Juggling Patterns and Programs

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Juggling Patterns and Programs Steve Miner @miner

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Anthony Gatto Cirque du Soleil

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Simple Made Easy Rich Hickey Strange Loop 2011

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Metaphor Alert RH ~ incidental complexity Me ~ essential complexity https://schani.wordpress.com/tag/juggling/

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Scientiﬁc Aspects of Juggling Claude Shannon (1916 - 2001) written in1980s

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Egyptian Wall Painting circa 2040 B.C.

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Uniform Juggle • one throw at a time • alternating hands • constant rhythm

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3 Ball Cascade • Odd numbers: cascade • Even numbers: fountain

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4 Ball Fountain • Odd numbers: cascade • Even numbers: fountain

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Shannon’s Juggling Theorem • Flight time • Dwell time • Vacant time • number of Balls • number of Hands

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Complex Made Hard • B ≈ F • F ≈ (sqrt height) • small errors compound

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Flying Karamazov Brothers scaling H

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Shannon’s Juggling Theorem • Flight time • Dwell time • Vacant time • number of Balls • number of Hands

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Lessons from Shannon • historical analysis • domain understanding • choosing right abstraction • exploring trade-offs

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Science of Juggling • Peter J. Beek and Arthur Lewbel • Scientiﬁc American, November, 1995, Volume 273, Number 5, pages 92-97 • www.juggling.org/papers/science-1/

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Siteswap Notation • sequence of integers • e.g. 531 = [5, 3, 1] …, 5, 3, 1, 5, 3, 1, … • 3 = standard three-ball cascade • odd for cascade, even for fountain • empty 0, switch1, hold 2

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531

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Inventors • Paul Klimek - UC Santa Cruz 1981 • Bruce Tiemann and Bengt Magnusson - Caltech 1985 • Michael Day, Colin Wright and Adam Chalcraft - Cambridge 1985

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Number of Balls • average of throws, must be an integer • 531 (/ (+ 5 3 1) 3) 㱺 3 • 71 (/ (+ 7 1) 2) 㱺 4 • 97531 (/ (+ 9 7 5 3 1) 5) 㱺 5

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Validate Pattern (defn siteswap? [pattern] (let [cnt (count pattern)] (or (zero? cnt) (apply distinct? (map #(mod % cnt) (map-indexed + pattern))))))

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Spec (s/def ::siteswap (s/and (s/coll-of (s/int-in 0 10) :kind vector?) siteswap?))

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Orbits • Decompose pattern into orbits (sub-patterns) • 531 = 501 & 030 • 4413 = 4000 & 0400 & 0013 • 97531 = 90001 & 07030 & 00500 • Practice separately

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Quil • Clojure library for graphics and animations • quil.info • Rastelli - Clojure juggling library

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453 3 balls in 450 1 ball in 003

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97531 2 balls in 90001 2 balls in 07030 1 ball in 00500

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Isomorphic Patterns • repeat: 3 㱺 333 • rotate: 531 㱺 315 㱺 135

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New Patterns • add period to element: 33 㱺 53 • swap sites i & j • add distance earlier, subtract distance later • guarantees same landing schedule • 333 㱺 531 531 㱺 441

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531

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State Diagram https://plus.maths.org/content/juggling-maths-and-beautiful-mind

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Siteswap Features • simple data representation • ﬂexible interpretation • sharing • composition • veriﬁcation • generation

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Additional Resources • juggling.org • thewjf.com • wikipedia.com • siteswap.net/JsJuggle.html • jugglinglab.sourceforge.net

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The Mathematics of Juggling • Book by Burkard Polster, Monash University • Survey article based on his book • www.qedcat.com/articles/juggling_survey.pdf • YouTube videos on juggling

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– Burkard Polster The way that I feel when I look at a nice equation is the same way I feel when I look at a nice juggling pattern.

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Allen Knutson • Math professor at Cornell • Siteswap FAQ on rec.juggling • YouTube video on mathematics of juggling

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Neuroscience • Plasticity In The Adult Brain: Why We Care About Taxi Drivers & Jugglers • Marc W. Haut, PhD • youtube.com/watch?v=JVsZVW2HRYQ • nature.com/nature/journal/v427/n6972/full/ 427311a.html

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Jennifer Slaw: Juggling Life • TEDxPrincetonlibrary talk • motivational speaker, teaches juggling • improves memory, concentration, ﬂexibility, patience, balance • youtube.com/watch?v=S- Rohq5649A

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– Michael Moschen What you learn is how to feel with your eyes and see with your hands.

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Recap • Juggling inspires mathematicians • Siteswap notation is a juggling DSL • Rastelli juggles with Clojure