## The Dynamical Hypothesis in Cognitive Science (1997)

Venue: | Behavioral and Brain Sciences |

Citations: | 111 - 1 self |

### BibTeX

@ARTICLE{Gelder97thedynamical,

author = {Tim Van Gelder},

title = {The Dynamical Hypothesis in Cognitive Science},

journal = {Behavioral and Brain Sciences},

year = {1997},

volume = {21},

pages = {615--665}

}

### Years of Citing Articles

### OpenURL

### Abstract

The dynamical hypothesis is the claim that cognitive agents are dynamical systems. It stands opposed to the dominant computational hypothesis, the claim that cognitive agents are digital computers. This target article articulates the dynamical hypothesis and defends it as an open empirical alternative to the computational hypothesis. Carrying out these objectives requires extensive clarification of the conceptual terrain, with particular focus on the relation of dynamical systems to computers. Key words cognition, systems, dynamical systems, computers, computational systems, computability, modeling, time. Long Abstract The heart of the dominant computational approach in cognitive science is the hypothesis that cognitive agents are digital computers; the heart of the alternative dynamical approach is the hypothesis that cognitive agents are dynamical systems. This target article attempts to articulate the dynamical hypothesis and to defend it as an empirical alternative to the compu...

### Citations

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Citation Context ... characterization offered here is just the standard philosophical account, as developed in numerous places. 21 Second, a great many models in cognitive science (e.g., those developed within the SOAR (=-=Newell, 1991) fr-=-amework) do in fact conform to that account. The other issue is whether the standard account misunderstands the “true” CH, i.e., deeply misconceives computers and computational modeling in cogniti... |

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Citation Context ...od approximation, the purview of effective computation was gradually extended to embrace real numbers, functions over real numbers, differential equations, and so on (Earman, 1986; Grzegorczyk, 1957; =-=Turing, 1936-=-). In this way, issues of effective computability can be raised for all the standard mathematical constructs of analysis and physics. Just what is and is not effectively computable rapidly becomes a r... |

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Citation Context ...appears to constitute an objection to the DH because it equivocates on the term “dynamical system”. The DH takes cognitive agents 18 (Mill, 1975) Chapter 2. In “Computing Machinery and Intellige=-=nce” (Turing, 1950-=-), Turing rebuts nine objections to his stance on whether computers can think; most are not attributed to anyone in particular. This paper follows these august precedents. Except where noted, the obje... |

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Citation Context ...s “simply a smooth manifold M, together with a vector field v defined on M.” (Casti, 1992) p.109 4. Mapping on a metric space “A dynamical system is a transformation f:Z→Z on a metric space (Z=-=, d).” (Barnsley, 1988) p.-=-134. 5. State-determination “a dynamical system...is one whose state at any instant determines the state a short time into the future without any ambiguity.” (Cohen & Stewart, 1994) p.188 6. Any m... |

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Citation Context ...that subserve such “seeing” actually instantiate symbols and their manipulations. Imagining the Eiffel Tower does not entail that one has the Eiffel Tower, or even a picture of it, inside one’s =-=head (Ryle, 1984-=-, Ch.8). We must not confuse the content of experience with the mechanisms implementing it. As usual, the question turns out to be the empirical one: in the long run, what kind of models provide the b... |

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Citation Context ...ome five decades after Principia Mathematica, David Hume dreamt of a scientific psychology in which mathematical laws would govern the mental realm, just as Newton’s laws governed the material realm=-= (Hume, 1978-=-). The universal force of gravitation, whereby bodies attract in proportion to their masses, would be replaced by a universal force of association, whereby ideas attract in proportion to their similar... |

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Citation Context ... 97) may differ in some small ways from the final publication version.s- 2 - most notable developments has been the rise of connectionism, which models cognition as the behavior of dynamical systems (=-=Smolensky, 1988-=-), and often understands those models from a dynamical perspective. Equally significant is the emergence of cognitive neuroscience, and within it, the increasing prevalence of dynamical theorising. Dy... |

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Citation Context ...yer and Jim Townsend (Busemeyer & Townsend, 1993). In their “Decision Field Theory” (DFT) model, relevant aspects of the decision situation are represented not by 1 Examples: cognitive neuroscienc=-=e: (Amit, 1989-=-; Babloyantz & Lourenco, 1994; Cohen, 1992; Guckenheimer, Gueron, & Harris-Warrick, 1993; Mpitsos, forthcoming; Skarda & Freeman, 1987); psychophysics: (Gregson, 1995); perception: (Bingham, Rosenblum... |

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Citation Context ...ine, 1996; Tabor, Juliano, & Tanenhaus, 1996); situated robotics and autonomous agents research: (Beer, 1995b; Cliff, Harvey, & Husbands, 1993; Smithers, 1994); artificial intelligence (Jaeger, 1996; =-=Pollack, 1991-=-); social psychology (Kaplowitz & Fink, 1992; Vallacher & Nowak, 1993); ecological psychology (Kugler, Kelso, & Turvey, 1980; Kugler, Kelso, & Turvey, 1982; Turvey & Carello, 1995); synergetics (Haken... |

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Citation Context ...chology: (Busemeyer & Townsend, 1993; Grossberg & Gutowski, 1987; Grossberg & Stone, 1986; Leven & Levine, 1996; Tabor, Juliano, & Tanenhaus, 1996); situated robotics and autonomous agents research: (=-=Beer, 1995-=-b; Cliff, Harvey, & Husbands, 1993; Smithers, 1994); artificial intelligence (Jaeger, 1996; Pollack, 1991); social psychology (Kaplowitz & Fink, 1992; Vallacher & Nowak, 1993); ecological psychology (... |

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Citation Context ... x < y, or y < x, or x = y. 7 For expressions of this consensus see, for example, (Clark, 1989; Copeland, 1993; Dreyfus, 1992; Fodor, 1975; Fodor & Pylyshyn, 1988; Newell, 1980; Newell & Simon, 1976; =-=Pylyshyn, 1984).-=- The version of this consensus now most widely accepted as definitive is probably that laid out in (Haugeland, 1985). The account of digital computers here is essentially just Haugeland’s definition... |

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Citation Context ...fus, 1992; Fodor, 1975; Fodor & Pylyshyn, 1988; Newell, 1980; Newell & Simon, 1976; Pylyshyn, 1984). The version of this consensus now most widely accepted as definitive is probably that laid out in (=-=Haugeland, 1985).-=- The account of digital computers here is essentially just Haugeland’s definition of computers as interpreted automatic formal systems as massaged into the present framework.s- 6 - concrete case, th... |

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Citation Context ...is one which changes in time.” (Hirsch, 1984) p.3 “The term dynamic refers to phenomena that produce time-changing patterns...the term is nearly synonymous with time-evolution or pattern of change=-=.” (Luenberger, 1979-=-) p.1 An obvious feature distinguishing dynamical models in cognitive science from standard computational models is that their variables are numerical. One reason numbers are so useful in science is t... |

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Citation Context ...matic reorientations in our understanding of dynamical systems for the purposes of understanding biological or cognitive systems. See, for example, the work of Robert Rosen on “anticipatory systems�=-=�� (Rosen, 1985) an-=-d George Kampis on “component systems” (Kampis, 1991). Contemporary dynamics provides powerful resources for describing general properties of the behaviour of systems. These resources can be broug... |

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Citation Context ... there is a relation < over its elements with the property that for each x,y ∈ X, either x < y, or y < x, or x = y. 7 For expressions of this consensus see, for example, (Clark, 1989; Copeland, 1993=-=; Dreyfus, 1992-=-; Fodor, 1975; Fodor & Pylyshyn, 1988; Newell, 1980; Newell & Simon, 1976; Pylyshyn, 1984). The version of this consensus now most widely accepted as definitive is probably that laid out in (Haugeland... |

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Citation Context ... Via arbitrarily good approximation, the purview of effective computation was gradually extended to embrace real numbers, functions over real numbers, differential equations, and so on (Earman, 1986; =-=Grzegorczyk, 1957-=-; Turing, 1936). In this way, issues of effective computability can be raised for all the standard mathematical constructs of analysis and physics. Just what is and is not effectively computable rapid... |

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Citation Context ...ains speakers’ computational power, but not the kind of computer they instantiate. It remains an open empirical question whether the computers in question are best thought of as digital or dynamical=-= (Elman, 1995-=-). On the latter interpretation, the argument simply equivocates. The premises establish that speakers must be computers in some sense; the conclusion claims they must be digital computers. The domina... |

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Citation Context ...vely computed. Via arbitrarily good approximation, the purview of effective computation was gradually extended to embrace real numbers, functions over real numbers, differential equations, and so on (=-=Earman, 1986-=-; Grzegorczyk, 1957; Turing, 1936). In this way, issues of effective computability can be raised for all the standard mathematical constructs of analysis and physics. Just what is and is not effective... |

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Citation Context ...ins (van Gelder, 1990). For example, arbitrarily many structures can be mapped onto states of a dynamical system, such that these states can then be used as the basis of systematic processing (e.g., (=-=Chrisman, 1991-=-; Pollack, 1990)). Other work has found combinatorial structure in the attractor basins of appropriate dynamical systems (Noelle & Cottrell, 1996), or in the trajectories induced by sequences of bifur... |

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Citation Context ...result from adopting different constraints. In particular, we can focus attention on some class of dynamical systems (Blum, Cucker, Shub, & Smale, forthcoming; Blum, Shub, & Smale, 1989; Moore, 1991; =-=Moore, 1996). As lo-=-ng as there is some way to specify the “questions” and “answers” we can see dynamical processes as computing functions. For example, Hava Siegelmann has extensively studied the computational p... |

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Citation Context ...chology: (Busemeyer & Townsend, 1993; Grossberg & Gutowski, 1987; Grossberg & Stone, 1986; Leven & Levine, 1996; Tabor, Juliano, & Tanenhaus, 1996); situated robotics and autonomous agents research: (=-=Beer, 1995-=-b; Cliff, Harvey, & Husbands, 1993; Smithers, 1994); artificial intelligence (Jaeger, 1996; Pollack, 1991); social psychology (Kaplowitz & Fink, 1992; Vallacher & Nowak, 1993); ecological psychology (... |

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Citation Context ...n, 1992; Guckenheimer, Gueron, & Harris-Warrick, 1993; Mpitsos, forthcoming; Skarda & Freeman, 1987); psychophysics: (Gregson, 1995); perception: (Bingham, Rosenblum, & Schmidt, in press; Grossberg & =-=Rudd, 1992-=-; McClelland & Rumelhart, 1981; Port, Cummins, & McAuley, 1995); motor control: (Bullock & Grossberg, 1988; Saltzman, 1995; Turvey, 1990); developmental psychology: (Smith & Thelen, 1993; Thelen & Smi... |

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Citation Context ... computation result from adopting different constraints. In particular, we can focus attention on some class of dynamical systems (Blum, Cucker, Shub, & Smale, forthcoming; Blum, Shub, & Smale, 1989; =-=Moore, 1991; Moore,-=- 1996). As long as there is some way to specify the “questions” and “answers” we can see dynamical processes as computing functions. For example, Hava Siegelmann has extensively studied the co... |

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Citation Context ... theory (e.g., “a set of elements standing in interrelations,” (von Bertalanffy, 1973), p.55). The stance on the metaphysical status of sets adopted here is the “set-theoretic realism” elabora=-=ted in (Maddy, 1990-=-). In this account, sets of physical entities are themselves physical entities, as much part of the ordinary world as planets, people and PCs. 5 In set theory, set identity is a matter of having exact... |

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Citation Context ...perception: (Bingham, Rosenblum, & Schmidt, in press; Grossberg & Rudd, 1992; McClelland & Rumelhart, 1981; Port, Cummins, & McAuley, 1995); motor control: (Bullock & Grossberg, 1988; Saltzman, 1995; =-=Turvey, 1990-=-); developmental psychology: (Smith & Thelen, 1993; Thelen & Smith, 1993); cognitive psychology: (Busemeyer & Townsend, 1993; Grossberg & Gutowski, 1987; Grossberg & Stone, 1986; Leven & Levine, 1996;... |

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Citation Context ...A dynamical system may be defined as a deterministic mathematical prescription for evolving the state of a system forward in time.” (Ott, 1993) p.6 “A dynamical system is one which changes in time=-=.” (Hirsch, 1984) p.-=-3 “The term dynamic refers to phenomena that produce time-changing patterns...the term is nearly synonymous with time-evolution or pattern of change.” (Luenberger, 1979) p.1 An obvious feature dis... |

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