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Books Video icon An illustration of two cells of a film strip. Video Audio icon An illustration of an audio speaker. Underscoring his point that simplicity begets complexity, Wolfram wrote this book in mostly nontechnical language. Any informed, motivated reader can, with some effort, follow from chapter to chapter, but the work as a whole and its implications are probably understood fully by the author alone.
Had this been written by a lesser scientist, many academics might have dismissed it as the work of a crank. Given its source, though, it will merit discussion for years to come. Essential for all academic libraries. I'm still not sure what he's done By Michael J. Edelman The world of mathematics is regularly disrupted by paradigm-shattering inventions and discoveries, some of which turn out to have great important, and most of which turn out to be nothing more than sound and fury, signifying nothing.
Sometimes it takes a decade or more to fully evaluate a piece of work. Consider Benoit Mandelbrot's work with fractals, which was at first discarded as a sort of epiphenomenal curiosity, but which later revolutionized fields as far ranging as computer animation and cardiac medicine. But for every Mandelbrot there are a dozen circle squarers or people like G.
He's clearly brilliant, as evidenced by his citation index numbers over 30,! He's also contributed major papers to the field of cellular automata and complexity theory. He spent a decade working on A New Science, and his argument that the underlying nature of reality is expressed not in physical laws, but in programs.
So is Wolfram right? Is there, contained within the multitude of patterns and algorithms in this book, a new insight into the nature of reality? Frankly, I'm nowhere near a good enough mathematician to evaluate his work, or to compare it to the work of others in the CA field. This book may in fact contain hidden within it the secrets to the underlying reality of the universe, or it may be, as another reviewer wittily put it, 'an undergraduate project gone haywire.
Until we do, the prospective reader is probably better served by the variety of inexpensive programs that are now available to explore CA than to slog through 1, pages of finely-printed diagrams. Boring By Kalifer Deil Although I think there is merit in looking for simple fundamental mechanisms to explain nature this book could have been reduced to a 8 page pamphlet to thoroughly explain his concepts.
If you sorted the words in this book around one hundred pages would be filled with the word 'I'. There is nothing Earth shaking here just some basic cellular automata and lots of really boring-you-to-tears examples. Wolfram calls these systems simple programs and argues that the scientific philosophy and methods appropriate for the study of simple programs are relevant to other fields of science.
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 s, 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 s, computing has been described as being at the crossroads of mathematical, engineering, and empirical traditions. 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.
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; recursive functions; nested recursive functions; combinators; tag systems; register machines; reversal-addition.
For a program to qualify as simple, there are several requirements:. 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.
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 type 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.
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