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# Wolfram Science™

Using the basic science of the computational universe to create a new kind of technology

Often known as "NKS" after the title of Stephen Wolfram's 2002 book *A New Kind of Science*, Wolfram Science is a branch of basic science concerned with understanding the computational universe of possible programs: their behavior, general properties and applications.

Wolfram Science opens up a new way of thinking about computation, and a new approach to creating computational—and other—technology.

Mining the computational universe of possible programs using the ideas of Wolfram Science has become a key approach for creating algorithms used in Wolfram products. And as a company committed to a long-term vision, Wolfram Research continues to support Wolfram Science and its intellectual development.

A core discovery in Wolfram Science is that even extremely short programs—say less than a line of Wolfram Language code—can behave in irreducibly rich and complex ways.

Stephen Wolfram's favorite discovery: an incredibly simple program that produces behavior so complex that many aspects of it seem random—and they're random enough to make a great pseudorandom generator.

Like the telescope enabled modern astronomy and led to modern physics, the Wolfram Language and its precursors enabled exploration of the computational universe, and led to Wolfram Science.

Stephen Wolfram's central principle, inferred from years of studying the computational universe—with deep implications for science, technology and our ways of thinking about the world.

Today's mathematics—as captured in many functions in Mathematica—is based on specific axioms. Wolfram Science highlights the rich space of other possible axioms that yield uninvented branches of mathematics.

Following extensive work by Stephen Wolfram and many others, simple programs are beginning to overtake mathematical equations as the favored modeling approach for a wide range of systems, especially where complex behavior is seen.

What does it take to make a universal computer? A key result in Wolfram Science is that even incredibly simple systems can serve as universal computers capable of being programmed to compute anything.

Just as the concept of digital information led us to genomics, so ideas about the computational universe may lead us to an understanding of diverse biological processes—and the complexity that makes medicine difficult.

If simple programs can yield infinitely complex behavior, perhaps our whole universe can be represented as just a simple program. Stephen Wolfram has long explored this idea, generating a rich set of results, but not yet finding our universe...

Each program in the computational universe is like a new idea, with its own consequences—that can surprise and amaze us with their unexpectedness, cleverness, usefulness or beauty.

Nature creates complex and beautiful forms by following specific simple programs—but with all the programs in the computational universe, we have an inexhaustible supply of nature-like beauty to explore.

Built in 2005 at the height of the ringtone craze, WolframTones creates short musical pieces by mining them from the computational universe.

The idea of searching simple programs isn't new: in fact, it's probably a major force in biology, alongside natural selection, that leads to the endlessly creative and complex forms we see in biology.

Simple programs—especially cellular automata—have been widely used to produce decorative art, with forms evoking different styles found by searching the computational universe of programs.

When an architectural project calls for a form with inner logic but rich and complex structure, it's become common to turn to Wolfram Science to find simple programs that can generate it.

We've been mining the physical universe for technology for millennia. Now it's time to mine the computational universe—and discover algorithms we'd never imagine. Wolfram Research has been doing it for years.

An increasing number of Wolfram Language algorithms—for image analysis, function evaluation, randomness generation, machine learning, and much more—were found by mining the computational universe.

Most traditional algorithms have very regular iterative (periodic) or recursive (nested) structures. Wolfram Science searches often yield more optimal algorithms that do not have any such recognizable structure.

Like drug discovery in the chemical universe, algorithm discovery in the computational universe needs targets—often defined as Wolfram Language programs to compare with or test potential algorithms.

Traditional methodology involves building up algorithms in incremental steps. The Wolfram Science methodology involves large-scale searches that, if successful, immediately give the final result.

Wolfram Research often searches trillions of programs to find the best algorithm for a particular purpose, typically avoiding incremental and evolutionary methods that tend not to reach the truly unexpected.

In the computational universe, it's common to find optimal programs whose operation is at best difficult to understand—necessitating automated methods for assessing performance or proving correctness.

Wolfram|Alpha is in many ways the first "killer app" of Wolfram Science—made possible both by the conceptual discoveries of the science, and by the practical methods it introduces.

Stephen Wolfram often credits the Principle of Computational Equivalence for convincing him that computational knowledge doesn't require human-like AI—and that the Wolfram|Alpha project might be doable.

Wolfram|Alpha is full of heuristics that effectively automate human judgment and aesthetic choice. Many of these heuristics were either found or deeply informed by Wolfram Science methods.

The Wolfram|Alpha language understanding system relies heavily on ideas from Wolfram Science, in effect setting up collections of interacting simple programs that represent primitive linguistic processes.

Research in Wolfram Science tends to involve extensive visualization of computational processes—a technique widely used in the development of Wolfram|Alpha.

Like mathematics, Wolfram Science provides an introduction to abstract thinking—while also giving students an important theoretical and conceptual foundation for their life in today's world of ubiquitous computation.

Following the rules to create a cellular automaton pattern is an activity accessible to kindergartners, already teaching the concept of an algorithm and the importance of precision, and showing connections to the real world.

Particularly at lower levels, Wolfram Science teaches the same kind of abstract and rigorous thinking as math—but is often more concrete and accessible, and has immediate surprising connections to the real world.

Art. Technology. Nature. Programming. Exploration. Abstract thinking. Wolfram Science has components that appeal to a remarkably wide range of students.

Wolfram Science offers teachers a unique opportunity to show the process of discovery in action by doing live classroom computer experiments with unscripted results.

Without requiring any math, Wolfram Science introduces the concepts of computation, and gives students a strong framework for later education in traditional computer science.

Wolfram Science involves computer experiments and experimental observation, theoretical abstract thinking, creating and assessing models—as well as visual thinking, with connections to aesthetics.

Partly because it's so new, and partly because of its methodologies, research in Wolfram Science is uniquely accessible to students—so even young students can potentially make their own discoveries.

Since 2003, the annual Wolfram Summer School has served as a highly successful model for project-based education in Wolfram Science.

Precursors of the Wolfram Language are what made Wolfram Science possible—and the Wolfram Language now provides a highly optimized environment for Wolfram Science work.

The symbolic primitives—and pattern-matching capabilities—of the Wolfram Language make it ideally suited to represent a broad range of models of computations and types of simple program.

The Wolfram Language has a variety of built-in functions for doing common operations in Wolfram Science—such as running cellular automata, Turing machines, and so on.

Once a Wolfram Science discovery is made in the Wolfram Language, it's easy to take the algorithm, model, etc. and scale it up for production use.

The interactive and highly automated character of the Wolfram Language makes it uniquely suitable for doing computer experiments as soon as one thinks of them.

Wolfram Language CDF documents are ideal for recording computer experiments, showing the sequence of steps taken, and inserting text with relevant observations.

Wolfram Science is an outgrowth of many people's work, with core contributions made since 1980 by Stephen Wolfram—culminating in his 2002 book *A New Kind of Science*.

Since the 1600s, most of exact science has been based on constructing mathematical equations for the world. Wolfram Science is about generalizing this by using programs instead of equations to model the world.

Spawned in some ways by Stephen Wolfram's work in the early 1980s, Complexity Theory studies systems with complex behavior, but doesn't take the same kind of global view of the computational universe as Wolfram Science.

When Stephen Wolfram's book appeared in 2002, it encountered the same kind of turbulence seen in many historical scientific paradigm shifts, but soon began the long process of widespread acceptance.

Concepts like the Principle of Computational Equivalence are long-term scientific ideas that require progressive validation—like the 2007 Wolfram-sponsored proof of the simplest universal Turing machine.

Stephen Wolfram's discoveries in the early 1980s were made in a class of simple programs known as cellular automata. It took his 2002 book to show how broad the discoveries in fact are.

Stephen Wolfram started building Mathematica in 1986 so that he could have a tool to continue his work in basic science—and from 1991 to 2002 he used it to make the discoveries in *A New Kind of Science*.

Large numbers of academic papers have used Wolfram Science methodologies to create models and make discoveries across an amazing diversity of natural, social and mathematical sciences—and beyond.

The ultimate test of a science is whether it's useful—and Wolfram Science has firmly established itself as a major source of scientific, technological, artistic, philosophical and other results.