The Survival, Origin and Mathematics of String Figures

Includes a detailed inventory of over 1200 string figure artefacts in more than 20 museums worldwide, papers on "The Origin of String Figures" and "String Figures and Knot Theory", plus sixteen of the author's 21st-century string figures.

by Martin Probert

"the World's Most Widespread Game"
(James Hornell, Discovery, 1928)

1) Museums and other institutions with string figure artefacts

Begun 1999. Last revised April 2003.

  1. Museums and artefacts. Collections containing string figures mounted on card, string figures on film, string figure photographs, and recordings of string figure songs. Over 20 public institutions are included - the British Museum, the Harvard University Peabody Museum, the Australian Museum, and many others. Over 1200 items are listed.

"A wonderful project"
Museum Archivist, North America (pers. comm.)

"A wonderful website"
Museum Archivist, Oceania (pers. comm.)

2) The Origin of String Figures

Posted 1999. Abstract revised August 2002.

In Part I we suggest a possible context for the discovery of string figures. In Parts II and III we propose that the most widely distributed string figures are those most capable of independent invention. This conclusion is derived through an analysis of the mechanical constructions of the collected figures. The theory is to be seen in contrast to the alternative hypothesis that these widely distributed figures have a common origin.

  1. How old are string figures?
  2. Where and how did string figure making originate?
  3. Why is Jacob’s Ladder so widely distributed?

"Looks at string figures from a whole new point of view and opens up a brand new field for exploration. A landmark paper..."
(pers. comm.)

3) String Figures and Knot Theory
- mathematics of the unknot under tension

Posted February 2001. Last revised April 2003.

Many ethnographical string figures have come down to us only in the form of an ambiguous photograph in which, at the crossings, it is impossible to determine by eye which string lies over which. A knowledge of the set of all look-alikes ('similar-looking string figures') is a considerable aid in attempting to reconstruct such a figure. Part I shows how such a set may be determined mathematically (using the techniques of knot theory). Part III shows how members of the set of look-alikes may be obtained manipulatively. Several conjectures are made concerning this manipulative process on the set of all look-alikes.

Featured in the Math Forum Internet News 19 March 2001
KaBoL cool math site
Featured by the Canadian Mathematical Society: Cool Math Site 13 September 2002
Canadian Mathematical Society

4) 21st-Century String Figures

- sixteen string figures that continue the ancient tradition of portraying stories, objects and ideas from contemporary culture

  1. String Figure Maker's Garden with Young Loops Growing
  2. Double Crow’s Feet (double string figure)
  3. Alice in Wonderland (string figure sequence with moving figures)
  4. Jabberwock (string figure sequence with moving figure)
  5. Hamlet's Cloud (string figure sequence)
  6. Macbeth (3-second string figure)
  7. Symbol Cycle (cyclic string figure sequence)
  8. Eye of the Cyclops (string figure sequence)
  9. Persistent Vision (repeating string figure)
  10. Mitosis (Cell Division) (moving string figure)
  11. Spinal Vertebrae (iterative string figure)
  12. Cladogram (Evolutionary Tree) (iterative string figure)
  13. Dromedary - Bactrian Camel - Loch Ness Monster (iterative string figure)
  14. Millipede (iterative string figure)
  15. Evolving Star (iterative string figure)
  16. Footballer (moving string figure)

"Martin Probert is admired worldwide for his fanciful, fun-filled string figure creations."
Joseph D'Antoni, String Figure Magazine

Other comments received:
"Highly original", "Enormously entertaining... I am consistently amazed by your creativity and inventiveness - I may say that I've never encountered anyone like you in the string figure world. You are truly gifted...", "Ingenious and elegant ... are you sure you didn't grow up on a South Pacific Island?", "So very original!", "Outstanding", "Beyond comment... You really are a creative genius when it comes to string", "Wonderfully ingenious", "Your creations are fabulous!", "What a glorious accomplishment", "Spectacular", "Magnificent", "You have invented too many wonderful new figures", "You are a real gift to the string figure world."

The above figures are taken from a large collection of original string figures.
Any publisher interested in publishing the collection is invited to contact the author.

The author has also written extensively on juggling and the mathematics of juggling.