Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5

Cellular Automata (SEP update)

#1
C C Offline
Cellular Automata -- First published Mon Mar 26, 2012; substantive revision Tue Aug 22, 2017
https://plato.stanford.edu/entries/cellular-automata/

INTRO: Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogenous, simple units, the atoms or cells. At each time unit, the cells instantiate one of a finite set of states. They evolve in parallel at discrete time steps, following state update functions or dynamical transition rules: the update of a cell state obtains by taking into account the states of cells in its local neighborhood (there are, therefore, no actions at a distance). Secondly, CA are abstract: they can be specified in purely mathematical terms and physical structures can implement them. Thirdly, CA are computational systems: they can compute functions and solve algorithmic problems. Despite functioning in a different way from traditional, Turing machine-like devices, CA with suitable rules can emulate a universal Turing machine (see entry), and therefore compute, given Turing’s thesis (see entry on Church-Turing thesis), anything computable.

The mark of CA is in their displaying complex emergent behavior, starting from simple atoms following simple local rules. Because of this, CA attract a growing number of researchers from the cognitive and natural sciences willing to study pattern formation and complexity in a pure, abstract setting. This entry provides an introduction to CA and focuses on some of their philosophical applications: these range from the philosophy of computation and information processing, to accounts of reduction and emergence in metaphysics and cognition, to debates around the foundations of physics.

We will proceed as follows. In the introductory Section 1, CA are first explained via an example: Section 1.1 describes a simple one-dimensional automaton displaying an intuitively manifest behavior. Sections 1.2–1.3 provide a short survey of the history and main applications of CA.

In Section 2, the general theory of CA is explained, together with a selection of computational and complexity-theoretic results in the field. Section 2.1 provides a fourfold schematic definition of CA. Sections 2.2–2.3 explain the classification of one-dimensional CA proposed by Stephen Wolfram. Section 2.4 introduces the Edge of Chaos hypothesis, a key CA-related conjecture in complexity theory. Sections 2.5–2.7 generalize to automata occupying more than one spatial dimension, and/or relaxing some parameters in the definition of 2.1. We focus on the Game of Life—possibly the most popular CA—and its computational capabilities.

Section 3 describes four main uses of CA in philosophical investigation. Firstly, since CA display complex behavioral patterns emerging from simple local rules, they have been naturally linked to emergence: this topic is dealt with in Section 3.1, where different notions of emergence are considered. Secondly, Section 3.2 explores how CA have been put to work, both by philosophers and by scientists, to address the traditional philosophical problems of free will and determinism. Thirdly, Section 3.3 describes the impact of CA theories on the philosophy of computation. Finally, Section 3.4 addresses ontological issues ranging from the sense in which CA count as modelling portions of reality, to the bold philosophical conjecture of some scientists, who claim that the physical world itself may be, at its bottom, a discrete, digital automaton....

MORE: https://plato.stanford.edu/entries/cellular-automata/
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  SEP updates + Philosophy: It's only just getting started? C C 2 589 Apr 30, 2018 07:18 PM
Last Post: Ostronomos
  Challenge to scientific realism + Causation in scientific methods + Recent SEP update C C 3 1,496 Mar 21, 2017 03:07 AM
Last Post: RainbowUnicorn
  Beauvoir’s political philosophy resonates today+ Dennett's new book + SEP updates C C 0 399 Mar 11, 2017 01:48 AM
Last Post: C C
  How boom times ended for West + Humans in dark times + PhilosophyComics & SEP updates C C 0 352 Feb 25, 2017 06:52 AM
Last Post: C C
  SEP: The Philosophy of Computer Science C C 0 446 Jan 24, 2017 01:42 AM
Last Post: C C
  Cosmology: Methodological Debates in the 1930s and 1940s (SEP update) C C 0 557 Jun 8, 2015 04:50 AM
Last Post: C C
  The Experience and Perception of Time: SEP update C C 0 435 Apr 9, 2015 10:23 PM
Last Post: C C
  Intrinsic vs. Extrinsic Value - SEP entry update C C 1 853 Jan 1, 2015 08:00 PM
Last Post: Magical Realist
  Kant's Philosophical Development - update to SEP entry C C 0 780 Nov 30, 2014 08:53 PM
Last Post: C C
  Kyoto philosophy - SEP update C C 0 601 Nov 18, 2014 06:18 AM
Last Post: C C



Users browsing this thread: 1 Guest(s)