The latest on exploring the computational universe, with free online access to Stephen Wolfram's classic page breakthrough book. Book review appeared in Applied Mechanics Reviews, vol. 56, no. (Wolfram Research, Inc., Trade Center Drive, Champaign, IL ). Princeton and Illinois; significant contributions to cellular automata and complexity theory; developer of the popular. makers of Mathematica), Wolfram has self-published his magnum opus A New. Kind of Science which continues along those lines of thinking. The book itself.
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Volume 40, Number 1, Pages – S (02) Article electronically published on October 17, A new kind of science, by Stephen . s. Contribute to muditbac/Reading development by creating an account on GitHub. This long-awaited paintings from one of many world's most beneficial scientists provides a sequence of dramatic discoveries by no means sooner than made.
Wolfram advocates using models whose variations are enumerable and whose consequences are straightforward to compute and analyze.
Computational irreducibility[ edit ] Wolfram argues that one of his achievements is in providing a coherent system of ideas that justifies computation as an organizing principle of science.
For instance, he argues that the concept of computational irreducibility that some complex computations are not amenable to short-cuts and cannot be "reduced" , is ultimately the reason why computational models of nature must be considered in addition to traditional mathematical models. Likewise, his idea of intrinsic randomness generation—that natural systems can generate their own randomness, rather than using chaos theory or stochastic perturbations—implies that computational models do not need to include explicit randomness.
Principle of computational equivalence[ edit ] Based on his experimental results, Wolfram developed the principle of computational equivalence PCE : the principle states that systems found in the natural world can perform computations up to a maximal "universal" level of computational power.
Most systems can attain this level. Systems, in principle, compute the same things as a computer.
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Computation is therefore simply a question of translating input and outputs from one system to another. Consequently, most systems are computationally equivalent. Proposed examples of such systems are the workings of the human brain and the evolution of weather systems. The principle can be restated as follows: almost all processes that are not obviously simple are of equivalent sophistication. From this principle, Wolfram draws an array of concrete deductions which he argues reinforce his theory.
Possibly the most important among these is an explanation as to why we experience randomness and complexity : often, the systems we analyze are just as sophisticated as we are. Thus, complexity is not a special quality of systems, like for instance the concept of "heat," but simply a label for all systems whose computations are sophisticated.
Wolfram argues that understanding this makes possible the "normal science" of the NKS paradigm. At the deepest level, Wolfram argues that—like many of the most important scientific ideas—the principle of computational equivalence allows science to be more general by pointing out new ways in which humans are not "special"; that is, it has been claimed that the complexity of human intelligence makes us special, but the Principle asserts otherwise.
In a sense, many of Wolfram's ideas are based on understanding the scientific process—including the human mind—as operating within the same universe it studies, rather than being outside it. Applications and results[ edit ] There are a number of specific results and ideas in the NKS book, and they can be organized into several themes. One common theme of examples and applications is demonstrating how little complexity it takes to achieve interesting behavior, and how the proper methodology can discover this behavior.
First, there are several cases where the NKS book introduces what was, during the book's composition, the simplest known system in some class that has a particular characteristic.
Some examples include the first primitive recursive function that results in complexity, the smallest universal Turing Machine , and the shortest axiom for propositional calculus. In a similar vein, Wolfram also demonstrates many simple programs that exhibit phenomena like phase transitions , conserved quantities , continuum behavior, and thermodynamics that are familiar from traditional science.
Simple computational models of natural systems like shell growth , fluid turbulence , and phyllotaxis are a final category of applications that fall in this theme. Another common theme is taking facts about the computational universe as a whole and using them to reason about fields in a holistic way. For instance, Wolfram discusses how facts about the computational universe inform evolutionary theory , SETI , free will , computational complexity theory , and philosophical fields like ontology , epistemology , and even postmodernism.
Wolfram suggests that the theory of computational irreducibility may provide a resolution to the existence of free will in a nominally deterministic universe. He posits that the computational process in the brain of the being with free will is actually complex enough so that it cannot be captured in a simpler computation, due to the principle of computational irreducibility.
Thus, while the process is indeed deterministic, there is no better way to determine the being's will than, in essence, to run the experiment and let the being exercise it. The book also contains a vast number of individual results—both experimental and analytic—about what a particular automaton computes, or what its characteristics are, using some methods of analysis.
The book contains a new technical result in describing the Turing completeness of the Rule cellular automaton. Very small Turing machines can simulate Rule , which Wolfram demonstrates using a 2-state 5-symbol universal Turing machine. Wolfram conjectures that a particular 2-state 3-symbol Turing machine is universal.
In this pair of book reviews, the long-anticipated book from the creator I look at two very different books of the Mathematica computing package. The first, A book.
The other, Prey would be hard put to identify a treatise I have by Michael Crichton, is a technology-based ever enjoyed less. For example, Richard Feyn- fantasy. After the reviews, I discuss some of man is notable for digging deep into the mys- the interesting threads of fact and fantasy teries of physics and then developing long, jar- that weave their ways through both books.
Heineman and William T. In this pair of book reviews, the long-anticipated book from the creator I look at two very different books of the Mathematica computing package. The first, A book.
The other, Prey would be hard put to identify a treatise I have by Michael Crichton, is a technology-based ever enjoyed less. For example, Richard Feyn- fantasy. After the reviews, I discuss some of man is notable for digging deep into the mys- the interesting threads of fact and fantasy teries of physics and then developing long, jar- that weave their ways through both books. Heineman and William T.Is there a way to work out how a weather system will develop?
A New Kind of Science: A 15-Year View
We can simulate the candidate universe for billions of steps. Those computations would reflect the rich history of our civilization, and all the things that have happened to us. We can even have a general-purpose computer that can be programmed to do a full range of different tasks.
The Path to Computational Thinking Probably the greatest intellectual shift of the past century has been the one towards the computational way of thinking about things. From this principle, Wolfram draws an array of concrete deductions which he argues reinforce his theory.
But my guess is that there are tasks where for the foreseeable future access to the full computational universe will be necessary to make them even vaguely practical.
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