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Wolfram and the Computing Nature

Publication Type:

Book chapter


Irreducibility and Computational Equivalence: 10 Years After the Publication of Wolframs A New Kind of Science




WolframÂ’s work, and especially his New Kind of Science, presents as much a new science as a new natural philosophy ‐ natural computationalism. In the same way as Andrew Hodges, based on Alan TuringÂ’s pioneering work on computability and his ideas on morphological computing and artificial intelligence, argues that Turing is best viewed as a natural philosopher we can also assert that WolframÂ’s work constitutes natural philosophy. It is evident through natural and formal computational phenomena studied in different media, from the book with related materials to programs and demonstrations and computational knowledge engine. WolframÂ’s theoretical studies and practical computational constructs including Mathematica and Wolfram Alpha reveal a research program reminiscent of LeibnizÂ’ Mathesis universalis, the project of a universal science supported by a logical calculation framework. WolframÂ’s new kind of science may be seen in the sense of NewtonÂ’s Philosophiæ Naturalis Principia Mathematica being both natural philosophy and science, not only because of the new methodology of experimental computer science and simulation, or because of particular contributions addressing variety of phenomena, but in the first place as a new unified scientific framework for all of knowledge. It is not only about explaining special patterns seen in nature and models of complex behaviors; it is about the computational nature derived from the first computational principles. WolframÂ’s as well as TuringÂ’s natural philosophy differs from GalileoÂ’s view of nature. Computation used in modeling is more than a language. It produces real time behaviors of physical systems: computation is the way nature is. Cellular automata as explored by Wolfram are a whole fascinating computational universe. Do they exhaust all possible computational behaviors that our physical universe exhibit? If we understand physical processes as computations in a more general sense than the computations performed by symbol manipulation done by our current computers, then universal Turing machines and universal cellular automata exhibit only a subset of all possible information‐processing behaviors found in nature. Even though mathematically, there is a principle of computational equivalence, in physical nature exists a hierarchy of emergent processes on many levels of organization that exhibits different physical behavior and thus can be said compute with different expressive power. This article argues that, based on the notion of computing nature, where computing stands for all kinds of information processing, the development of natural computationalism have a potential to enrich computational studies in the same way as the explorations in the computational universe hold a promise to provide computational models applicable to the physical universe.


author = {Gordana Dodig-Crnkovic},
title = {Wolfram and the Computing Nature},
editor = {Hector Zenil },
pages = {417--437},
month = {January},
year = {2013},
booktitle = {Irreducibility and Computational Equivalence: 10 Years After the Publication of Wolframs A New Kind of Science},
publisher = {Springer},
url = {}