Looking to the Future of A New Kind of Science


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an inexhaustible supply of new, original, material. And one consequence of this is that it makes all sorts of mass customization broadly feasible.

There are many immediate examples of this in art. WolframTones did it for simple musical pieces. One can also do it for all sorts of visual patterns—perhaps ever changing, and selected from the computational universe and then grown to fit into particular spatial or other constraints. And then there is architecture. Where one can expect to discover in the computational universe new forms that can be used to create all sorts of structures. And indeed in the future I would not be surprised if at first the most visually obvious everyday examples of NKS were forms of things like buildings, their dynamics, decoration and structure.

Mass production and the legacy of the industrial revolution have led to a certain obvious orderliness to our world today—with many copies of identical products, precisely repeating processes, and so on. And while this is a convenient way to set things up if one must be guided by traditional mathematics and the like, NKS suggests that things could be much richer. Instead of just carrying out some processes in a precisely repeating way, one computes what to do in each case. And putting together many such pieces of computation the behavior of the system as a whole can be highly complex. And finding the correct rules for each element—to achieve some set of overall objectives—is no doubt best done by studying and searching the computational universe of possibilities.

Viewed from the outside, some of the best evidence for the presence of our civilization on Earth comes from the regularities that we have created (straight roads, things happening at definite times, radio carrier signals, satellite orbits, and so on). But in the future, with the help of NKS methods, more and more of these regularities will be optimized out. Vehicles will move in optimized patterns, radio signals will be transferred in complicated sequences of local hops… and even though the underlying rules may be simple, the actual behavior that is seen will look highly complex—and much more like all sorts of systems in physics and elsewhere that we already see in nature.

There are other—more abstract—situations where computation and NKS ideas will no doubt become increasingly important. One example is in commerce. Already there is an increasing trend toward algorithmic pricing. Increasingly commercial terms and contracts of all kinds will be stated in computational terms. And then—a little like a market of algorithmic traders—there will be what amounts to an NKS issue of what the overall consequences of many separate transactions will be. And again, finding the appropriate rules for these underlying transactions will involve understanding and searching the computational universe—and presumably various kinds of mass customization, that eventually make concepts like money as a simple numerical quantity quite obsolete.

Future schemes for such things as auctions and voting may also perhaps be mined from the computational universe, and as a result may be mass customized on demand. And, more speculatively, the same might be true for future corporate or political organizational structures. Or for example for mechanisms for social and other human networks.

In addition to using NKS in “technology mode” as a way to create things, one can also use NKS in “science mode” as a way to model and understand things. And typically the goal is to find in the computational universe some simple program whose behavior captures the essence of whatever system or phenomenon one is trying to analyze. This was an important focus of the NKS book, and has been a major theme in the past decade of NKS research. In general in science it has been difficult to come up with new models for things. But the computational universe is an unprecedentedly rich source—and I would expect that before long the rate of new models derived from it will come to far exceed all those from traditional mathematical and other sources.

An important trend in today’s world is the availability of more and more data, often collected with automated sensors, or in some otherwise automated way. Often—as we see in many areas of Wolfram|Alpha or in experiments on personal analytics—there are tantalizing regularities in the data. But the challenge that now exists is to find good models for the data. Sometimes these models are important for basic science; more often they are important for practical purposes of prediction, anomaly detection, pattern matching and so on.

In the past, one might find a model from data by using statistics or machine learning in effect to fit parameters of some formula or algorithm. But NKS suggests that instead one should try to find in the computational universe some set of underlying rules that can be run to simulate the essence of whatever generates the data. At present, the methods we have for finding models in the computational universe are still fairly ad hoc. But in time it will no doubt be possible to streamline this process, and to develop some kind of highly systematic methodology—a rough analog of the historical progression from calculus to statistics.

There are many areas where it is clear that NKS models will be important—perhaps because the phenomenon being modeled is too complex for traditional approaches, or perhaps because, as is becoming so common in practice, the underlying system has elements that are specifically set up to be computational.

One area where NKS models seem likely to be particularly important is medicine. In the past, most disorders that medicine successfully addressed were fundamentally either structural or chemical. But today’s most important challenge areas—like aging, cancer, immune response and brain functioning—all seem to be associated more with large-scale systems containing many interacting parts. And it certainly seems plausible that the best models for these systems will be based on simple programs that exist in the computational universe.

In recent times, medicine has slowly been becoming more quantitative. But somehow it is still always based on small collections of numbers, that lead to a small set of possible diagnoses. But between the coming wave of automated data acquisition, and the use of underlying NKS models, I suspect that the future of medicine will be more about dynamic computation than about specific discrete diagnoses. But even given a good predictive model of what is going on in a particular medical situation, it will still often be a challenge to figure out just what intervention to make—though the character of this problem will no doubt change when algorithmic drugs and computational materials exist.

What would be the most spectacular success for NKS models? Perhaps models that lead to an understanding of aging, or cancer. Perhaps more accurate models for social or economic processes. Or perhaps a final fundamental theory of physics.

In the NKS book, I started looking at what might be involved in finding the underlying rules for our physical universe out in the computational universe. I developed some network-based models that operate in a sense below space and time, and from which I was already able to derive some surprisingly interesting features of physics as we know it. Of course, we have no guarantee that our physical universe has rules that are simple enough to be found, say, by an explicit search in the computational universe. But over the past decade I have slowly been building up the rather large software and analysis capabilities necessary to mount a serious search. And if successful, this will certainly be an important piece of validation for the NKS approach—as well as being an important moment for science in general.

Beyond science and technology, another important consequence of a new worldview like NKS is the effect that it can have on everyday thinking. And certainly the mathematical approach to science has had a profound effect on how we think about all kinds of issues and processes. For today, whether we’re talking about business or psychology or journalism, we end up using words and ideas—like “momentum” and “exponential”—that come directly from this approach. Already there are analogs from NKS that are increasingly used—like “computationally irreducible” and “intrinsically random”. And as such concepts become more widespread they will inform thinking about more and more things—whether it’s describing the operation of an organization, or working out what could conceivably be predictable for purposes of liability.

Beyond everyday thinking, the ideas and results of NKS will also no doubt have increasing influence on many areas of philosophical thinking. In the past, most of the understanding for what science could contribute to philosophy came from the mathematical approach to science. But now the new concepts and results in NKS in a sense provide a large number of new “raw facts” from which philosophy can operate.

The principles of NKS are important not only at an intellectual level, but also at a practical level. For they give us ideas about what might be possible, and what might not. For example, the Principle of Computational Equivalence in effect implies that there can be nothing general and abstract that is special about intelligence, and that in effect all its features must just be reflections of computation. And it is this that made me realize soon after the NKS book appeared that my long-term goal of making knowledge broadly computable might be achievable “just with computation”—which is what led me to embark on the Wolfram|Alpha project.

I have talked elsewhere about some of the consequences of the principles of NKS for the long-range future of the human condition. But suffice it to say here that we can expect an increasing delegation of human intellectual activities to computational systems—but with ultimate purposes still of necessity defined by humans and the history of human culture and civilization. And perhaps the place where NKS principles will enter most explicitly is in making future legal and other distinctions about what really constitutes responsibility, or a mind, or a memory as opposed to a computation.

As we look at the future of history, there are some inexorable trends, and then there are some wild cards. If we find the fundamental theory of physics, will we be able to hack it to achieve something like instantaneous travel? Will we find some key principle that lets us reverse aging? Will we be able to map memories directly from one brain to another, without the intermediate step of language? Will we find extraterrestrial intelligence? About all these questions, NKS has much to say.

If we look back at the mathematical approach to science, one of its societal consequences has been the injection of mathematics into education. To some extent, a knowledge of mathematical principles is necessary to interact with the world as it exists today. It is also an important foundation for understanding fields that have made serious use of the mathematical approach to science. And certainly learning mathematics to at least some level is a convenient way to teach precise structured thinking in general.

But I believe NKS also has much to contribute to education. At an elementary level, it can be viewed as a kind of “pre-computer science”, introducing fundamental notions of computation in a direct and often visual way. At a more sophisticated level, NKS provides a conceptual framework for understanding the foundations of many computational fields. And even from what I have seen over the past decade, education about NKS—a little like physics before it—seems to provide a powerful springboard for people entering all sorts of modern areas.

What about NKS research? There is much to be done in the many applications of NKS. But there is also much to be done in pure NKS—studying the basic science of the computational universe. The NKS book—and the decade of research that has followed it—has only just begun to scratch the surface in exploring and investigating the vast range of possible simple programs. The situation is in some ways a little like in chemistry—where there are an infinite variety of possible chemical compounds each with their own features, that can be studied either for their own sake, or for the purpose of inferring general principles, or for diverse potential applications. And where even after a century or more, only a small part of what is possible has been done.

In the computational universe it is quite remarkable how much can be said about almost any simple program with nontrivial behavior. And the more one knows about a given program, the more potential there is to find interesting applications of it, whether for modeling, technology, art or whatever. Sometimes there are features of programs that can be almost arbitrarily difficult to determine. But sometimes they can be important. And so, for example, it will be important to get more evidence for (or against) the Principle of Computational Equivalence by trying to establish computation universality for a variety of simple programs (rule 30 would be a particularly important achievement).

As more is done in pure NKS, so its methodologies will become more streamlined. And for example there will be ever clearer principles and conventions for what constitutes a good computer experiment, and how the results of investigations on simple programs should be communicated. There are fields other than NKS—notably mathematics—where computer experiments also make sense. But my guess is that the kind of exploratory computer experimentation that is a hallmark of pure NKS will always end up largely classified as pure NKS, even if its subject matter is quite mathematical.

If one looks at the future of NKS research, an important issue is how it is structured in the world. Some part of it—like for mathematics—may be driven by education. Some part may be driven by applications, and their commercial success. But in the long term just how the pure basic science of NKS should be conducted is not yet clear. Should there be prizesInstitutions? Socially oriented value systems? As a young field NKS has the potential to take some novel approaches.

For an intellectual framework of the magnitude of NKS, a decade is a very short time. And as I write this post, I realize anew just how great the potential of NKS is. I am proud of the part I played in launching NKS, and I look forward to watching and participating in its progress for many years to come.

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Stephen Wolfram is the creator of Mathematica, the author of A New Kind of Science, the creator of Wolfram|Alpha, and the founder and CEO of Wolfram Research. Follow @stephen_wolfram

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One response to “Looking to the Future of A New Kind of Science”

  1. A great blog and an exiting book. I am a synthetic biologist. I was especially curious about this remark “NKS will also no doubt be important in figuring out how to set up synthetic biological organisms.” It would be very interesting, if you could expand your thoughts around this a bit more. Thanks a lot in advance.