CHAOS Theory Documentary

[Music] form and chaos order and disorder like rifles competing for supremacy in the vast arena that is our universe Nature throws grotesque shapes and turbulent events at us and yet within them we strive to find evidence of patty's we can classify and understand for centuries man has struggled to impose order on a perversely irregular world and what he couldn't understand was often ignored now armed with a new weapon the computer man is at last challenging the kingdom of chaos describing the shapes and forms of a world where the only straight lines are the ones he was introduced the new science is emerging from this challenge the science which promises to describe and explain the infinite complexity of the busy world in which we live it's a science which is producing a new geometry that offers an insight into the surprising paradox that there is order even within discipline is the science which is turning conventional thinking on its head the science chaos [Music] mercurial and capricious storms flipped ghost life across the earth an uncaring of the consequences cause heat waves in Sydney and hurricanes in Kent these are the satellite pictures which show the hurricane of October 1987 sweeping north from the Bay of Biscay towards the south coast of Britain the aftermath of such an event is a harsh reminder that weather is one of the more unpredictable features of our daily life for a hundred years scientists have struggled to find the rules that govern our weather hoping that this would enable them to produce accurate long-range forecasts we now know that they struggled in vain but even with today's technology the task is simply too the European Centre for medium-range weather forecasts is the most advanced meteorological center in the world here they try to make sense of the diversity of our weather every day a hundred million measurements gathered from around the world are fed into an enormous computer model of the atmosphere what we do is divide the atmosphere up into segments that are about a hundred kilometers by hundred kilometers in the horizontal and about one kilometer in the vertical and it takes about a million of these segments to represent the whole the whole atmosphere and every day we run the model to produce a weather forecast for ten days into the future now on this the present machine which is essentially one of the most powerful computers in the world this takes about three hours just under three hours of computing time to produce a 10 day forecast now to give you some idea of the complexity that's involved with all these interactions going on every second of that three hour integration period the computer performs about 400 million calculations as recently as 20 years ago this ability to compute 400 million calculations per second was simply inconceivable indeed in 1959 meteorologist Edward Lorenz was more than satisfied with the 17 calculations per second that his brand-new computer could perform with it he made the discovery that gave birth to a new science the computer that we did our original work on this while McBee LGP 30 here with a console and the working portion here this was a medium speed computer in its day we first got a hold of it in 1959 it sounds rather crude by modern standards because the computer took 10 whole seconds to print out just one line of data we had condensed the number so it printed things out to three significant places all they were carried in the computer the six but we didn't think we cared about the last places at all so I simply typed in what the computer printed out one time I decided to have it printed out in more more detail that is more frequently and I let the thing run while I went out for coffee and a couple of hours later when it had simulated a couple of months of data I came back and found it was doing something quite different from part of the done before it became obvious that what happened was that I hadn't started with the same conditions I started with round off conditions so that I started with the original conditions plus extremely small errors but in the course of a couple simulated months these errors had grown they doubled about every four days that meant in two months they'd doubled 15 times a factor of 30,000 or so and the two solutions are doing something entirely different and I have some of the original output here from the computer what I've done it did with the print symbols and then go over it in blue pencil also Illustrated and this is one of the graphs that I obtained if you look at a fair stretch of this you see that there are certain typical things that this particular system of equations does it has rather pointed minima if brother extended maximo with little waves in them but it doesn't do exactly the same thing twice it does one thing then it does something like it but something that isn't quite the same it's a bit different the desktop weather from this second slightly modified computer run appeared tantalizingly familiar Lorentz studied the new data looking for regions where the output appeared to match the first run and yet although many of the peaks and troughs looked similar to the first printout when he tried to match them up the patterns soon drifted apart Laurentiis computer had a message for him and science what Lorentz's work tells us is that no matter how complex our models become a no matter how good the initial data becomes there will be a limit beyond which we cannot provide accurate forecasts of the instantaneous weather the discovery has since become known as the butterfly effect because in theory even the tiny disturbance in the air caused by a single butterfly in flight can tip the balance of our weather and create a chain reaction straddling time and distance ultimately altering the course of a tornado on the other side of the world it's an effect which is upset quite a few scientific Apple cars since it means that even the tiniest errors of measurement make accurate prediction impossible in many if not all physical systems until quite recently we explained the world using the rigid geometry of the Greeks we lived it seemed in a clockwork universe governed by immutable laws they were the laws of motion first identified by Sir Isaac Newton in the 17th century initially he described how gravity rules the motion of the planets subsequently it was believed that all physical systems obeyed these laws and that the key to accurate prediction was simply accurate measurement in fact this new natural philosophy seemed to lead inevitably to a conclusion first proposed by French mathematician pierre-simon Laplace but if you could exactly measure the position and motion of every point in the universe predicting the rest of eternity would be simply a matter of doing the sums towards the end of the last century Laplace is compatriot Bari Poincare a began to realize that if the universe were driven by clockwork then it ticked in a complex and even unpredictable way applying a new geometry to Newton's laws of motion he tried to reach a deeper understanding of the dynamics of nature but time and again he came to the edge of a mathematical abyss face-to-face with unpredictability and chaos what had happened was Newton wrong clearly Newton was right we've been using Newton for 300 years to predict the motion of heavenly bodies to predict the motion of spaceships etc on the other hand when you try to fine-tune Newton what you find is a little what you find is something that's a little bit different Newton says that yes if we know the initial behavior the initial conditions perfectly then we can predict what will happen the unfortunate problem there is the if we don't know anything perfectly in nature it's impossible to pin down precisely to 15 30 50 million decimal places the position of a particle in space let me show you what this little machine does what we basically have is a little metal ball and underneath this plate are a bunch of magnets so this little ball can be attracted to various of these magnets now it's a very simple physical problem to take the ball and let it go and ask what happens that's a motion that should be described by Newtonian physics yet here's something that behaves totally chaotically watch how the ball goes and bounces back and forth from side to side in a very irregular pattern let me try to start the ball exactly where I started it before right about there I start the ball from essentially the same position you'll notice that after a very short time the ball starts to behave in a completely different manner it's the butterfly effect again in an inherently unpredictable system in a predictable system such as when a ball drops onto a flat surface the behavior of one ball closely matches the behavior of others dropped from the same height there will be small discrepancies but plotting the path of the first ball allows you to approximately predict the paths future balls will take and be right bouncing a ball off some round white pegs changes everything now knowing the path of one ball will not help you to predict what the paths of others would be this is the butterfly effect again tiny variations in the paths of the balls are being amplified on every bounce making prediction impossible this match is igniting a video version of the butterfly effect known as feedback this picture is being generated by a camera which is pointing at its own output on a nearby TV screen if we just shut off that picture you see that as the camera looks at the monitor and doesn't see a picture it won't reproduce one so to start a picture we should somehow ignite it and as we do that here we just put a little bit of light in the center of the picture which is seen by the camera and then fed back into the monitor and the cause has going the process of video feedback but I guess you would like to know do we understand the pattern can we describe how the pattern is emerging and I think the honest answer to that question is no but to convince you how difficult the question is let's change the set up slightly and one way to do this would be for example to just rotate the camera slightly around its axis and maybe we do this at this point and as we do that you see by just rotating the camera about a degree or two the picture resulting and the feedback system is totally different the video camera is scanning the monitor 50 times every second but because the camera system is never perfect tiny distortions to the picture are created by the cameras electronics the lenses and the monitor itself camera distortions represented here by the letter C are added to the original picture to create a new but significantly different picture on the monitor the camera sees this new picture and alters it again each frame changes from the preceding one as the system repeats the process over and over if C changes such as by tilting the camera then the type of image changes this process of repetition or iteration as it's known is something that computers are very good at doing but computers need numbers not pictures so change the pictures to a symbol at and the mathematical equivalent of feedback might look something like this the interesting part is what happens to X when you change C the equivalent of tilting the camera sometimes the variations in X will smooth themselves out and add other values of C X may seesaw periodically from one point to another but at certain other values of C the resulting X's will bounce chaotically in a pattern the sequence one of the surprises of Kaos is that all these different behaviors can be displayed in just one system this computer simulation shows the behavior of a particular kind of pendulum a double pendulum sometimes it will follow a regular path which it will repeat forever it's a prisoner on that path tracing out what is known to mathematicians as its attractor but not slightly harder a subtle change occurs in the motion it still looks periodic and regular but it's not it never actually repeats itself the pendulum has started on the road to chaos and under these new conditions it's now drawn to a different attractor as the pendulum is pushed even more or something quite startling occurs its behavior is now truly a chaotic displaying no apparent pattern and yet still subject to the laws of motion it has started to follow what has come to be known somewhat mystically as a strange attractor strange attractors are the hidden patterns of order in disorder the structure within the chaos this is the strange attractor that lies behind Edward Lorenz his early weather models it's a computer representation of the rules which generated his apparently random results when I first drew up the attractor this was before the tournament a tractor had had been introduced and I think in meteorology you could identify a tractor with climate it's a set of states which do occur as opposed to those which the things that don't happen mapped out in an imaginary mathematical space deep inside the computer those weather states that do occur trace out this beautiful and appropriately butterfly light and shape each point on the light blue lines represents a single condition of the world's weather and as we follow the little red cursor we are seeing the weather unfold in time in the computers mind there are an infinite number of possible pathways which the weather can follow on this the Lorentz attractor and yet paradoxically those pathways never cross even as we swing from one lobe of the structure to the other where then is the chaos in such an apparently well organized pattern the chaos derives from the attractors ability to behave like a mathematical food mixer jumbling up the constituent elements of even a simple straight line until each point on that line is traveling in different directions the line is stretched and folded repeatedly like so much dough this is again the butterfly effect at work but ed Lorentz also indicated that there are states of the weather system that do not occur that are not allowed and that the points representing those improbable states shown here in red as the edges of the cube are like snow in the Sahara or heat waves at the South Pole if they happen at all they can't last and will very soon be pulled in towards the attractor sucked in until the system is once again it's old unpredictable self in the new science of chaos it seems the closer you look the more you see even a dripping tap regular as clockwork indeed the basis of many early timekeeping instruments turns out to have a chaotic trick or two up its piping it is one of many dynamic systems showing a type of behavior that has convinced many scientists that the rules of chaos are universal when you gently increase the water flow the drips start coming in groups then longer groups and even longer groups until the cascade is truly a chaotic amazingly even here it seems there's a mathematical rule at work a rule that describes one of the pathways from order to chaos a rule that has come to be known as period doubling in the period doubling root you start off with the system being in a periodic State a simple periodic state and as you change the parameter this period periodic solution changes its period it doubles in length then it quadruples as you increase the parameter further than eight tuples and so on this sequence occurs very very fast and very very quickly the system becomes chaotic let me demonstrate it by this electrical circuit which is based on a simple radio valve well the circuits off at the moment so the state of the system is attracted towards the most simple possible sort of a tractor you can have at a simple point attractor here when I turn it on the circuit will start to oscillate and you'll see the this state get attracted towards a periodic attractor here's the periodic attractor you saw how quickly the state got attracted towards it now I'm going to change what one of the settings in the circuit and we'll see the attractor evolve and go through a sequence of period doublings there its period doubled let's change it a little bit more there's a period for you see that now there are one two three four revolutions it's go round now let's change the parameter very very slightly and already we've got a strange attractor in 1975 a young physicist was working on the problem of how frequently this doubling occurred in two totally different and unrelated systems although the now-familiar dark regions of order in the unfolding chaotic cascade were no longer much of a surprise when he compared the rate at which each different system was doubling it was clear that something very odd was going on I immediately realized it was the same convergence rate and in fact those numbers were the same which was a completely extraordinary result because what it meant was that there were two completely different problems that I had considered and yet a number came out that in the way depended on either of the problems and then of course you have to start wondering to yourself what then does it depend upon so I said about trying to figure out what it depended upon which produced the theory of period doubling and as a twelve mark has the problem of property of universality which is exactly to say that the measurable things in any one of these very different systems is always decisively to say and this constant about four and two thirds is one property that's the same for all of these different systems to apply the lessons of chaos to complex systems mathematicians draw pictures of the behavior as we watch this circle distort into ever new curious shapes it's hard to believe that they're all even the original circle computer representations of that innocuous equation x squared plus C the equation that gave us video feedback simple rules it seems can produce fiendishly complicated results there is complexity here that was implied but never realized by Newton glimpsed but never resolved by Porcari but this is only part of a much greater object the icon of chaos its mascot perhaps is this strange mathematical creature it has been derived from the simplest of equations and yet it has turned out to be the most complicated creation in the mathematical universe using the computer as our microscope to travel into the valleys and peaks of this extraordinary object known as the Mandelbrot set we see literally infinite complexity however deeply we probe and that turns out to be one of the hallmarks of both chaos and [Music] this unique and paradoxical mathematical marvel is a single image a single image comprising an infinite universe of numbers every shimmering speck of color in each spiral and tail is itself a coded key to other unseen mathematical creatures other new galaxies of color and form this is the Mandelbrot set it lives on the frontier of a new geometry fractal the basic elements of the language affected geometry were known to mathematicians about 50 years ago but at that time they were considered to be mathematical monsters objects only useful to discuss the limit of certain theories but nothing basic in nature and I think that's the true merit of wonderboard - to have pointed out to us and to convince us that indeed these monsters are right things to this point nature the fractal is a geometric shape a geometric shape having a very special property that as you look closer and closer and closer to it you see essentially the same things now let me contrast that with the straight line as you come closer and closer and closer you see all the same thing it is true let me contrast you the circle from a distance it's a circle as you come closer and closer and closer it becomes a straight line it changes and the fractal is something a coastline of a country as you come closer and closer you see more and more of the irregularity of the coastline but in a kind of general way the coastline looks very much the same whether you look at it for a very big distance or from a small distance so you see that two kinds of shapes have this property of invariance the straight line which we all know know everything about and some other shapes which are like coastlines well the fractals are the shapes which have this property and are not straight lines [Music] this computer-generated coastline is a fractal it was created like the Mandelbrot set by giving a computer a set of formulae encodes that encapsulate the shape of the coastline remarkably however much it is magnified however closely you look it always contains an identical degree of kring cleanness many natural objects are fractal in this way every snowflake is different although amazingly they all obey the same snowflake rules variations on a six-sided theme one of the snow figures is branching a fractal on smaller and smaller scales this computer crystal repeats nature's laws [Music] variations in those branching rules differentiate crystals from plants each grows minut differences in form are magnified the butterfly effect at work again [Music] the slow geological crawl of mountain growth is recreated in seconds conjured by the computer magician from fractal moons reminding us of the dynamic nature of these events however slow [Music] in fact we can now create a whole fractal world with fractal forests clothing fractal slopes in a fractal Valley fractal range from fractal clouds bathes a fractal globe resting in a fractal universe and all of it in the mind of a computer [Music] and yet the most complex fractal of them all the Mandelbrot set obey is one of the simplest rules we saw the set for the first time in the middle of night we being my assistant myself and frankly at the beginning we thought that we are dreaming or that something that happened the mistake had happened because never did we expect to find this wealth of structure as a result of formula which was of a ridiculous simplicity hidden within the Mandelbrot set is all the wealth of variety that can be extracted from the equation x squared plus C the rules of chaos govern it on an infinite scale you could magnify it forever and never run out of detail incredibly beautiful if you look at it if you do computer experiments visit if you compute blow-ups of it you always find incredibly beautiful structures which you have not expected or even seen before so in other words one might say that the mandible set is the most complicated and maybe also the most beautiful mathematical object we have ever seen all natural shapes are dynamic distinct from the fixed and Static geometry of man growing and evolving over time the unfolding patterns of nature are dictated by the ephemeral presence of chaos of strange attractors betrayed by the textures of bark and the branches of trees air currents twist water vapor into the fractal shapes of clouds but it's one thing to generate images that resemble real objects quite another to divine the rules that made them that way in the first place this real fern branches repeatedly but can we identify the rule that makes it grow in this way this fern seems to be a perfect copy of the real thing created by a set of rules in a computer again the rules are simple and repetitive they involve a sort of computer gymnastics called affine transformations with them apparently lifelike and yet wholly artificial images may be constructed what then is an affine transformation if I take this picture here and I then bend it oh no bet I know a good way to tell you if you're watching the TV and you move to one side and look at it from here instead look at the TV set from a different angle you actually see an affine transformation of the image on the TV screen it's a lot of the graphics that are used nowadays on TVs do kind of panning in pictures full squeezing out a page there various very simple geometrical motions of of images one was the example of a reflection that's an affine transformation a rotation is an affine transformation and then rather queerer things are them if I take a picture drawn on graph paper and then I skew one of the axes says everything suddenly becomes deformed I just do one axis that's actually carried out an affine transformation the extraordinary fact is that if you keep only the transformations and you throw away the image you forget it your mind is wiped clean then you drive those transformations with a random number generator you drive them it turns out that always you get back the same original image that you started from which is precisely how dr. Barnsley created this computer image of a maple leaf simply by following the maple leaf rules but following even the simplest rules can produce an image of bewildering complexity to play this game the Chaos game choose three points and devise some rules rule one take a starting point anywhere on the screen rule two randomly choose a number from one two or three rule three move half way from the starting point towards the number chosen in rule two sir select a starting point and run the rules take the new point and run the rules again and again and again and again and so on surprisingly what emerges is not a filled-in triangle but a fractal triangle its fractal because as we zoom into it copies of the original are successively revealed receding literally to infinity in the jargon of Kaos this curious triangle is the attractor for those simple rules it's a new mathematics which sheds light on the old and intransigent problems of physics problems such as turbulence in a slowly flowing stream the eddies and tiny whirlpools died out almost as soon as they formed but as the stream quickens the eddies live longer until a moment comes when the turbulence grows building upon itself to produce a flow that swirls and tumbles Wow [Music] disturbingly turbulence seemed to rear its head wherever scientists looked although little was known of how it occurred for decades the theories proposed by the Russian physicist Lev Landau and seemed the closest to providing the answer landau had the idea that turbulence would occur through a sequence of transitions each transition would bring a new frequency into the motion so the flow would become more complicated and after many of these transitions then the flow would appear very complicated but fundamentally it would be no different than it would be after one transition would still be described by a few frequencies we had in mind testing this idea by looking in detail at the transitions to see each new frequency appear it was hoped that Landau's transitions could be made to show up as patents forming and dissipating in a thin layer of liquid trapped in the gap between two carefully controlled rotating cylinders to show the patterns more clearly tiny flecks of aluminium were added to the liquid the question was would the transition to turbulence be ordered appearing at certain clear frequencies as Landau suggested or not we saw that there was indeed a transition where a frequency came into the motion some waves and then another transition where more waves diamond promotional but then the next thing that happened was as we increase the speed of rotation in assembly the next transition was one in which the flow became irregular chaotic we were very excited by this because Landau was one of the great men of the 20th century physics he has enormous intuition into physical phenomena and he was rarely wrong so we we recognize that if we saw something it was different from what Landau heads expected that this this was something that could be exciting and what we can show is that that the flow really does have this property when it becomes irregular that is the flow beyond this point of transition becomes inherently unpredictable you can predict the behavior for the short period of time but the long term behavior is completely unpredictable no matter how accurately you measure the velocity or whatever the crime with us are you cannot predict the long term behavior what Harry Sweeney's group of seen and measured are the milestones that occur on the unpredictable road to chaos for many modern technologies understanding how and when those milestones will occur is crucial whether it's ensuring that the flow of air over an aircraft's wing remains smooth or the turbulent mixing with the atmosphere will occur for certain industrial emissions a knowledge of the onset of chaos is vital surprisingly it's now clear that we need look no further than our own bodies to find turbulence and chaos not only can turb Yulin blood flow damage blood vessels but it can even affect the electrical activity of the heart itself we have often seen the rhythmic electrical pattern associated with the normal ECG but when the pattern changes when the electrical rhythm fails the heart fib relates this quivering chaotic activity is more familiar to us as a heart attack however research in the USA on the ECG patterns of animals indicates that just before the heart begins to fibrillate the normal pattern changes displaying alternating high and low beats when the research team at MIT first saw these new patterns in 1983 they called them electrical alternans about that time mitchell Feigenbaum came gave a lecture to the MIT physics department on period doubling and since the pattern that we were noticing had a period which was twice the period of the normal ECG which is just the normal interviewed interval it occurred to us that perhaps this was a period doubling which may be the first step in the progress to an apparently chaotic behavior the immediate question was whether the period doubling that we had observed was in fact the first in a cascade of period doublings what we did was to take 25 studies and to record on those patients surfer the surface electric cardiogram and to use our computer algorithms to determine whether electrical alternans was present in those patients at to a significant extent we found that in about 90% of the individuals that he was able to induce seriously arrhythmias in indeed electrical commands was present we would hope that we would be able to detect electrical instability you know on the order of 6 months or a year before an individual would you know might sustain tricular fibrillation but this is really projecting far into the future as I say this research is an early stage and we're in the process of testing some of these hypotheses and you know the technique is not it's not in general clinical use at this time no one knows how many heart attacks were caused in October 1929 when Wall Street crashed it's now believed to have been the manifestation of chaos in a social system triggering a cascade of calamity and misery [Applause] when it happened again in October 1987 economists turned to the new mathematics of chaos for some answers there are very strong elements of chaotic phenomena involved in economic downturn consequently that tells me that the forecasts ability or the predictability of economic event events is strictly limited now the question really is what is the degree of limitation how many time cures ahead can you really forecast when when does your predictability dial consider the following simple scenario a group of people all have exactly the same preferences they have the same wishes and desires they all go to the same cinema to see the same show and want to sit into the same scene and immediately having all the same preferences and desires in the same information try immediately to shift to the same alternative seat what do you have chaos you cannot do it similarly for example in the stock market to be a little more realistic if everyone is truly convinced at the same time that the price of the given stock is going to go up then everybody wants to buy no one wants to sell you have a very unstable situation so here we have an irony by increasing equality and speed of delivery of information of creating a situation which is potentially very unstable suffering potentially from what we call think of a catastrophe what happened October 19th was the culmination of a long period of a dynamical process that had in its inherent structure this very close that is a dynamical process was started which inevitably was going to sort of hit a peak and then fall off recover and then sort of follow on an epoch that's what happened and it is foolish I think to go looking for what I call a dot escape there they aren't there or alternatively you could just think of all sorts of things that might possibly have precipitated it only discover that if you have this problem happen again you'll have to look for a difference of alternative Dhanam scapegoats there is a sort of ongoing joke in many academic circles amongst economists that while one would hope that in ignorance governments with at least half the time you get their actions right the irony seems to be that very seldom do they get their actions right they take actions to alleviate a situation Yuri evaluated several years later discovered the situation far being alleviated and improved as we made worse now I'm not saying that the study of dynamics will eliminate that entirely there are many other reasons leading to these problems having to do with the nature of the political process but I think in large part a big deal of why we take inappropriate action is because we are acting in a linear fashion but we are in fact in a nonlinear world we also live in a nonlinear universe a universe where even the orbit of a planet can be unpredictable imagine what it would be like to live on this planet orbiting not one but two suns with no predictable orbit there would be no predictable day lengths and no predictable seasons in fact no constant cycles at it is difficult to see how life could evolve on such a planet we're lucky that our own star system exists in a stable region space one of many islands of stability lying within chaos [Music] nevertheless using space probes like Voyager we are now discovering that despite Newton's laws some planetary bodies bear the stamp of tails one of them is a small moon of Saturn called Hyperion Hyperion mixes chaos and regularity in in one object what's happening is Hyperion is going around Saturn and the orbit around Saturn is just regular elliptical orbit very predictable if you want to know where it will be in orbit a hundred thousand years from now then people can tell you and they'll be right if you want to know what direction it's pointing that's much more difficult it's it's like a potato it's a very irregularly shaped thing and it tumbles chaotically and randomly or apparently randomly as it goes around the orbit so it goes round regularly but tumbles chaotically paradoxically newton's laws allow not only for the existence of chaos within order as shown by Hyperion but also for the existence of order within chaos the red spot of Jupiter is the most prominent atmospheric feature on this turbulent planet it's an unlikely island of order within chaos but Denis Harry Sweeney points out Jupiter is a most unusual place there are horizontal bands which are Jets of fluid like the jet stream if you look in detail as was done in the Voyager photographs the Voyager measurements at these the flow in these bands it's highly turbulent so the question is if you look at Jupiter you see large spots vortices that had been observed for a long time in fact the original observations go all the way back to a man named Robert Hooke in 1660 for which he observed a large coherent spot on Jupiter so the question is if you have such a spot it's in the midst of a turbulent flow why doesn't the turbulence just tear up this spot how does it persist for centuries and that's the question we we set out to address so we constructed the experiment laboratory experiment tank which is about 1 meter in diameter which we rotate very fast to simulate the rapid rotation of Jupiter [Music] we have the conditions which mimic to a reasonable degree the conditions of the atmosphere of Jupiter and we observe the spontaneous formation out of a very turbulent flow of a single coherent spot like the red spotted [Music] if there are two spots present we can see that in a short period of time they will approach one another they're attracted to one another and then it will merge making a single spot like Jupiter's red spot there are also some stable features in the Earth's atmosphere yet mostly chaos seems to rule is there then no hope for accurate weather forecasting with advancing computer technology it appears there might be a way now of determining in advance whether the atmosphere is going to be predictable or chaotic over the period of interest and therefore whether the weather forecast is going to be reliable or not and that is instead of running a single weather forecast from a single set of initial data we would run an ensemble a hot a set of forecasts in parallel from similar but not quite identical sets of initial data if Jim Palmer's weather maps develop in similar ways then he can conclude that that day's weather is in a predictable state and that his forecast will be reliable but if the weather patterns diverge then the forecasts will inevitably be unreliable here are two nearly identical weather systems each showing a blue low-pressure center and a red high-pressure once the computer begins to run its model forward we can see that after 10 days in both cases the pattern of isobar lines have stayed in step resulting in high pressure over southern Europe and low pressure over Scandinavia and in both cases the weather of the UK would be very similar in this second run again the initial pictures are similar but this time as the forecast is run forward the right hand map develops a strong low over the North Sea while on the left this low develops much further north the final frame shows widely different pictures suggesting that the initial weather state was unstable the significance of Tim Palmer's work is that through chaos he can now predict the limits of his predictions increasingly chaos is teaching us what can and perhaps more importantly what cannot be foretold one of the main lessons that it teaches us is that we should be far more concerned and far more skeptical about the sort of long-term predictions and promises and forecasts which are offered to us about complex systems such as the environment and the economy the environment is essentially the weather system and that is driven by the rotation of the earth and the differential heating between the poles in the equator and we're gradually changing that heating by the increasing pollution and the depletion of the ozone layer now one lesson we learn from dynamics is that as you change the underlying conditions of a dynamical system in this case that the heating then you can cause the attractor of the dynamical system in this case the climate to suddenly disappear and one gets a sudden jump from one attractor to another in this case from one climate to another and so you see how with a slow and gradual change in the underlying conditions you can cause a sudden and abrupt jump in the state of the system in the climate and that in this case would be an environmental catastrophe [Music] the consequences is such a sudden catastrophe are almost unimaginable the prospect is all the more chilling because if it does happen it will be the unpredictable result of an apparently insignificant action we will have taken this is the lesson of chaos but chaos can also provide an insight into how to detect and avoid the catastrophic and how to measure and explain the commonplace it has already changed the way scientists view the world and could one day change the way we choose to run it central to this new perspective is geometry and the gateway to geometry is the computer through it we may enter into the kingdom of chaos a realm populated with mathematical monsters realm in which order [Music]

Channel: John PBP

Views: 79,083

Rating: 4.7887325 out of 5

Keywords: CHAOS, FRACTAL, MANDELBROT, WEATHER, ORDER, DISORDER, documentary

Id: 6BvTKBYBMFY

Length: 50min 12sec (3012 seconds)

Published: Thu Jan 19 2017