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1.5: Complexity thinking

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    We are getting farther afield now, but the shifts I am postulating in the criteria of scientific modeling are related to 20th century developments in logic and epistemology.

    Aristotelian logic many-valued logic
    In traditional logic, any proposition is either true or false. This system lends itself to math-like proofs, but fails (in dramatic ways) for many real-world applications. Alternatives include many-valued logic, fuzzy logic, and other systems designed to handle indeterminacy, vagueness, and uncertainty. Bart Kosko discusses some of these systems in Fuzzy Thinking.
    Frequentist probability Bayesianism
    Bayesian probability has been around for centuries, but was not widely used until recently, facilitated by the availability of cheap computation and the reluctant acceptance of subjectivity in probabilistic claims. Sharon Bertsch McGrayne presents this history in The Theory That Would Not Die.
    Objective subjective
    The Enlightenment, and philosophic modernism, are based on belief in objective truth, that is, truths that are independent of the people that hold them. 20th century developments including quantum mechanics, Gödel’s Incompleteness Theorem, and Kuhn’s study of the history of science called attention to seemingly unavoidable subjectivity in even “hard sciences” and mathematics. Rebecca Goldstein presents the historical context of Gödel’s proof in Incompleteness.
    Physical law theory model
    Some people distinguish between laws, theories, and models. Calling something a “law” implies that it is objectively true and immutable; “theory” suggests that it is subject to revision; and “model” concedes that it is a subjective choice based on simplifications and approximations.

    I think they are all the same thing. Some concepts that are called laws are really definitions; others are, in effect, the assertion that a certain model predicts or explains the behavior of a system particularly well. We come back to the nature of physical laws in Section 4.8, Section 5.9 and Section 8.8.

    Determinism indeterminism
    Determinism is the view that all events are caused, inevitably, by prior events. Forms of indeterminism include randomness, probabilistic causation, and fundamental uncertainty. We come back to this topic in Section 5.5 and Section 10.6.

    These trends are not universal or complete, but the center of opinion is shifting along these axes. As evidence, consider the reaction to Thomas Kuhn’s The Structure of Scientific Revolutions, which was reviled when it was published and is now considered almost uncontroversial.

    These trends are both cause and effect of complexity science. For example, highly abstracted models are more acceptable now because of the diminished expectation that there should be a unique, correct model for every system. Conversely, developments in complex systems challenge determinism and the related concept of physical law.

    This chapter is an overview of the themes coming up in the book, but not all of it will make sense before you see the examples. When you get to the end of the book, you might find it helpful to read this chapter again.

    This page titled 1.5: Complexity thinking is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Allen B. Downey (Green Tea Press) .