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Invariances in Theory

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Invariants of Behavior

Part of the book series: Springer Series in Cognitive and Neural Systems ((SSCNS,volume 1))

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Abstract

This chapter surveys the multifaceted roles that invariants play in theorizing, from physics and mathematics to biology and neurobiology. The question “What is an invariant of behavior?” is posed, and some alternatives are proposed and discussed: genes, neuroanatomy, and reflex theory. From that, the cybernetic take on the issue is introduced and placed in an evolutionary context, in which single behaviors are identified in respect to the goals they achieve and how they subserve the organism’s viability. The search for invariants of behavior is framed as a search for mechanisms. This search is far from trivial, as assumptions play a prominent role.

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Notes

  1. 1.

    Other purely theoretical examples exist, such as the entities in the study of topology. For example, a torus – a donut – will always have one hole irrespective of deformations, because its shape identity is defined by its topological properties. The invariant property is a part of the entity’s definition.

  2. 2.

    Noether’s theorem informally stated: differentiable symmetries generated by local actions have correspondent conserved current. An English translation of the original paper is found in [45].

  3. 3.

    Coextensive: If P is an invariant property of a system, then for all members of set A, it is true that A has P. In the example of life, if all the living A have life (property L), then ∀A : L(A) → L(A), a tautology. An explanatory principle such as this has vaporous foundation, and no logical derivations are possible. Nothing can be learned; life becomes magic.

  4. 4.

    See also [15] for an insightful book review on Oyama’s cycles of contingency.

  5. 5.

    Our working definition of behavioral function: when a goal can be attributed to a behavior, then the behavior is a functional behavior. Contrast that with behavior in toto.

  6. 6.

    Gross in the sense of coarse, at first glance.

  7. 7.

    Schema theory (see more in Sect. 2.3.12) exemplifies the attempts to overlay the brain with a structure of functional components, “boxes,” to aide in explanation of overall behavior. But although being a tenable level of functional analysis, it encounters the problems of arbitrariness. That is because, in an important sense, a function only exists while it is being executed, and only within the frame of a theory. Often, there will be no fundamental way to distinguish between different overlaying schemas which one is better or best.

  8. 8.

    Environmental context is meant broadly: a cell can be an environment for DNA, as blood can be an environment for a cell, or the body can be a contextual environment for a neural system.

  9. 9.

    This is one of the main difficulties with analogies in ethology and neuroethology. Descriptions of functions are shared across different organisms, whereas mechanisms are not.

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Authors and Affiliations

  1. Okinawa Institute of Science and Technology, Okinawa, Japan

    Mario Negrello

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  1. Mario Negrello
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Negrello, M. (2011). Invariances in Theory. In: Invariants of Behavior. Springer Series in Cognitive and Neural Systems, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8804-1_2

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