Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his 2002 book A New Kind of Science, although the concept goes back to studies from the 1980s.
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Many physical systems are complex enough that they cannot be effectively measured. Even simpler programs contain a great diversity of behavior. Therefore no model can predict, using only initial conditions, exactly what will occur in a given physical system before an experiment is conducted. Because of this problem of undecidability in the formal language of computation, Wolfram terms this inability to "shortcut" a system (or "program"), or otherwise describe its behavior in a simple way, "computational irreducibility." The idea demonstrates that there are occurrences where theory's predictions are effectively not possible. Wolfram states several phenomena are normally computationally irreducible[citation needed].
Computational irreducibility explains observed limitations of existing mainstream science. In cases of computational irreducibility, only observation and experiment can be used.
Implicationsedit
There is no easy theory for any behavior that seems complex.
Complex behavior features can be captured with models that have simple underlying structures.
An overall system's behavior based on simple structures can still exhibit behavior indescribable by reasonably "simple" laws.
Analysisedit
Navot Israeli and Nigel Goldenfeld found that some less complex systems behaved simply and predictably (thus, they allowed approximations). However, more complex systems were still computationally irreducible and unpredictable. It is unknown what conditions would allow complex phenomena to be described simply and predictably.
Compatibilismedit
Marius Krumm and Markus P Muller tie computational irreducibility to Compatibilism.[1] They refine concepts via the intermediate requirement of a new concept called computational sourcehood that demands essentially full and almost-exact representation of features associated with problem or process represented, and a full no-shortcut computation. The approach simplifies conceptualization of the issue via the No Shortcuts metaphor. This may be analogized to the process of cooking, where all the ingredients in a recipe are required as well as following the 'cooking schedule' to obtain the desired end product. This parallels the issues of the profound distinctions between similarity and identity.
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This article has multiple issues Please help improve it or discuss these issues on the talk page Learn how and when to remove these template messages This article relies excessively on references to primary sources Please improve this article by adding secondary or tertiary sources Find sources Computational irreducibility news newspapers books scholar JSTOR April 2020 Learn how and when to remove this message This article possibly contains original research Please improve it by verifying the claims made and adding inline citations Statements consisting only of original research should be removed April 2020 Learn how and when to remove this message This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Computational irreducibility news newspapers books scholar JSTOR May 2019 Learn how and when to remove this message Learn how and when to remove this message Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his 2002 book A New Kind of Science although the concept goes back to studies from the 1980s Contents 1 The idea 2 Implications 3 Analysis 4 Compatibilism 5 See also 6 External links and references 7 ReferencesThe idea editThis section needs expansion You can help by adding to it January 2022 Many physical systems are complex enough that they cannot be effectively measured Even simpler programs contain a great diversity of behavior Therefore no model can predict using only initial conditions exactly what will occur in a given physical system before an experiment is conducted Because of this problem of undecidability in the formal language of computation Wolfram terms this inability to shortcut a system or program or otherwise describe its behavior in a simple way computational irreducibility The idea demonstrates that there are occurrences where theory s predictions are effectively not possible Wolfram states several phenomena are normally computationally irreducible citation needed Computational irreducibility explains observed limitations of existing mainstream science In cases of computational irreducibility only observation and experiment can be used Implications editThere is no easy theory for any behavior that seems complex Complex behavior features can be captured with models that have simple underlying structures An overall system s behavior based on simple structures can still exhibit behavior indescribable by reasonably simple laws Analysis editNavot Israeli and Nigel Goldenfeld found that some less complex systems behaved simply and predictably thus they allowed approximations However more complex systems were still computationally irreducible and unpredictable It is unknown what conditions would allow complex phenomena to be described simply and predictably Compatibilism editMarius Krumm and Markus P Muller tie computational irreducibility to Compatibilism 1 They refine concepts via the intermediate requirement of a new concept called computational sourcehood that demands essentially full and almost exact representation of features associated with problem or process represented and a full no shortcut computation The approach simplifies conceptualization of the issue via the No Shortcuts metaphor This may be analogized to the process of cooking where all the ingredients in a recipe are required as well as following the cooking schedule to obtain the desired end product This parallels the issues of the profound distinctions between similarity and identity See also editChaos theory Godel s Theorem Computation Principle of Computational Equivalence Artificial intelligence Robert Rosen Emergent behaviourExternal links and references editWeisstein Eric W et al Computational irreducibility MathWorld A Wolfram Web Resource Wolfram Stephen A New Kind of Science Wolfram Media Inc May 14 2002 ISBN 1 57955 008 8 Wolfram Stephen Computational irreducibility A New Kind of Science Wolfram Stephen History of computational irreducibility A New Kind of Science Wolfram Stephen History of computational irreducibility notes A New Kind of Science Wolfram Stephen Undecidability and intractability in theoretical physics Physical Review Letters 1985 Israeli Navot and Nigel Goldenfeld On computational irreducibility and the predictability of complex physical systems Physical Review Letters 2004 Computational Irreducibility ISAAC EINSTein research and development Archived from the original on 2011 12 11 Berger David Stephen Wolfram A New Kind of Science Serendip s Bookshelves Complexity is Elusive Physical Review Letters March 4 2004 Tomasson Gunnar Scientific Theory and Computational Irreducibility A New Kind of Science The NKS Forum References edit Computational irreducibility and compatibilism towards a formalization https arxiv org pdf 2101 12033 pdf Retrieved from https en wikipedia org w index php title Computational irreducibility amp oldid 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