Circular Logic

  • Arthur T. Winfree
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 12)


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 to 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, with emphasis on the consequences of a nonzero winding number

  4. D.

    Technical details on the application of circular logic to biological rhythms

The next chapter goes on to examine experimental examples of mappings to the ring that contain phase singularities. Discussion specifically focusing on the physical nature of phase singularities in each case is reserved to Chapter 10.


Circadian Rhythm Topological Space Target Space Biological Rhythm Full Cycle 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Arthur T. Winfree
    • 1
  1. 1.Department of Ecology and Evolutionary BiologyUniversity of ArizonaTucsonUSA

Personalised recommendations