 The mathematicians in this college have informed me that they have been playing around with strange attractors for quite some time The adjective strange as we all know fits some of them They are like field goal kickers or like those extra point kickers we have out at the stadium on the football team You learn and I'm their chaplain and I go down to try to to assist them But I what I learned some years ago is that you don't talk to them about what they do That's the same the same is true with these mathematicians. They say it's mental they say So chaos mathematics had to come to me along another route Then third floor old main so it came For me in 1987 at Christmas I went down to visit to visit our organ builder in the village Charles Henriksen Who was building an organ just now for the cathedral in Sioux Falls? and I stopped in for a little Christmas cheer and he handed me this book that his sister had just given him for Christmas And he said here LB. Take it along. It would make a good Nobel conference so when Professor John Holti and the math mafia pressed This conference on me said hey, we want to do a math conference and we want to do chaos and so on and so on I said I was ready for them. I Had read the book Now I suspect that this book of James Glick is also the reason that this commons is so full tonight Triple last year's dinner gathering That it was his reconstruction of this piece of intellectual history its people or characters its Journals its meetings its ideas its conversation in his book chaos the new science that Really finally inspired us those of us who were not mathematicians to help to organize This conference and I I think inspired many of you to come to it James Glick is a native of New York City. He's a graduate of Harvard He's a writer he's Residing in in New York with his wife and a new child son He is currently working on a biography of Richard Feynman. I I expect when that book is finished we may have to do a Feynman conference In any event We owe James Glick an enthusiastic welcome to this gathering and his title for his talk his chaos And beyond James Glick Well first of all before I say anything else President Kendall The organizers of this conference our faculty and student hosts All of the speakers want to thank you for what has really been a very unusual event for us extraordinarily stimulating and a Treat, thank you very much. I'm told that my job here is to wrap everything up and and then I've got roughly 38-minute window between dessert and unconsciousness I Think instead it might be it might be better if I try to unwrap everything One of the dangers in a conference like this is that after a while You might start to think that it all makes sense You listen to the the eloquent presentations we've heard over the past two days And you begin to glimpse an intellectual framework with structure logic beauty You feel it's only natural that Mitchell Feigenbaum found Universal laws Governing systems that make a transition from order to chaos You you feel it makes perfect sense that Benoit Mandelbrot spent the battle the better part of a lifetime uncovering the strange Patterns that exist in the paths of lightning bolts and the clustering of galaxies You think what else would someone like Steve Smale do? But invent a new approach to the mathematics of dynamical systems. What else would Heinz Otto Peitgen do but explore the wonders of computer-generated fractals Unfortunately, what you've witnessed here is a little like what happens after a crime when the perpetrators have had time to get their stories together Sure, it makes sense now Now chaos is a recognized movement in science It's it's trendy. There are not only chaos conferences But chaos institutes and chaos journals if you if you're a scientist for an oil company and You tell your boss or your funding officer that you're working on fractals nowadays. He thinks that's great But it wasn't always that way We tend to suffer from the false impression that the progress of science is tidy rational somehow inevitable and that somewhere there's a List of problems to be solved and that scientists pluck the next one off the top of the pile We tend to assume that ideas are communicated more or less smoothly from one place to another That when a scientist discovers something worthwhile The discovery finds its way to the other scientists who need to know about it What I've learned from the short recent history of this business called chaos is that none of these assumptions are true None of them and they are they are least true when scientists are producing something truly new The scientists who have come together to address this symposium were all Each in a different way pioneers they all experienced the difficulties of Working on Problems that their peers did not perceive as legitimate They all experienced the awkwardness of trying to communicate discoveries that lay outside the ordinary way of thinking about things discoveries that Didn't have the decency to observe the customary boundaries between scientific disciplines chaotic dynamics and Fractal geometry weren't on anyone's list of unsolved problems. They simply weren't a Natural subject of study until these scientists made them one There's something about the the ordinary way of portraying the history of science that works to clean up messes like the screed sweeper Coming up behind the parade In reality the most creative science involves mistakes guesses false steps miscommunication uncertainty a sort of Stumbling through the fog that makes the exhilaration of true discovery All the more remarkable the set of ideas that come under the rubric of chaos in particular run Counter to a conventional way of thinking about things It's not always easy even for scientists to see that all of us have preconceptions About the way the world works the way nature works these these preconceptions these biases Can be very hard to shed I? Want to give you a simple example Imagine a river Not a real river surface rippling in the squall trout quivering under submerged rocks Currents carving the banks. That's not what I'm talking about nothing nothing so fancy Just imagine a river's basic shape The way you might draw it on a piece of mental scratch paper. In fact Go ahead use your napkins You heard Benoit Mandelbrot say yesterday a river is not a straight line But I'm willing to bet that virtually everyone here even those of you who thought you were paying attention to Mandelbrot Has imagined a line of some kind Maybe in your mind's eye you drew it with some sort of curve or wiggle That's the way that's just the way people think a river is shaped when we when we speak of a river by name We think of an entity flowing from one place to another from source to outlet from a mountain spring down to the sea a Geographer might ask for example What is North America's longest river? Is it the Mississippi the river whose source is a little north of here or is it the combination? That doesn't quite have a name the the Mississippi, Missouri In reality the question makes no sense in reality a River's basic shape and it does have a basic shape repeated wherever nature empties the land of water Is not a line but a tree a River is fundamentally in its very soul a thing that branches So are most plants Trees themselves of course bushes ferns like the ones you saw today and computer simulation lightning Contrary to our common stereotype a sort of stretch Z So is the human lung a tree of ever smaller tubes bronchi bronchia bronchi owls Intertwining with another tree the the network of blood vessels the circulatory system so North America's longest river is actually a very messy object Spanning 31 American states and two Canadian provinces it embodies without distinction The great tributaries that we think of as separate rivers the Mississippi, Missouri, Ohio, Tennessee, Arkansas Minnesota and so on Except in human perception and human language Nothing really separates It's few wide and deep stretches from its many small and narrow ones Although it flows inward Toward its trunk in Geological time it grew and continues to grow outward like an organism from its ocean outlet to its many headwaters Now as all of you know by now in the vernacular of this new science it is fractal its structure Echoing itself on all scales from river to stream to brook to creek to rivulet Branches too small to name too many to count When a child draws a tree You get a green mass sitting on top of a brown trunk as if the basic shape were something like a popsicle a child's cloud is a smoothly rounded bulk Perhaps with wavy or scalloped edges These are not the clouds we see they are highly stylized forms like the like the international symbols for railroad crossing or no smoking as Children or as adults we own a Repertoire of such stylized images. They're they're like Idiograms in Chinese painting they they help us see for without these templates Our minds are powerless to sift the welter of sensations that bombard us, but they hinder our seeing as well Before they were scientists Mandelbrot and Feigenbaum and the other pioneers of chaos were people who saw Nature's complexity a little more clearly than the rest of us the rivers the clouds the snowflakes of our usual Perceptual toolkits miss the point the intricate recursion the convoluted flows within flows within flows our mental lightning bolts are Z's our volcanoes are inverted and Decapitated cones our rivers are lines Nature's are not so simple This is not just a matter of terminology. It's a matter of of true understanding of Recognizing and avoiding a kind of foolishness about nature Again think about the Mississippi River How many tributaries does it have? How small is the smallest tributary? How long are all the branches added together? to make sense of such Innocent seeming questions begins to require at least a feeling for the infinite One hears such questions Constantly questions that cannot be answered as simply as people imagine What is the average height of an ocean wave? What is the average size of icebergs breaking off the Antarctic shelf? What's the average? Duration of the El Nino climate pattern or of an economic recession when you when you hear questions like these a New kind of bell should go off in your mind In the case of a river the number of branches and their total length Approaches infinity just as the size of the smallest branch approaches the infinitesimal And it has to be that way What is a river anyway, but a thing that drains water from the earth's surface? In some sense if it is to function that way its fingers must penetrate every part of that area Furthermore a river is a dynamical thing The microscopic rivulets that feed a river Appear and disappear with the rains at its at its farthest edges a river's precise shape and size fluctuate dynamically With the day's rainfall or the year's wet and dry seasons one brook appearing as another dries out There is no simple dividing line between the transient and the permanent parts of a river fluctuations Affect every timescale from the seconds of an ephemeral rain shower to centuries and millennia if you could If you could film the life of a river and replay it in fast motion You would see a symphony of rhythms from the base notes of the great branches to the treble flickering of the tips The traditional view of nature overlooks such rhythms many flows escape our perception because they're too slow or too grand in compass a cloud Floating overhead gives the illusion of a static object Simply born from one place to the next by the wind, but that's not how it is Even when a cloud looks most like Frozen cotton candy it it slowly seeds and tumbles in the air a motion picture film of clouds Played ten or a hundred times too fast Always chose the wildness that lurks in what seemed like gentle puffs the contention of this new science of chaos the motivating contention Seeming irregularities in nature even in rivers and clouds contemplated Sorted measured and understood Traditionally looked for a more Conventional order in nature and treated the erratic as a side issue and unpredictable and Therefore unimportant kind of marginalia Not anymore If any of you for example follow the technical literature of population biology ecology You may have noticed a striking change in attitude just in the last few years For several generations Less time than you may think actually the dominating assumption In ecology was an attitude of prejudice that can be summed up in a single phrase the balance of nature When people go into a wild area and start tinkering spraying insecticides What is it they're disturbing the balance of nature the idea is left to itself a wild Ecosystem finds a a harmonious balance and equilibrium. It settles down. It regulates itself Now of course, there's some truth to that idea complex non-linear systems do become self-regulating when suddenly perturbed They can be thrown into regimes of behavior that are unexpectedly different witness for example the Frightening appearance of ozone depleted holes over Antarctica in the past decade But ecologists led by chaos theorists have begun to realize that the balance of nature idea was Profoundly naive by and large Ecosystems may seek a sort of equilibrium But that equilibrium bears as much resemblance to the traditional idea as as a roller coaster does to a golf cart In their natural state left all alone Ecosystems can fluctuate wildly Populations rising and falling dying out and springing up again. Wildness really does mean chaos not the Slightly saccharine kind of harmony that ecologists used to imagine The same is true in economics if you think the natural thing would be for a complex system made up of all the Interacting intertwining commercial activities of humanity to find some sort of static equilibrium or To rise and fall in regular predictable economic cycles Well, you're not alone, but but you're missing the boat If you've listened carefully to the speakers over the past two days You may well feel that a richer view of the possibilities is in order now I'd like to offer another somewhat deeper example of a sort of Perceptual prejudice that I believe has skewed the path of science in this case of fundamental physics for much of this century Consider the following statement At bottom the root of unpredictability in the world is Quantum uncertainty the subatomic measurement uncertainty first expressed by Werner Heisenberg in the 1920s This is sort of a true false test true or false The uncertainty principle of quantum mechanics is the fundamental cause of unpredictability in nature. I Say on predictability, but I might also say indeterminacy or In the evocative phrase that John Polkinghorne used yesterday every day openness It's it's not an easy question. And of course if you're smart, you don't want to give a yes or no answer You want to add a 10,000 word footnote? Nor is it easy to know what most physicists believe But I think it's fair to say that many physicists anyway have talked or acted as though they believe this is the case Here's an example. I'm gonna quote The uncertainty principle Signaled an end to Laplace's dream of a theory of science a model of the universe that would be completely Deterministic one certainly cannot predict future events exactly if one cannot even measure the present state of the universe precisely exclamation mark Now that could have been any of a dozen prominent physicists But it happens to be Stephen Hawking in his in his recent book a brief history of time He adds quantum mechanics Therefore introduces an unavoidable element of unpredictability or randomness into science Well, there's an inverse corollary to this statement, too The corollary is if it weren't for quantum uncertainty The laws of elementary particle physics would allow one at least in principle to calculate and to predict everything Hawking doesn't shrink from this implication I'll quote again Since the structure of molecules and their reactions with each other underlie all of chemistry and biology Quantum mechanics allows us in principle to predict nearly everything we see around us within the limits set by the uncertainty principle Well, you can see why the question starts to seem far from trivial In practice as Hawking goes on to say you can't do the calculations The equations are too complicated and so on but but those are just details messy details In principle according to this point of view the laws of elementary particles are the fundamental laws and The ultimate limit on predictability comes from quantum uncertainty Now I don't happen to believe this and I think that as the lessons of chaos sink in both versions of this statement are going to start to seem somewhat disreputable Are the fundamental laws of physics the laws that govern elementary particles they are if you mean fundamental in a sort of Geographical way or anatomical way to refer to the tiny things of which larger things are built up But if by the fundamental laws you mean the laws with the greatest generality The most profound laws the laws with the greatest planetary power Then I think you have to look elsewhere How do the laws of quarks and gluons or even the laws of quantum electrodynamics Help us understand bigger things like the great red spot of Jupiter or the general problem of turbulence and fluids or the formation of clouds and snowflakes or the working of the human brain or the Balance of nature or any other mystery of the universe as it exists outside of particle accelerators Well, the truth is that they don't really I Would contend and now I'm Since I'm not a scientist. I have the privilege of waving my hands wildly here I would contend that if you could imagine a universe with no Heisenberg uncertainty principle you can imagine that right It's a universe in which the position and momentum of a subatomic particle can be specified Simultaneously if you can imagine a universe with no Heisenberg uncertainty principle You would have a universe in which it would be Precisely as difficult as it is in our universe to predict next Sunday's weather Or to predict What will happen to the price of oil next month or to predict just about anything about the behavior of any macroscopic complex system much of this the standard language of The physics community over the past two generations has embraced a reductionist perspective Yesterday you heard John Polkinghorne declare that he was an anti reductionist Just a few years ago It would have been about as likely for a high-energy physicist to declare himself an anti reductionist as to declare himself an Anglican priest physicists have believed and have stated proudly that Before one can understand the whole one must understand the parts Chaos is anti reductionist this new science makes a strong claim about the world namely that When it comes to the most interesting questions questions about order and disorder decay and Creativity pattern formation and life itself the whole cannot be explained in terms of the parts. There are Fundamental laws about complex systems, but they are new kinds of laws They are mathematical laws of the kind that smell Figenbaum and Mandelbrot and others have discovered they are laws of structure and organization and scale and They simply vanish when you focus on the individual Constituents of a complex system. I think we all understand that intuitively From our own everyday experience. I think that most of us now believe that when science comes to understand The interesting things about how the brain works The things we all want to know what is memory what are thoughts? What are emotions? How are symbols? Stored and processed the answers to those questions are not going to depend on the particular chemistry of Individual neurons that chemistry may be what it is because of a thousand Accidents in the history of life on earth intelligence is something else something dynamical Oddly I think that the very best quantum physicists if not most quantum physicists have understood this all long Having stressed what a great new surprise chaos has been now. I'd like to quote something Richard Feynman said 28 years ago. I know at least one person in this room tonight was there when he said it he said The complexities of things can so easily and dramatically escape the equations which describe them Man has often concluded that nothing short of God not mere equations is required to explain the complexities of the world We have written the equations of water flow From experiment we find a set of concepts and approximations to use to discuss the solution vortex streets turbulent wakes boundary layers When we have similar equations in a less familiar situation We try to solve the equations in a primitive halting and confused way to try to determine what new qualitative features may come out Our equations for the Sun for example as a ball of hydrogen gas Describe a Sun without sunspots without the rice grain structure of the surface without Prominences without coronas yet. All of these are really in the equations. We just haven't found the way to get them out There are those who are going to be disappointed when no life is found on other planets not I I want to be reminded and Delighted and surprised once again through interplanetary exploration with the infinite variety and novelty of phenomena that can be generated from such simple principles The test of science is in its ability to predict Had you never visited the earth could you predict the thunderstorms the volcanoes the ocean waves the auroras and the colorful sunset? The next great era of awakening of human intellect Feynman said May well produce a method of understanding the qualitative content of equations Today, we cannot Today, we cannot see that the water flow equations Contains such things as the barber pole structure of turbulence that one sees between rotating cylinders Today, we cannot see whether Schwerdinger's equation contains frogs musical composers or morality or whether it does not We cannot say whether something beyond it like God is needed or not And so we can all hold strong opinions either way Incidentally, whether Feynman's God and John Polkinhorns are the same. I'll leave it to you to figure out. I Want to finish by saying that there is a danger in all of this Steve's mail was right to warn us today that if scientists use the language of chaos and fractals merely to describe what is there Then they will not have accomplished much Furthermore, there's a danger in listening too much to people like me. My language is not science at all It's metaphor. I believe that chaos Offers some useful ways of thinking about the world beyond science, but metaphors don't always work Not every good idea in science survives the process of translation Darwinism for example was one of the great triumphs in the history of science Social Darwinism on the other hand was one of the great disasters Survival of the fittest turns out not to be a helpful guiding principle for those thinking about human society As a description of space and time Einstein's relativity works beautifully but contrary to a good deal of 20th century philosophizing The laws of physics do not mean that everything is relative Nothing in science tells us that relativity must apply to ethics to art to human values Another well-known gift from science is the second law of thermodynamics the law that says that the cosmos is winding down That entropy always increases that the universe and any closed system within it have an inexorable tendency toward disorder As a rule about thermodynamics the second law is undeniable But too many people have taken it too much to heart. The second law has been called on to explain decadence in civilization Decay in cities the decline of manners as though science were telling us that Disorder is our destiny. I Don't believe that I believe Ilya Prigashin is right when he tells us to look again at the science underlying dissipation and pattern formation Billions of years from now the universe may well wind down to a featureless heat bath of Maximum entropy, but in the meantime it is managing to create some interesting structures Just look around and you know that the important laws of nature The creative laws lie elsewhere Thank you