Circular Logic

  • Arthur T. Winfree
Part of the Biomathematics book series (SSE)


My objective for this chapter is to draw your attention to a few peculiarities inherent in the logic of periodic functions. I find a visual approach the most fruitful for thinking about such matters. As the pictures involved consist mainly of mappings between circles and products of circles, I must first say a few words about the notions of topological spaces and mappings. This chapter thus has four sections:
  1. A.

    Spaces, with emphasis on rings (i.e., closed loops. To avoid the more exact connotations of the word circle I use ring, trusting the reader do not confuse my meaning with algebraic rings.)

  2. B.

    Mappings, with emphasis on the winding number of mappings to a ring

  3. C.

    Phase singularities of maps (Parts I and II), with emphasis on the consequences of a nonzero winding number

  4. D.

    Technical details on the application of circular logic to biological rhythms



Topological Space Target Space Biological Rhythm Phase Singularity Stimulus Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Arthur T. Winfree
    • 1
  1. 1.Department of Biological Sciences, Lilly Hall of Life SciencesPurdue UniversityWest LafayetteUSA

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