Siteswap  Siteswap is a numeric juggling notation used to describe or represent juggling patterns. It is also referred to as Quantum Juggling, or The Cambridge Notation. "Siteswap" may also be used to describe siteswap patterns, possible patterns transcribed using siteswap. Throws are represented by positive integers that specify the number of beats in the future when the object is caught, which is related to their relative height, and the hand to which the throw is to be made: "The idea behind siteswap is to keep track of the order that balls are thrown and caught, and only that." It is an invaluable tool in determining which combinations of throws yield valid juggling patterns for a given number of objects, and has led to previously unknown patterns (such as 441). However, it does not describe body movements such as behind-the-back and under-the-leg. Siteswap assumes that, "throws happen on beats that are equally spaced in time." For example, a three-ball cascade may be notated "3", while a shower may be notated "5 1". The notation was invented by Paul Klimek in Santa Cruz, California in 1981, and later developed by undergraduates Bruce "Boppo" Tiemann and the late Bengt Magnusson at the California Institute of Technology in 1985, and by Mike Day, mathematician Colin Wright, and mathematician Adam Chalcraft in Cambridge, England in 1985 (whence comes an alternative name). The numbers derive from the number of balls used in the most common juggling patterns. Siteswap has been described as, "perhaps the most popular" name. The name "siteswap" comes from the ability to generate patterns by "swapping" landing times of any 2 throws in a siteswap using the . For example, swapping the landing times of throws "5" and "1" in the siteswap "51" generates the siteswap "24". Its simplest form, sometimes called vanilla siteswap, describes only patterns whose throws alternate hands and in which one ball is thrown from each hand at a time. If one were juggling while walking forward, something like the adjacent diagram would be seen from above, sometimes called a space-time diagram or ladder diagram. In this diagram, three balls are being juggled. Time progresses from the top to the bottom. This pattern can be describe by stating how many throws later each ball is caught. For instance, on the first throw in the diagram, the purple ball is thrown in the air (up out of the screen, towards the bottom left) by the right hand, next the blue ball, the green ball, the green ball again, and the blue ball again and then finally the purple ball is caught and thrown by the left hand on the fifth throw, this gives the first throw a count of "5".