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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
816:. Some scientists criticized the book as abrasive and arrogant, and perceived a fatal flaw—that simple systems such as cellular automata are not complex enough to describe the degree of complexity present in evolved systems, and observed that Wolfram ignored the research categorizing the complexity of systems. Although critics accept Wolfram's result showing universal computation, they view it as minor and dispute Wolfram's claim of a paradigm shift. Others found that the work contained valuable insights and refreshing ideas. Wolfram addressed his critics in a series of blog posts.
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continuous. He suggests that space consists of a set of isolated points, like cells in a cellular automaton, and that even time flows in discrete steps. Following an idea of Edward
Fredkin, he concludes that the universe itself would then be an automaton, like a giant computer. It's possible, but I can't see any motivation for these speculations, except that this is the sort of system that Wolfram and others have become used to in their work on computers. So might a carpenter, looking at the moon, suppose that it is made of wood."
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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.
316:. 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;
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918:(PCE) has been criticized for being vague, unmathematical, and for not making directly verifiable predictions. It has also been criticized for being contrary to the spirit of research in mathematical logic and computational complexity theory, which seek to make fine-grained distinctions between levels of computational sophistication, and for wrongly conflating different kinds of universality property. Moreover, critics such as
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1045:. However, the notes section at the end of his book acknowledges many of the discoveries made by these other scientists citing their names together with historical facts, although not in the form of a traditional bibliography section. Additionally, the idea that very simple rules often generate great complexity is already an established idea in science, particularly in
374:. 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
576:: 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
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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
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wrote, "Wolfram himself is a lapsed elementary particle physicist, and I suppose he can't resist trying to apply his experience with digital computer programs to the laws of nature. This has led him to the view (also considered in a 1981 paper by
Richard Feynman) that nature is discrete rather than
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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
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is optimized to make experimentation as direct, easy, and meaningful as possible while maximizing the chances that the experiment will do something unexpected. Just as this methodology allows computational mechanisms to be studied in their simplest forms, Wolfram argues that the process of doing so
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argues that systematically exploring the space of simple programs will lead to a base of reusable knowledge. However, many scientists believe that of all possible parameters, only some actually occur in the universe. For instance, of all possible permutations of the symbols making up an equation,
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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,
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is investigating the structure of the possibility space. Wolfram argues that science is far too ad hoc, in part because the models used are too complicated and unnecessarily organized around the limited primitives of traditional mathematics. Wolfram advocates using models whose variations are
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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
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has been criticized for not providing specific results that would be immediately applicable to ongoing scientific research. There has also been criticism, implicit and explicit, that the study of simple programs has little connection to the physical universe, and hence is of limited value.
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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.
470:
While
Wolfram advocates simple programs as a scientific discipline, he also argues that its methodology will revolutionize other fields of science. The basis of his argument is that the study of simple programs is the minimal possible form of science, grounded equally in both
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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
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have argued that it ignores the distinction between hardware and software; while two computers may be equivalent in power, it does not follow that any two programs they might run are also equivalent. Others suggest it is little more than a rechristening of the
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tries to take these ideas as its own, but
Wolfram's model of the universe is a rewriting network, and not a cellular automaton, as Wolfram himself has suggested a cellular automaton cannot account for relativistic features such as no absolute time frame.
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presents a vast number of examples and arguments has been criticized as leading the reader to believe that each of these ideas was original to
Wolfram; in particular, one of the most substantial new technical results presented in the book, that the
524:. 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.
483:
Wolfram argues that the computational realities of the universe make science hard for fundamental reasons. But he also argues that by understanding the importance of these realities, we can learn to use them in our favor. For instance, instead of
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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.
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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.
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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
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wrote, "Just because
Wolfram can cook up a cellular automaton that seems to produce the spot pattern on a leopard, may we safely conclude that he understands the mechanism by which the spots are produced on the leopard, or
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is universal. In 2007, as part of commemorating the book's fifth anniversary, Wolfram's company offered a $ 25,000 prize for proof that this Turing machine is universal. Alex Smith, a computer science student from
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has also been criticized for being heavily visual, with much information conveyed by pictures that do not have formal meaning. It has also been criticized for not using modern research in the field of
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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.
520:(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
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The book also contains a number of individual results—both experimental and analytic—about what a particular automaton computes, or what its characteristics are, using some methods of analysis.
969:, the former by writing a line in his book on how the world might be like a cellular automaton, and later further developed by Fredkin using a toy model called Salt. It has been claimed that
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205:, published by his company Wolfram Research under the imprint Wolfram Media in 2002. It contains an empirical and systematic study of computational systems such as
560:. Most systems can attain this level. Systems, in principle, compute the same things as a computer. Computation is therefore simply a question of translating
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phenomena. Another feature of simple programs is that, according to the book, making them more complicated seems to have little effect on their overall
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YouTube playlist — extensive discussion of each NKS chapter; (As of 2022, Stephen
Wolfram discusses the NKS chapters in view of recent developments.
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Wolfram suggests that the theory of computational irreducibility may provide a resolution to the existence of free will in a nominally
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is that the simpler the system, the more likely a version of it will recur in a wide variety of more complicated contexts. Therefore,
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is not the fundamental cause of complexity in biology has led journalist Chris Lavers to state that
Wolfram does not understand the
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Wolfram argues that one of his achievements is in providing a coherent system of ideas that justifies computation as an organizing
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943:, Professor of Computer Science at University of Texas Austin, also claims that Wolfram's methods cannot be compatible with both
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has pointed out that no real world system has been explained using
Wolfram's methods in a satisfactory fashion. Mathematician
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Another common theme is taking facts about the computational universe as a whole and using them to reason about fields in a
1752:"Note (C) for the Rule 110 Cellular Automaton: A New Kind of Science | Online by Stephen Wolfram [Page 1115]"
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Wolfram's speculations of a direction towards a fundamental theory of physics have been criticized as vague and obsolete.
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cellular automaton. Very small Turing machines can simulate Rule 110, which Wolfram demonstrates using a 2-state 5-symbol
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has also been criticized for asserting that the behavior of simple systems is somehow representative of all systems.
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must be explored experimentally, and that the results of these experiments have great relevance to understanding the
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The basic subject of Wolfram's "new kind of science" is the study of simple abstract rules—essentially, elementary
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Another type of production involves the creation of programs for the analysis of computational systems. In the
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in 1 and 2 dimensions; several varieties of substitution and network systems; recursive functions; nested
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engages with the mathematical basis of the physical world, and therefore has much to offer the sciences.
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has been heavily criticized as not being original or important enough to justify its title and claims.
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was stolen without attribution, namely his idea on enumerating possible Turing-computable universes.
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the spots are there, or what function (evolutionary or mating or camouflage or other) they perform?"
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argues that this is evidence that simple programs are enough to capture the essence of almost any
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and methods appropriate for the study of simple programs are relevant to other fields of science.
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1535:"In search of a scientific revolution: controversial genius Stephen Wolfram presses onward"
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Simple programs are capable of a remarkable range of behavior. Some have been proven to be
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The number of its possible variations is small enough so that all of them can be computed.
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way. For instance, Wolfram discusses how facts about the computational universe inform
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systems and then try to match them to the behaviors we observe. A major theme of
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enumerable and whose consequences are straightforward to compute and analyze.
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Its operation can be completely explained by a simple graphical illustration.
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and empirical experimentation. Every aspect of the methodology advocated in
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255: in this section. Unsourced material may be challenged and removed.
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1368:"A Revolution or self indulgent hype? How top scientists view Wolfram"
344:. For a program to qualify as simple, there are several requirements:
1196:"'A New Kind of Science': You Know That Space-Time Thing? Never Mind"
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may have been created or edited in return for undisclosed payments
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are a final category of applications that fall in this theme.
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violations, and hence cannot explain the observed results of
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The book contains a new technical result in describing the
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universe. He posits that the computational process in the
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through all of the possible components for the best match.
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Berry, Michael; Ellis, John; Deutch, David (15 May 2002).
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Based on his experimental results, Wolfram developed the
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1602:"Reflections on Stephen Wolfram's A New Kind of Science"
1502:"A Mathematician Looks at Wolfram's New Kind of Science"
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There are a number of specific results and ideas in the
1437:"Living a Paradigm Shift: Looking Back on Reactions to
993:, the Nobel laureate and elementary particle physicist
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mathematical definitions, nor does it attempt to prove
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It can be completely explained in a few sentences of
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869:rather than standard notation. Along these lines,
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1248:"The Man Who Cracked The Code to Everything ..."
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1130:"The Wolfram 2,3 Turing Machine Research Prize"
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1155:"The Wolfram 2,3 Turing Machine Is Universal!"
514:. For instance, he argues that the concept of
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1568:Bulletin of the American Mathematical Society
437:Mapping and mining the computational universe
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910:Principle of computational equivalence (PCE)
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1407:"It's Been 10 Years: What's Happened with
1101:"Weighing Wolfram's 'New Kind of Science'"
756:. Please do not remove this message until
399:sensitive dependence on initial conditions
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776:Learn how and when to remove this message
596:First, there are several cases where the
271:Learn how and when to remove this message
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752:Relevant discussion may be found on the
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1701:Weinberg, S. (24 October 2002).
1589:from the original on 2012-03-17.
1522:from the original on 2003-03-08.
1465:Bailey, David (September 2002).
1435:Wolfram, Stephen (12 May 2012).
1257:from the original on 27 May 2009
1136:from the original on 15 May 2011
792:coverage, including articles in
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664:, and philosophical fields like
393:behavior, conserved quantities,
284:Computation and its implications
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1726:"How the cheetah got his spots"
1724:Lavers, Chris (3 August 2002).
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1405:Wolfram, Stephen (7 May 2012).
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1304:"Review: A New Kind of Science"
1194:Johnson, George (9 June 2002).
712:2-state 3-symbol Turing machine
662:computational complexity theory
362:using just a few lines of code.
240:needs additional citations for
1302:Rucker, Rudy (November 2003).
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1703:"Is the Universe a Computer?"
1600:Kurzweil, Ray (13 May 2002).
1580:10.1090/S0273-0979-02-00970-9
1467:"A Reclusive Kind of Science"
1312:American Mathematical Monthly
1220:Levy, Stephen (27 May 2002).
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540:): the principle states that
189:A New Kind of Science, online
36:, a violation of Knowledge's
1707:The New York Review of Books
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517:computational irreducibility
506:Computational irreducibility
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1774:What We've Learned from NKS
1277:"The science of everything"
1246:Levy, Stephen (June 2002).
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758:conditions to do so are met
501:Philosophical underpinnings
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584:Applications and results
1778:Wolfram Physics Project
1500:Gray, Lawrence (2003).
1068:Scientific reductionism
556:("universal") level of
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1814:Complex systems theory
1809:Computer science books
1794:2002 non-fiction books
1099:Rosen, Judith (2003).
851:scientific methodology
845:A common criticism of
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1849:Computational science
1824:Metatheory of science
1768:A New Kind of Science
1686:Schmidhuber, JĂĽrgen.
1655:"ZUSE-FREDKIN-THESIS"
1623:A New Kind of Science
1559:A New Kind of Science
1533:Weiss, Peter (2003).
1439:A New Kind of Science
1409:A New Kind of Science
1006:Wolfram's claim that
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790:A New Kind of Science
427:A New Kind of Science
405:, material fracture,
290:A New Kind of Science
215:scientific philosophy
198:A New Kind of Science
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1839:Systems theory books
1445:Stephen Wolfram Blog
1415:Stephen Wolfram Blog
989:In a 2002 review of
925:Church–Turing thesis
627:computational models
619:conserved quantities
512:principle of science
249:improve this article
213:and argues that the
1819:Mathematics and art
1376:The Daily Telegraph
1012:theory of evolution
967:computable universe
857:does not establish
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650:evolutionary theory
605:, and the shortest
558:computational power
522:mathematical models
486:reverse engineering
383:universal computers
326:recursive functions
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1625:(Postscript file)"
1509:Notices of the AMS
1200:The New York Times
976:JĂĽrgen Schmidhuber
945:special relativity
795:The New York Times
376:brute-force search
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1834:Self-organization
1804:Cellular automata
1641:10.26421/QIC2.5-7
1553:Krantz, Steven G.
1105:Publishers Weekly
1074:Calculating Space
1008:natural selection
1002:Natural selection
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