Mathematicians and others are endeavoring to apply insights gleaned from the sciences of complexity to the seemingly intractable problem of understanding the world economy. I have a guess, however, that if this problem can be solved (and that is unlikely in the near future), then it will not be possible to use this knowledge to make money on financial markets. One can make money only if there is real risk based on actual uncertainty, and without uncertainty there is no risk.
THE QUICK BUCK BECOMES QUICKER
[EDITOR'S NOTE:] Heinz R. Pagels, died on July 23, 1988, in a mountain climbing accident on Pyramid Peak in Aspen, Colorado. A physicist, he was Executive Director of The New York Academy of Sciences, adjunct professor of physics at Rockefeller University, and president of the International League for Human Rights. He was the author of three books: The Cosmic Code, Perfect Symmetry, and Dreams of Reason. He was also a founding member, and, at the time of his death, president of "The Reality Club," which, in 1997, moved to the Web as Edge.
It was before and after Reality Club meetings at the New York Academy of Sciences around 1985-6 that Heinz began to talk about the themes that became central to his 1988 book Dreams of Reason: The Rise of the Sciences of Complexity, (Simon & Schuster):
He notes that "the computer, with its ability to manage enormous amounts of data and to simulate reality, provides a new window on that view of nature." In other words new technology equals new perception. He also had interesting insights into how the new sciences of complexity would impact global financial markets. He wrote:
Given the current global economic meltdown, it's instructive to re-read Pagels. Below, please find the Preface and Chapter 7: "The Quick Buck Becomes Quicker". The Edge Introduction is by Emanuel Derman, a physicist who was at Rockefeller University with Pagels, and went on to become the world's best know "Quant".
All of these 'or's are choices between complex mental constructs that merely sound simple or primitive; every 'or' is an attempt to forcibly convert the duality into a unity. But the fact that that we can see (at least) two sides to each of these issues signifies intrinsic complexity. Physicists long ago learned to turn wave or particle into wave and particle and live with it, or at least stop thinking about it for as long as they could keep successfully calculating.
Heinz Pagels' 1998 book The Dreams of Reason tackled the science of complexity and the use of computers to understand complex systems that defy reduction. I met Heinz when I was a colleague in particle physics, the most reductionist of fields, in an office down the hall at The Rockefeller University in the late 1970s. An enthusiastic iconoclast with wide interests, Heinz devoted one chapter to the consequences he foresaw of putting science and computing in the service of banking, finance and trading. He presciently warned about the possibility of uncontrollably complex markets, and of the way in which finance, intended to finance investment and construction, may be tempted to incestuously turn in upon itself to recursively finance merely more financial activities.
— Emanuel Derman
EMANUEL DERMAN is a professor in Columbia University's Industrial Engineering and Operations Research Department, as well as a partner at Prisma Capital Partners. He is a former managing director and head of the Quantitative Strategies group at Goldman, Sachs & Co. He is the author of My Life As a Quant. He was recently featured in "They Tried to Outsmart Wall Street" [3.9.09], a front page New York Times "Science Times" profile by Dennis Overbye.
THE REALITY CLUB: Joseph Traub, Jaron Lanier, Lee Smolin
It seems that we live in two different worlds — the world of our mind and the natural world of things. This dualism, a rift in the perceived order of reality, stands as a persistent challenge to Western thought. Can we accommodate it?
Most natural scientists hold a view that maintains that the entire vast universe, from its beginning in time to its ultimate end, from its smallest quantum particles to the largest galaxies, is subject to rules — the natural laws — comprehensible by a human mind. Everything in the universe orders itself in accord with such rules and nothing else. Life on earth is viewed as a complex chemical reaction that promoted evolution, speculation, and the eventual emergence of humanity, replete with our institutions of law, religion, and culture. I believe that this reductionalist-materialist view of nature is basically correct.
Other people, with equal intellectual commitment, maintain the view that the very idea of nature is but an idea held in our minds and that all of our thinking about material reality is necessarily transcendent to that reality. Further, according to this view, the cultural matrix of art, law, religion, philosophy, and science form an invisible universe of meanings, and the true ground of being is to be found in this order of mind. I also believe that this transcendental view, which affirms the epistemic priority of mind over nature, is correct.
These two views of reality — the natural and the transcendental — are in evident and deep conflict. The mind, it seems, is transcendent to nature. Yet according to the natural sciences that transcendent realm must be materially supported and as such is subject to natural law. Resolving this conflict is, and will remain, a primary intellectual challenge to our civilization for the next several centuries. The great temptation will be to resolve the conflict by collapsing the differences between these views into one viewpoint or the other and then claiming a solution. The Buddha, it is said, when confronted with a similar temptation, held aloft a flower and smiled, indicating that neither dualism nor nondualism provide a resolution. That insight, however, provides us with the beginning of an inquiry, and not its end.
The emergent new sciences of complexity and the order of being that they study are a first step toward a resolution of this problem. What are the sciences of complexity?
Science has explored the microcosmos and the macrocosmos; we have a good sense of the lay of the land. The great unexplored frontier is complexity. Complex systems include the body and its organs, especially the brain, the economy, population and evolutionary systems, animal behavior, large molecules — all complicated things. Some of these systems are simulatable on computers and can be easily modeled rather precisely; others cannot be simulated by anything simpler than the system itself. Scientists, in a new interdisciplinary effort, have begun to meet the challenge of complex systems and, remarkably, are understanding how complexity can emerge from simplicity. For example, cellular automata, an artificial set of video dots that rearrange themselves according to definite, simple rules on a screen are an example of complex behavior emerging from simplicity. The evolution of life and culture may be another example, in this instance, of a three-dimensional cellular automata made of atoms instead of video dots and which fills the entire universe. All of existence may be viewed as a complex system built out of simple components.
Some of the themes of the new sciences of complexity — the importance of biological organizing principles, the computational view of mathematics and physical processes, the emphasis on parallel networks, the importance of nonlinear dynamics and selective systems, the new understanding of chaos, experimental mathematics, the connectionist's ideas, neural networks, and parallel distributive processing — are described in the first part of this book. Where these new developments are headed no one can tell. But they portend a new synthesis of science that will overturn our traditional way of organizing reality. Already institutes and centers for the study of complexity are springing up on campuses and within corporations around the world — a sign of what is to come.
In this book I will focus on three main themes: first, the rise of the sciences of complexity that stand at the newest frontier of knowledge; second, the role of the computer as a research instrument and the reordering of knowledge it implies; and finally, the philosophy of science.
The primary research instrument of the sciences of complexity is the computer. It is altering the architectonic of the sciences and the picture we have of material reality. Ever since the rise of modern science three centuries ago, the instruments of investigation such as telescopes and microscopes were analytic and promoted the reductionalist view of science. Physics, because it dealt with the smallest and most reduced entities, was the most fundamental science. From the laws of physics one could deduce the laws of chemistry, then of life, and so on up the ladder. This view of nature is not wrong; but it has been powerfully shaped by available instruments and technology.
The computer, with its ability to manage enormous amounts of data and to simulate reality, provides a new window on that view of nature. We may begin to see reality differently simply because the computer produces knowledge differently from the traditional analytic instruments. It provides a different angle on reality. I will be describing some uses of the computer — simulating intelligence, simulated annealing, modeling molecules, computer modeling of both real and artificial life, the discovery of deterministic chaos, nonlinear dynamics, modeling evolution, neural nets, Boltzmann machines, experimental mathematics, to name a few. The technology that emerges from these applications will have profound implications in the commercial and business world, the financial services industry, the legal profession, and the military. The world will be changed. As a new mode of production, the computer creates not only a new class of people struggling for intellectual and social acceptance, but a new way of thinking about knowledge. It will transform the scientific enterprise and bring forth a new worldview.
The second part of the book deals with the impact of the sciences of complexity on the philosophy of science. Philosophy of science has fallen on hard times, deserted by even the professional philosophers, some of whom think it has come to an end. Once the handmaiden of theology, in this century philosophy became the whore of science, and finally, today, it is all but abandoned. Practicing scientists like myself tend to be antiphilosophers, often rejecting the efforts of professional philosophers to clarify and interpret our enterprise. This was not always the case. A few decades ago many scientists, especially my tribe — the physicists — were intellectually interested in, debated, and wrote about the philosophy of science. Today the pendulum has swung from thinking to doing. The external activities of scientists are more ethically oriented and less philosophically inclined. They have become involved in issues — the environment, war and peace, and human rights. So writing about the philosophy of science today, especially by an "antiphilosopher," requires an explanation.
Thinking about and doing science have become two very distinct professional activities, one philosophical, the other empirically investigative. This schism between the philosophy of science and science itself was wrought by Kant more than two centuries ago and has persisted until the present day. I believe that these two activities will become less distinct in the future, an influence of the new sciences of complexity. I welcome that. Philosophers and scientists may begin to collaborate more directly, especially in the cognitive sciences. It may turn out that philosophy has not so much come to an end, rather it has reintegrated with the activity of science, to where it was prior to the Kantian schism.
I am not a philosopher, and what I am writing in this book does not qualify as professional philosophy because it is not sufficiently closely argued. But I am trying to expose the new outlook on science that is arising out of the study of complexity, and I am using the themes and problems of traditional philosophy to do this — the nature of physical reality, the problem of cognition, the mind-body problem, the character of scientific research, the nature of mathematics, and the role of instruments in research.
I am profoundly biased in my views by my training as a professional physicist. As a physicist I feel more at home writing about the natural sciences. But some of the most exciting new developments in the sciences of complexity deal with social, economic, and psychological behavior. Interestingly, the interdisciplinary nature of these new sciences will in some cases cut across the traditional distinction between the natural and the social sciences. This will be lauded by some people and abhorred by others.
A recurrent theme in my thinking about science is the notion of "a selective system," a generalization of the Darwin-Wallace idea of natural selection to a general pattern-recognizing system. Empirical science itself exemplifies such a selective system. Instead of selecting species, natural science selects the theories of nature, our repertoire of reality. Empirical science may be viewed as a selective system for finding the invariant rules that order the universe. While these ideas are familiar in biology, the impact of the selective systems way of thinking on the social and psychological sciences is just beginning. It has been a long time in coming, and it will change them profoundly, a change that will be resisted by more traditionally oriented scientists.
I believe that the problem of the dualism of mind and nature will not so much be solved as it will disappear. Fundamental problems have disappeared before. Centuries ago natural philosophers debated the distinction between "substance" and "appearance," a distinction that vanished as empirical science matured. Likewise the radical distinction between mind and nature will disappear with the development of the new sciences of complexity and the categories of thought that development entails. As we deepen our understanding of how the mental world of meaning is materially supported and represented, an understanding coming from the neurosciences, the cognitive sciences, computer science, biology, mathematics, and anthropology, to name but a few contributing sciences, there will result a new synthesis of science, and a new cosmopolitan civilization and cultural worldview will arise. I am convinced that the nations and people who master the new sciences of complexity will become the economic, cultural, and political superpowers of the next century. The purpose of this book is to articulate the beginnings of this new synthesis of knowledge and to catch a first glimpse of the civilization that will arise out of it.
During the Second World War, Albert Einstein at the urging of Leo Szilard wrote a now famous letter to Franklin Roosevelt. This letter, expressing Einstein's view that nuclear fission could be used to build a weapon and that Germany might well be pursuing such a direction, set in motion a chain of events which led to the Manhattan Project and the first and only use of atomic weapons by the United States against Japan. The abstract subject of nuclear physics leapt to the foreground in people's thinking, influencing the creation of foreign policy and the international order among nations. Some scientists who possessed the knowledge to build the weapons were lifted out of the obscure world of academic research into the public eye. What scientists thought could and could not be done took on added significance. This scenario — the transformation of abstract knowledge into practical artifacts — is today repeating itself in an entirely new area.
The banking industry, long insulated from major technological change, has been hit by a revolution that will alter forever the way it does its business. This revolution is a consequence of improvements in telecommunications, data processing, and, of course, the computer. A new class of people who have mastered this new technology has sprung into prominence and in several instances risen to leadership positions in major financial institutions.
Institutional survival in a highly competitive banking environment can depend on advances in computer modeling of markets and the economy, and software and algorithms, as well as telecommunications, that supply data input. Banks, which have long been hiring experts in data processing, are now hiring Computer scientists, engineers, and mathematicians to help design their equipment and algorithms. They used to depend on their vendors, computer and software producers, for their internal needs. But they soon realized that to maintain a competitive advantage they had to take on the research and development responsibility themselves. Major financial services institutions now have their own research staffs examining how they can improve their data processing performance by using new hardware and software. Abstract mathematics, sometimes developed to understand selective and adaptive systems, is now being applied to guide financial decisions. The sciences of complexity are impacting the business and financial world. And that impact is just beginning.
The real movers of the world economy today are the large international banks linked to each other electronically by a network that, seen as a whole, comprises the world's first global computer. In 1986 over $64 trillion was exchanged on this network, and that volume is still growing. (The other global computer, and second largest, is the U.S. military communications system.) The banking computer network is a parallel, not hierarchical, network, although it has hierarchical components. Within each financial institution the system is hierarchical, but globally no one is in charge, and there is no central, executive authority. In this sense it is a "free market." Some computer scientists are attempting to develop computer models of the world's first global computer to and understand it better. If we look back, we can see what events helped to bring about this global computer. A few decades ago the placement of the first satellites in orbit created a technological curiosity and a symbol of national accomplishment. Some people complained about the high cost of the satellites. However, satellites provided a highly reliable transcontinental and intercontinental communications link, and financial institutions quickly took advantage of them. Banks in London could release credit to banks in New York as the sun set in England and New Yorkers were still at work. Likewise New York banks were able to communicate credits to the West Coast and thence to Asia. While people slept, their money worked. The satellite system enabled a "bulge" of credit to rotate with the daylight zone around the planet. Some people estimate that satellites increased the world credit supply by as much as 5 percent — hundreds of billions of dollars — much more than the entire cost of the satellite systems.
When optic fibers are deployed across the Atlantic and Pacific oceans by the end of this decade, many functions of the satellites will become obsolete. The increased bandwidth afforded by photonic systems will enable supercomputers on different continents to talk to each other. It is conceivable that European and Asian computers will be buying and selling on the U. S. markets (and vice versa). Already, effective international telecommunications and computations have destroyed the arbitrage market that makes money on small differences in currency exchange rates. The only advantage of having a local computer near the market is the one hundred milliseconds or so that it takes light to travel between continents. But that is a significant advantage if one has a fast algorithm. I recently spoke to a mathematician newly employed at a New York investment house who was developing sophisticated algorithms to determine buy-sell options. Why? So that his institution could get their orders in a millisecond ahead of their competitors.
It is well known that one of the most rapid forms of communications is a good joke. Businesspeople routinely leave their office in London with a fresh joke, fly to New York on the Concorde, only to find out at an evening cocktail party that everyone had already heard it. How is this possible? Banks and investment houses maintain open phone lines around the world in case there is a news break. The operators who maintain the lines often have no business information to transmit, so they trade new jokes. That's how jokes circle the globe so quickly. They are still one of the fastest forms of human communication.
The introduction of high-speed computing, data processing, and innovative software has transformed the financial services industry. Leaders in the financial services industry, while keenly aware that such technology makes a difference today, were not always so aware. A decade ago the investment industry was hit by a technological revolution in the form of new electronic trading systems for stocks. Though suffering from an avalanche of paperwork (some called it the "paperwork holocaust"), the New York Stock Exchange delayed the installation of this innovative technology. They were too busy making money and thought they would lose orders during the change-over period. The exchanges in Tokyo and London, which were not so concerned about short-term profits, became electronic markets. By their understanding of where the industry was headed, they got a bigger piece of action. Even today a major problem is that as technology advances, systems quickly become obsolete and noncompetitive. How does one change over an entire network without bringing it down?
New skills are needed in order to manage the modern financial services industries — not just computer programmers, but high-level mathematicians who know how to design fast algorithms. In September of 1986 there was a "computer-assisted" slide of the market. One of the reasons for this slide was that the buy-sell programs for many investment and brokerage houses differed in such a way as to produce an instability in the system. While the first step in most houses; programs for buying and selling was the same, the second, third, and fourth steps differed. This can produce a positive feedback loop; when the market becomes unstable and before human beings can intervene, the market can drop precipitously, costing many people a lot of money. When I asked many stock analysts about "instabilities" or "singularities" in market behavior, they never heard of them. Most are not trained in even rudimentary modern mathematics.
What are the chances that we will ever understand economic systems? They are clearly examples of extremely complex systems, but there is lots of quantitative data to check one's ideas out on. Professional economists who bother to concern themselves with practical matters don't have an especially good batting average when it comes to predicting the future of the economy. They are smart, but they just don't have the right intellectual tools in their hands.
When I was in school learning about supply-and-demand curves, I asked my professor, "Where did those curves come from? Were they made up, based on data, or did they represent a theory?" The best answer I got, at least the one I remember, was that they represented the theory of economic equilibrium. The market, it was asserted, establishes an equilibrium, and the point at which the supply-and-demand waves intersect determines the price. This, reasonable as it seems, is of course nonsense.
The economic system, if it is anything, is a system far from equilibrium like the evolutionary system or the immune response. It is continually making adjustments to keep itself far from equilibrium (although there may be a local equilibria). Next to nothing is understood about dynamical systems far from equilibrium. Probably the various kinds of attractors — fixed points, limit cycles, and strange attractors — play a role in coming to grips with how a complex system like the economy functions. Some mathematical economists such as Stanford's Kenneth Arrow have expressed cautious excitement about the application of the new ideas about chaos to economic dynamics. Mathematicians and others are endeavoring to apply insights gleaned from the sciences of complexity to the seemingly intractable problem of understanding the world economy. I have a guess, however, that if this problem can be solved (and that is unlikely in the near future), then it will not be possible to use this knowledge to make money on financial markets. One can make money only if there is real risk based on actual uncertainty, and without uncertainty there is no risk.
As emphasized by the investment manager George Soros in his book The Alchemy of Finance (1987), human biases profoundly influence markets in a reflexive fashion. Because such biases are influenced by political developments and cultural factors it is probably impossible to make a reliable model of the international economy. Like the weather, the international economy is an unsimulatable system. Yet short-term prediction and seeing long-range global trends may be possible using mathematical models.
I remember that back in the 1960s popular intellectuals spoke about "the information age" and "the global village." Well, it has arrived, but not exactly in the form that these intellectuals anticipated. Felix Rohatyn, a New York investment banker and public-spirited citizen, recently remarked that we are now living in the "money culture," a development brought about by the new data processing technologies. By this he meant that the dominant form of commercial exchange between people is not goods and services, but money. Money is, of course, a form of information, and it can move at the speed of light. People can easily invest it, transfer it, and lend it. And lots of people are doing this, some accumulating great wealth.
Only a few decades ago, if one picked up American business magazines, the articles were about new products, industries that produced goods and services, and the people who made that happen. Today the big news stories are about deals, financial transactions, buying, selling, conglomerating, integrating, divesting, and destroying companies. Smart young people who want to enrich themselves are attracted by all these deals and want a piece of the action. Nothing is being produced, but wealth is seemingly created. This bubble burst with the collapse of the market on October 19, 1987.
One could even imagine a satire on the theme of the "money culture." People invest in the financial services industry, which, in turn, services their investment. Nothing but information is ever exchanged; no one produces anything; money, however, is always changing hands. The whole system bootstraps itself into existence — just money being exchanged and making more money based on the human confidence that it will continue to be exchanged. The image one gets is of an immense "chain letter" with promises of payments to all at a cost to none. Of course, it cannot work forever. At some point human confidence gets shaken, and a lot of people are hurt.
The real money culture, of course, invests in products and services. What has changed is the speed with which this is done. Speed, while a quantitative parameter, can, if dramatically increased, lead to qualitative changes — the changes we see in the global economy and, in particular, the large multinational corporations that play such an important role in maintaining it. In several such large corporations there has been a shift in both the leadership and the emphasis. The companies used to be run by traditional executives who understood the product and how it was produced and sold, whether it was automobiles or oil. But with the rise of the money culture many corporations, especially the oil companies, discovered that they could make more money investing and trading their surplus capital than doing what the company traditionally did — look for oil. Engineers and salesmen were replaced by international money market analysts and accountants. These new people began to run the companies. Which, of course, causes one to wonder who's minding the shop.
In 1986 I met with a group of bankers and businessmen. I told them that I knew of a "computer nest" operating in Luxembourg or Switzerland that was using a new "massively parallel computer" built by hackers in collaboration with a group of bright young traders for the express purpose of recognizing patterns in the commodities market. It had a learning capability similar to the Boltzmann machine. The traders were pulling in between two and three million dollars a day and wreaking havoc on the European commodities market.
My audience was stunned. "Who are they? What are they doing?" they asked, now on the edge of their seats. I told them that the story wasn't true, but could easily become true in the near future. This kind of "technical breakout" by an opponent, which is so often feared by military strategists, could also happen in the financial world.
Not only will advances in pattern-recognition systems influence financial decision making; so will the advent of detailed models of the global economy. There is an enormous amount of data generated by the world economy, so much that one human being or even a team cannot digest it. But computers can use that data in detailed models of various national and international economies and analyze it. Far-ranging supercomputer models will become a powerful asset in the hands of their creators — crystal balls that may make economic forecasting more realistic. One can foresee the characterization of economic systems in terms of different limit cycles and strange attractors. The international economy is a nonlinear system and can be understood as such.
There are dangers in the operation of the global computer system. A major instability could result in an international economic crash far worse than that in 1987. Many people predict that this can happen — that the markets will not stabilize after the October 1987 crash. Since no one person or group understands what is going on in the world economy and there is no central executive control, the entire system could end up in the basin of attraction of a fixed point presenting very low economic activity. National governments would have to intervene to get the system started again, and new international institutions would have to be established, at a sacrifice of some national sovereignty, in order to prevent the recurrence of a crash.
In spite of all the advantages in computer technology it is not possible to abrogate human judgment in decision making. Much of this implementation of the new computer equipment, however, is designed to do just that. I find that distressing. Elementary decisions, lots of them, can and are made by computers. Perhaps in the future more complex economic decisions will be made by computers as well. But people, with their innate desire to control their destinies, would be foolish to abrogate such high-level judgments to computers.
The diffusion of responsibility incurred by computers is a major danger, too. Once, waiting for breakfast to be served at a fancy new hotel, and after a long delay, I asked the waiter what was wrong — where was my breakfast? "The computer is down sir," came the reply. I commented to my colleagues at the table that one will be hearing that excuse far more often in the future. My delayed breakfast was not the fault of the waiter or the cook. Not even the manager could be blamed. Only the computer manufacturer, programmer, or installer, all long since gone, could be responsible for the fact that my breakfast was delayed. The diffusion of responsibility serves certain interests, and it is important in each instance to identify them carefully. We are in deep trouble if we can't identify a human agent for these kinds of problems and hold them immediately responsible. But there are still other dangers.
Some intellectual prophets have declared the end of the age of knowledge and the beginning of the age of information. Information tends to drive out knowledge. Information is just signs and numbers, while knowledge has semantic value. What we want is knowledge, but what we often get is information. It is a sign of the times that many people cannot tell the difference between information and knowledge, not to mention wisdom, which even knowledge tends sometimes to drive out.
I've examined just one of the many impacts that the new sciences of complexity will have on the world — that in the financial services industry. There are other impacts — on education, medicine, and the legal profession. The computer, a new mode of production, has come into existence and created new classes of people, new jobs, and new forms of wealth. What I find especially interesting about this development is that abstract mathematics, sophisticated algorithms, and vanguard technology are going to determine the future of industries and professions long immune to such changes.
Someday, sooner than many people think, the sciences of Complexity will impact on the legal system, not just in data processing but in actual decision making. Could an expert system replace an attorney or at least assist one? Probably a lot of mundane legal work can be done by computers, and lawyers will discover that they can serve their clients better by using computers. The use of content addressable memories, for example, would be a great aid in case work. Right now the impact of the new sciences of complexity on the legal profession is still minimal; but this will soon change.
A new salient of knowledge is being created, and our generation is privileged to see it unfold. Like all great changes throughout the course of human history, it provides challenge, opportunity, hope, and danger. We stand on the threshold of the human mastery of complexity — an agenda for science that may show us, for the first time, who and what we truly are.
Information, be it embodied in organisms, the mind, or the culture, is part of a larger selective system that determines through successful competition or cooperation what information survives. Information can be encoded in genes, nerve nets, or institutions, but the selective system that promotes survival remains similar. This insight is hardly original. Yet it remains a mystery to me why philosophers, psychologists, and social and cultural scientists have rarely grasped the import of the Darwin-Wallace notion of selection for their own work (this has recently been changing). A selective system is a pattern producing and recognizing system, be it the pattern of life on earth, the symbolic order of the mind, or the pattern of culture. A selective system manages complexity.
In the next part of the book I will take the reader on an intellectual journey through a forest of several philosophical issues that bear on contemporary science — the nature of material reality, the problem of cognition, the body-mind problem, the character of scientific research, the nature of mathematics, and the role of instruments in the conduct of inquiry. The issues form, in part, the framework of our thinking about the scientific enterprise, an enterprise that is now opening a new frontier-the frontier of complexity, exploring the very order of the mind, life, and nature.
The Preface and Chapter 7 ring even more true today then in 1988.
I have a small personal story about Dreams of Reason.
Heinz gave me the galleys for comments. At the time I was on the Executive Committee of the New York Academy of Sciences. I brought a copy of the book to a meeting for Heinz's autograph. As the meeting broke up a number of people gathered to speak to him. I decided to get his autograph another time.
I was never to see him again.
Pagels' thoughts on computation and complexity are still unsurpassed.
It is amazing how prescient Pagels was. We miss him now. There is one point I could take issue with: that the notion of equilibrium in economics is nonsense. Pagels appears to make a mistake here that has clouded discussions between economists and physicists for a long time. The physicists have jumped to the conclusion that economists mean by equilibrium something like thermodynamic equilibrium, and, as Pagels does here, they insist that an economy must instead be far from thermodynamic equilibrium and something like a self-organized steady state.