in the 70s and that's when people really grasped it you know this idea that there was this thing that we could call something that was that was indicative of what we could see in the world that we could use to excuse all sorts of things we couldn't predict by the late 60s and 70s the optimism of the 50s was in retreat once again the man-made worlds spun out of control there was social political and economic turmoil from Paris to Detroit and while ordinary people were shocked by the events what was shocking for the experts was their failure to predict them so he's a terrible shot when it did it was really very hard from the take people thought they'd understood it and it turned out not to be true in the late 60s and increasingly was moved into the 1970s all these laws broke down really quite spectacularly because he weren't lost he was simply statistical relationships which happened to hold for a relatively short period of time economists had thought they had understood the laws that govern how the economy worked and thought this then gave them the power to predict what would happen and what's clear is that forecasts only work when any sense almost anybody could make a good forecast when the economy's state when it's going along very nicely anybody can make a reasonable projection then and be reasonably correct what forecasts are very bad at when you precisely need them when there's a major tournament when there's a recession and the track record and forecasting recessions is really appalling it's essentially non-existent the turbulence of the 1970s convinced the economists as well as the environmentalists that their faith in large-scale prediction and control was just wrong they came to accept they would no more be able to control the economy to make the weather the era of command and control was over but there is a second or controversial parts of the mathematics upon which they fundamentally disagreed ruel and others had found that even very simple systems such as pendulums driven by a motor or double pendulums where two are connected together could give rise to highly complex chaotic babe and now as they use these simple systems to explore further they began to discover the rules of this chaotic world they found that the more connected and interlinked systems became the more likely they were to become chaotic and turbulent and that the more you pump the system the faster you ran it the more chaotic it would become and yet in the real world this is exactly what began to happen on October the 27th 1986 computers connected the world's financial systems together into a single global economy and the modern free-market was born there was a lack of confidence more in planning that's what came came about the idea that you could discover these relationships and quite rightly a lot of skepticism crept in from policymakers and the idea that we could somehow quantify this so in a sense we then went back to first principles and said well if we leave it to markets your markets will in sense not solve the problem and we needn't be as interventionist at the same time the computer was allowing us to understand this interconnected world it was also building it and driving it faster and faster and so there was a feeling just empirically that the idea of leaving it to the market was very soundly based but it wasn't just justified in equilibrium theory but mark is clearly worth delivering and they did dramatic results in terms of prosperity increases in lifespan this is the point where the environmentalists and the economists start to diverge from each other because for the economists it's all about bigger faster global they'd learned the lesson that the economy was not something they could just control instead they started to see it as a kind of natural system that you absolutely must not regulate which fed right into the new free-market ideology which declared you cannot fuck the market the global financial economy began to grow as never before but as it did so did its unpredictability from the point of view of stability control predictability it is a bad idea to drive a system to its limit to warm up the atmosphere to make mark to put more complication in the economy I think the issue of growth is obviously cut is the heart of economics but it's also at the heart of the climate problem the more you mess up with a nonlinear system the more likely it's to become chaotic the records of the meteorologists give cause for concern the mount we have economics forget about the environment we dump stuff in the environment use it we have environmental change and climate change which is like driven by humans but doesn't react back/on them that's quite odd with really the way the world operates which is that eventually your economic growth could be stopped by the impact shell on the environment because environment is the source of our wealth ignoring the warnings of the new maths we instead stoped the system for all we will work the free market economists assured us their model said we could simply leave the markets to their own devices and they would magically find their natural equilibrium the empirical models that economists use to make forecasts of the economy which the general public relate to in a sense these are throwbacks these are dinosaurs so the models of the sixties when they appear to work they're still searching even now if you like for empirical regularities which they believe will enable them to make successful predictions of the economy now one little tweet one little clever bit we can really discover what this law actually is and the forecast still rely ultimately on that same approach and it doesn't work now it never will do we live in a world that is increasingly going away from anything like an equilibrium or a steady state I mean you won't know to have growth 2% 3% more and this means exponential curves something that we know cannot last forever if something goes exponentially it must break down at some point that is something that can be predicted with safety the process must end somewhere how it will end I don't know our leaders tell you that we need two or three percent growth per year and this is necessary for the well-being because it may be necessary but it cannot be maintained forever exponential curve is basically a linear thing and the claim is that nonlinearities will put a stop to this exponential curve that is factual for over a century now we have not wanted to hear that the promises of prediction and control might be bankrupt not even wanting to admit the evidence of our own eyes this is the Detroit Public Schools Book Depository where the promises to the next generation were stored this is what has happened to it trees growing out of the rotting remains of yesterday's dreams all life is interrelated we are caught in an inescapable network of mutuality tied in a single garment of destiny whatever affects one directly affect or indirectly as long as there is poverty in this world no man can be totally rich even if he has a billion dollars Martin Luther King 1961 in there dream is gone someone finally woke up like this shit the American Dream is you bleep whatever mr. George Bush says he's full of crap there's no more dream you know it's you're afraid to dream now try to work on minimum wage job paying your gas your mortgage food you can't do it and I don't have those savings account no the only thing I deliver by the day basically you can't you can't get ahead around here how do you tell your child we have nowhere to live how can you tell your child we're not gonna have anywhere to live wake up in the morning and tell your kid all you can t dinner tray because there's no money for it that's unheard of because we can't pay our bill no and it happens though by the day around here why is he getting thrown off his house I don't understand it because it's not make enough money I'm its bottom line the loan you didn't default on your long the long defaulted on you you're right making payment they charge you extra because you're late I don't have money to begin with how you charge me more to be late I got a money that's my penalty then it's no making sense to me you know there is no communities a more spatially everybody for himself around here I don't know I'm just no commute no no there is how could I be a community look at something that's empty that's empty where's the neighbors at there is none you got two on the corner one in this corner there skip to house the next three houses are vacant across the street in here some down the street so it's been very badly here today the rate of change is increasing and our ability to predict has decreased is it any wonder we have become more anxious I would say that the sorts of ideas that you're talking about in terms of chaos theory and butterfly effect and global warming and all those kind of things that are happening that are causing people anxiety it's not just the words it actually has an impact on how people think about their lives it has an effect on what people look for in life and on how they kind of frame their thoughts and ideas about themselves and what they can control and what they can't control what worries me is that this is really quite a nihilistic kind of vocabulary it's a kind of a it doesn't give people a sense that there is something that they can do the problem with the mathematics of kales is that it doesn't offer us a new plan for how to achieve what we want prediction and control it takes away what we want to believe denies us the old icons of salvation of freedom through growth it gives us nothing comforting in return ah we're all living in a much less predictable more unstable world the question is what we want to do about it on the one hand the economists insist that because we can't regulate and control the economy the way we used to think we could our only salvation lies in obeying the market and going for growth anything else they insist will lead to economic chaos and collapse on the other hand the environmentalists say that it is precisely this unbridled economic growth which will push the world's natural systems to their own chaos and collapse from which there will be no coming back for most of the last hundred years despite the warnings for mathematics and history we have refused to see reality as needs this is a picture generated by the mathematics of that reality it is called a Lyapunov map it shows not the orderly and predictable reality we always wanted but an unstable and chaotic it is a distant descendant of Lyapunov original work the map shows regions of stability and others of chaos in a system between them other points where the system can abruptly tip from one to the other no one wanted to believe the economy could lurch from boom times to bust but it has no one wants to believe the climate could be approaching its own catastrophe but when it does it will affect us all the rich the poor the guilty and the innocent you know in the climate system there's this idea that there might be a tipping point associated with a certain warming pushing yourself up this hill with warming where the Greenland ice sheet would melt and we know on the other side in the long term I got 72 sea-level rise to deal with in other tipping points for example the possibilities that the Amazon rainforest could be badly affected by climate change that could happen quite quickly associated with fires and things like that as far as human systems are concerned them an adaptation the rate of changes at least as important as the final end point and it's really focused we limited how fast we can react the question now is if we have any time left for self-delusion a lot of ice up in green James Lovelock is the godfather of the environmental he fears that even today we still haven't really learned the lessons of the mathematics and we still want to believe in prediction and control with is the floor of the great climate models we have at the moment they all imply that if you could reduce the carbon dioxide bring it back stabilize it at some level all would be well we could handle the situation I think this is nonsense I think once you the system have started to slide there's no going back and I like to think of it not so much as a tipping point but as a slope that gets ever steeper and at some point it gets so steep you can't hang on any longer that's what you would see instead of at a tipping point yes it sounds worse well it is bad it's very bad and the tipping point all implies that well maybe you could tip it back the slope implies you can't is gone too far if you look at the Earth's history the climate goes along more or less steadily at some state either very cold as in an ice age and then it comes to a point where it slides over then goes up to a stable state the interglacial it's also in the past has gone upwards to another stable state a hot state and it did so 55 million years ago when about the same amount of carbon dioxide went into the atmosphere as we are putting in and it jumped 5 degrees quite suddenly and as you say you can't you can't pull a lever somewhere and make it go back well it took two hundred thousand years for it to go back after the 55 million year ago event and yet the carbon dioxide went down but it didn't get the temperature didn't it stayed up for that long which undermines the whole notion of control doesn't it it does it does indeed and I think it's a false notion at least I think they should think about it being a false notion I can't be certain in what I'm saying only if I come on very strong it's because I am so concerned about their certainty about their models and the way politicians are taking it and letting them form the basis of policy I think that's almost absurd your image of the slope where do you think we we or the the system we're in ease on that I wish I knew I suspect we're just about to drop off but I may be wrong we're maybe a little bit further back up the slope but I'm not sure don't see how we can do much about it I think one of the crucial bits of the system which everyone knows of change is the floating ice in the Arctic Ocean as you probably know last summer 60% of it went missing we'll see not many years perhaps little as five perhaps as much as 15 it'll all be gone when it does you can work out the back of an envelope what difference this makes to the heat load of the earth and you'll find it's about equal to all of the co2 we've added to the atmosphere to date in other words heating doubles when by the time that ice goes do you think there's any going back and we put had ice but no no way we can't put things back can't make right what is already wrong we still on the road to chaos but are once again standing at that place where possible futures divided only this time we have had a hundred years to learn the lessons of the mathematics perhaps this time we will be able to do what we could not back then face reality as it is for that reality is staring us in the face Marcus DeSoto continues his journey to the story of maths here on BBC four at 9:00 on Monday but next tonight it's comedy hour and time for that Mitchell and Webb look


  1. Earth and the Universe is under CHAOS. Look at our history of religoun promising love,change enlightment but in reality it is the reverse and to add to this injustice Humanity that promote religoun inssistes that it is all WELL. No we are in CHAOS period like it or not .

  2. I dont know why comments are negative… even emotional … almost personal… tf… math is not an uncle sam dressed nazi philosopher bent on twisting one's political vote so as to perturb the economic systems weathering large scale doom unto post modern GOP conspiracy solutions with which democratic initial conditions and anxiety regulate calculations of mathematics' predictability fundamentally warming scientists and concepts of controlling a linear graph to which one stares at … blankly, thoroughly and with uncertainty.


  3. Climate change "was just going to change anyway" hence, mankind's influence (the eddy of wind) is irrelevant. 24:45

  4. This documentary is really bad. It twists science and mathematics, here's a much better documentary : https://www.youtube.com/watch?v=d5Hv6-oJEqI

  5. Lesson the world is design to go from order to chaos to order to chaos to order to chaos. Hegel was right in his Thesis.

  6. The BBC claims to care about global warming but they deny the impact animal ag has on the environment and human-induced climate change because they're in bed with the meat, dairy, and egg industries.

  7. The comments on here are shameful and so philistine its heart breaking … if you really want to learn more on this topic, https://www.thegreatcourses.com/courses/understanding-complexity.html

  8. We are living in the Cambrian explosion of technology the same way that in a blink of an eye in evolutionary time there has been more advancement in technology in the last 100 years than in the previous 200000 years of homo sapiens history that is 0.1% of human history and is accelerated by an order of magnitude

  9. Government regulation of the economy creates further interdependence, increasing it's chances of failure. You cannot plan an economy, the necessary result is a genuine free market, without bailouts, without central banks, to minimise the dangers of recessions, and to make them less likely.

  10. I really can't watch this. 20 minutes of… "Well we think the universe isn't deterministic, even though it seems to be, because we don't have mathematical formulae to represent the entire spectrum of mind-boggling variables that affect everything!" Sorry, but that is the WORST reason ever to assume that the world is actually chaotic at the deepest levels of reality, when science clearly notices a trend between more complicated mathematics coinciding with many more variables. Even quantum mechanics uses DETERMINISTIC mathematics. What math is he talking about that isn't deterministic? Go home, documentary, you're drunk on assumptions and new-age nonsense. -Sincere Scientist

  11. false in assumption. politics diffusion not scientific. worse then religion (bible and what the priest tell us is an example of impertinence diffusion). you are so full and incompetence. and you are creating the anxiety by putting pressure on others and gain your own furry and the population mass blocks. you should look a bit about what is root of the anxiety in medicine and after you should look at your self impertinence. and of course is chaos, I would like to see pertinence before drawing yours fractal. The butterfly effect is what you just made with this shit of impertinence. shame on you

  12. Prediction is not the same as control. Just as the ability to split atoms and build factories is not the same as "God like" power. There's a theme of limited thinking about complex systems running through this doc. We call it chaos but really it's more like more factors than we currently know how to calculate for.

  13. Prediction is not the same as control. Just as the ability to split atoms and build factories is not the same as "God like" power. There's a theme of limited thinking about complex systems running through this doc. We call it chaos but really it's more like more factors than we currently know how to calculate for.

  14. heh heh heh Actually I like this presentation explaining chaos theory as it relates to the modern world at hand. Very valiant effort! I would say that "Tipping point is more of a slipping point and where as you had some measure of control on the assent you are in quite the opposite predicament on the decent. HAHAHAHAHA I suggest you all grab you surf board and ride the wave which is chaos! Hail Eris full of grace, leading lady in this place, holy queen of outer space. 馃槈

  15. wow, what idiots.聽 the crusty old fuck near the end said that 55 mya the co2 went up, and then the temp went up for 200 000 years after that even though the co2 went back down soon after it went up.聽 uuuuh the answer is right there in front of your face-c02 and temp increase are not correlated…..fucking gaia sjws can eat my nutsack with their carbon tax selling propaganda.

  16. capitalism must be replaced if we are going to adapt to change, or chaos will replace order those who have profited are pushing the limits of our ablity to control things. it is not enough to reduse co2…

  17. to claim that 2008 was the result of unpredictability is either stupidity or spin – or, as in the case of the BBC, both… but 12 minutes in, it becomes clear that this entire show is nothing but a show – disinformation writ large.

  18. Steven Bannon and Citizens United never heard of these ideas. In their documentary Generation Zero, they think they discovered math that predicts the cycles of the economy and revolution. Part of their mathamatical prediction says that blood must be shed per every certain number of cycles.

  19. From some of the comments I have read here there appears to be a fundumental misunderstanding of what this doco is trying to relay. Inter-related systems are chaotic. Once a system approaches a bifurcation point, its behaviour becomes chaotic. This has been demonstrated in both economics and in climate systems & the environment. Towards the end of the doco there is a statement that exponential economic growth relies upon our exploitation if our environment. I think this is a very resonable hypothesis. For those interested in Chaos Theory and would like a non-mathematical intro I'd recommend James Gleick's book "Chaos". For those more mathematically orientated I'd suggest Order Out of Chaos by Nobel Prize Winner, Ilya Prigogine and philospher Isabelle Stengers.

  20. Ignore all the right-wing comments about this – I used Chaos Theory for my Masters. It was just coincidence that Lorenz was studying weather systems, not some "global warming conspiracy". Chaos Theory applies to so many other disciplines if you watch the whole documentary. I don't really care who the narrator is – he's reading a script, which is clearly well written – a documentary well worth watching and one of the best "lay-person" descriptions of Chaos Theory and it's implications.

  21. This guy sure sp-ends a lot of the time showing artsy-fartsy stuff that doesn't do anything to advance the stated purpose of the video.

    Also, I think he's got a pretty simplistic view of the progression of…well…everything. I sup;pose it's not bad fiction if you like your fiction to be pretty…'pretty'.

  22. Science of unpredictability and uncertainty, one of the basic principle which rules out existence or omnipresence of god!! If god was there, then there is no chaos, otherwise, there is no god.

  23. Everything is interconnected. It is impossible to have the same initial conditions in two different trials. The law of identity says that nothing is the same as anything except itself, and this applies to situations. Unfortunately, this does not bode well for scientific methodology, in which all variables must be controlled, or for this "mechanical philosophy", the Newtonian sort of point of view that the universe can be broken down into discrete "things" for which you can apply principles of "cause" and "effect" and so gain definite understanding of objects in the universe. On a fundamental physical level, there are no discrete things as such. It's because reality is one system, and to predict anything exactly and without any doubt, one would have to take into account every detail of reality. In any smaller system, abstract as perceived by the human mind, the butterfly effect emerges as a result of minuscule, unpredictable components of the system eventually adding up, exponentially, to make large, system-transforming effects. It's not spooky, it's not a ghost in the machine, it's the things which we have been unable to factor into our calculations, the things for which doing so approaches impossibility, both because of their sheer numbers and the difficulty in detecting them.

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  26. If only the people with wealth and power in our day actually had concern for others or our planet. Most are trapped by ego and materialism without soul consciousness or spirituality.

  27. Haven't quite finished this vid yet, but one thing strikes – there is no mention of Heisenberg, Uncertainty Principle > Probability Theory, where the behaviour of large numbers of particles/people/etc are predictable to a large extent but where the behaviour of individual particles/people/etc is not, which might seem a bridge between the old Predict-And-Control and the more recent worries from Sensitivity to Initial Conditions and Unstable Systems ? ?

  28. Pause at 15:18-19 ….Who is she ? What happened to her ? We now聽have the ability to view partial moments of the past. Time travel is now.

  29. What I can't figure out, is that after billions of years of random chaos we have, somehow, 聽ended up with Nachos Bell Grande at Taco Bell.

  30. Like cliff swallow colonies, we continue to burrow and dig, until one day, the entire cliff face shears off..

  31. Yeah good luck try to explain to most people, either Democrats or GOP… ignorance and ego are what will trap them forever

  32. "Mathematics created anxiety".聽 This is a stupid premise on which to base a 59 minute documentary.聽 I will watch, with interest, to see this argument being proven.

  33. A good piece of quiet propaganda, with soothing music and oh-so muted rationality about how we humans do not deal well with 'chaos.' This documentary is very much a re-wording of Marx's critique of capitalism's "anarchy of production," but then, this documentary says not one word about the actual history in the 20C economics of government-mandated ownership and control in a planned economy, which resulted in 115.3 million dead, mostly innocent women and children who were starved to death by their socialist governments [since the early 20C, all famines have been government-made]. This documentary never once mentions that the worst environmental polluters in the 21C world are the present socialist economies, or that the most amount of improvement in environmental protection during the last forty years has been accomplished by the market economies. The opposite of anarchy and chaos is order and discipline, and that's what makes this documentary the not-so-subtle propagandist, clarion call by environmental socialists: they will relieve us of our "anxiety" once they are in power to impose order and discipline over the chaos in the environment. Oh, and not incidentally, the "butterfly effect" mentioned in this film actually reveals how chaos results in regularity, which completely contradicts this documentary's argument. A true-believer, whether socialist or religious, must filter the full facts or tell complete lies or blindly ignore their logical self-contradictions in order to make their proselytizing propaganda appear to be an intellectual argument.

  34. Oh my, the title of this documentary should be: "Let's travel across the US and France to keep us seem like busy government workers while pushing an environmentalist and leftist view of the world by vaguely using the mathematics of chaos."

  35. well, unfortunately human history is full of people with the noblest of intentions trying to open the eyes of the blinded and brainwashed by powerpsychopaths in high positions of decision making that which don't want things to change, for they feed from this chaos; sometimes they are the ones to instill chaos where there was some kind of order just to increase their power even more!

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