A New Kind of Science

wikipedia |  The thesis of A New Kind of Science (NKS) is twofold: that the nature of computation must be explored experimentally, and that the results of these experiments have great relevance to understanding the physical world. Since its nascent beginnings in the 1930s, computation has been primarily approached from two traditions: engineering, which seeks to build practical systems using computations; and mathematics, which seeks to prove theorems about computation. However, as recently as the 1970s, computing has been described as being at the crossroads of mathematical, engineering, and empirical traditions.^[2][3]

Wolfram introduces a third tradition that seeks to empirically investigate computation for its own sake: He argues that an entirely new method is needed to do so because traditional mathematics fails to meaningfully describe complex systems, and that there is an upper limit to complexity in all systems.^[4]

Simple programs

The basic subject of Wolfram's "new kind of science" is the study of simple abstract rules—essentially, elementary computer programs. In almost any class of a computational system, one very quickly finds instances of great complexity among its simplest cases (after a time series of multiple iterative loops, applying the same simple set of rules on itself, similar to a self-reinforcing cycle using a set of rules). This seems to be true regardless of the components of the system and the details of its setup. Systems explored in the book include, amongst others, cellular automata in one, two, and three dimensions; mobile automata; Turing machines in 1 and 2 dimensions; several varieties of substitution and network systems; primitive recursive functions; nested recursive functions; combinators; tag systems; register machines; reversal-addition. For a program to qualify as simple, there are several requirements:

1. Its operation can be completely explained by a simple graphical illustration.
2. It can be completely explained in a few sentences of human language.
3. It can be implemented in a computer language using just a few lines of code.
4. The number of its possible variations is small enough so that all of them can be computed.

Generally, simple programs tend to have a very simple abstract framework. Simple cellular automata, Turing machines, and combinators are examples of such frameworks, while more complex cellular automata do not necessarily qualify as simple programs. It is also possible to invent new frameworks, particularly to capture the operation of natural systems. The remarkable feature of simple programs is that a significant percentage of them are capable of producing great complexity. Simply enumerating all possible variations of almost any class of programs quickly leads one to examples that do unexpected and interesting things. This leads to the question: if the program is so simple, where does the complexity come from? In a sense, there is not enough room in the program's definition to directly encode all the things the program can do. Therefore, simple programs can be seen as a minimal example of emergence. A logical deduction from this phenomenon is that if the details of the program's rules have little direct relationship to its behavior, then it is very difficult to directly engineer a simple program to perform a specific behavior. An alternative approach is to try to engineer a simple overall computational framework, and then do a brute-force search through all of the possible components for the best match.

Simple programs are capable of a remarkable range of behavior. Some have been proven to be universal computers. Others exhibit properties familiar from traditional science, such as thermodynamic behavior, continuum behavior, conserved quantities, percolation, sensitive dependence on initial conditions, and others. They have been used as models of traffic, material fracture, crystal growth, biological growth, and various sociological, geological, and ecological phenomena. Another feature of simple programs is that, according to the book, making them more complicated seems to have little effect on their overall complexity. A New Kind of Science argues that this is evidence that simple programs are enough to capture the essence of almost any complex system.

Mapping and mining the computational universe

In order to study simple rules and their often complex behaviour, Wolfram argues that it is necessary to systematically explore all of these computational systems and document what they do. He further argues that this study should become a new branch of science, like physics or chemistry. The basic goal of this field is to understand and characterize the computational universe using experimental methods.

The proposed new branch of scientific exploration admits many different forms of scientific production. For instance, qualitative classifications are often the results of initial forays into the computational jungle. On the other hand, explicit proofs that certain systems compute this or that function are also admissible. There are also some forms of production that are in some ways unique to this field of study. For example, the discovery of computational mechanisms that emerge in different systems but in bizarrely different forms.

Another kind of production involves the creation of programs for the analysis of computational systems. In the NKS framework, these themselves should be simple programs, and subject to the same goals and methodology. An extension of this idea is that the human mind is itself a computational system, and hence providing it with raw data in as effective a way as possible is crucial to research. Wolfram believes that programs and their analysis should be visualized as directly as possible, and exhaustively examined by the thousands or more. Since this new field concerns abstract rules, it can in principle address issues relevant to other fields of science. However, in general Wolfram's idea is that novel ideas and mechanisms can be discovered in the computational universe, where they can be represented in their simplest forms, and then other fields can choose among these discoveries for those they find relevant.

Wolfram has since expressed "A central lesson of A New Kind of Science is that there’s a lot of incredible richness out there in the computational universe. And one reason that’s important is that it means that there’s a lot of incredible stuff out there for us to 'mine' and harness for our purposes."^[5]