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



Manifold Europe Mold Retina Polypeptide 


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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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