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Models as Tools to Aid Thinking

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Towards a Theory of Thinking

Part of the book series: On Thinking ((ONTHINKING))

Abstract

We offer a brief synoptical discussion of some major modeling methodologies and discuss these from a number of complementary dimensions of modeling and thinking: how can models aid our thinking, what are their different characteristics, how is modeling affected by the selection of features, how far is the reach of mappings and what in addition can be delivered by dynamical systems, how to cope with uncertainty, what are mechanisms of optimal inference, and how is modeling connected with learning? We conclude with a brief discussion of some inherent limitations of any model.

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Notes

  1. 1.

    Note that this time we are using discrete time steps and, therefore, have the “difference equation” analog of the continuous-time differential equation (8).

  2. 2.

    We omit the discussion of measure-theoretic fine points admitting the happening or nonhappening of events even if their probability is zero or one, as long as such “exceptions” are sufficiently seldom so as not to affect any “expectation values,” such as averages etc.

  3. 3.

    It may also happen that the new probability distribution p(x|c) is more spread out than the “old” one p(x): this possibility reflects the fact that a symptom can also be “confusing.”

  4. 4.

    We intentionally use for the models the same letter θ that we previously used for the model parameters to indicate that we mostly think of parameterized models, for which model identity and the associated parameter value can be identified.

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Author information

Authors and Affiliations

  1. CITEC – Cognitive Interaction Technology and Faculty of Technology, Bielefeld University, Bielefeld, Germany

    Helge Ritter

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  1. Helge Ritter
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Editor information

Editors and Affiliations

  1. Parmenides Foundation, Kardinal Faulhaber Str. 14 a, Munich, 80333, Germany

    Britt Glatzeder

  2. Dept. Psychology, York University, Keele Street 4700, Toronto, M3J 1P3, Canada

    Vinod Goel

  3. Parmenides Foundation, Kardinal Faulhaber Str. 14 a, Munich, 80333, Germany

    Albrecht Müller

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Ritter, H. (2010). Models as Tools to Aid Thinking. In: Glatzeder, B., Goel, V., Müller, A. (eds) Towards a Theory of Thinking. On Thinking. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03129-8_23

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