Don Herbison-Evans ,
Technical Report 330 (1988), updated 3 January 2010
Basser Department of Computer Science (now School of Information Technologies)
University of Sydney, Australia


This essay is a study of the history of the growth of creativity in dance over the last 100 years. Before 1900, most choreographers for dance were male. Theatrical dance in the first half of the twentieth century was dominated by female choreographers. The origins for this change are discussed.

Meanwhile, social dancing before 1900 involved mainly dances with prescribed steps. Males appear to have been released from this straight-jacket (inadvertently) to do creative social dance choreography by Vernon Castle in 1911. Females were not released until some 50 years later (again, inadvertently) by Chubby Checker.

Vernon Castle's method of dividing ballroom dances into "figures" may be viewed as the construction of a set of symbols. The mapping of these onto numerical digits is exemplified using figures from the modern Tango. Castle's catalysis of of the change from sequence dancing to ballroom dancing can then be viewed as a change from rational dancing (like rational numbers that have recurring groups of digits) to irrational dancing (like irrational numbers having digit sequences with no repetition).


Ordinary people in society can involve themselves in dancing in either of two ways: watching the the performance of specially trained dancers. and/or participating themselves in social dancing. Over the last 200 years in Western society, substantial changes to the creation of dance in these spheres has occurred.


Creation has been an important element in professional and academic dance throughout the last few centuries. The important creators of dance, the choreographers, however, up to the end of the nineteenth century, were all male. This gender bias in choreography has been previously discussed (Hanna, 1988, 129). Around 1900, this was changed by Isadora Duncan (1878-1927).

Isadora Duncan

She was inspired by the Delsarte Health System for Ladies (Kendall, 1979, 61) created by the French singing teacher Francois Delsarte (1811-1871). He devised this during 50 years of observation and analysis of the way normal people express their emotions through movement (Fonteyn, 1980, 102).

Francois Delsarte

Subsequently, choreography in the first half of the 20th century was dominated by a number of females dancers, including Ruth St Denis, Martha Graham, Doris Humphrey, Mary Wigman, and others. Thus this change was initiated by some lady's health programmes developed in the late Nineteenth Century.

Natural movements to bring health to ailing women were the prescription of Steele Mackaye, a major importer of the Delsarte health system the USA in the 1880's (Kendall, 1979, 24). It proved very popular, and was rediscovered as "Eurhythmics" by Emile Jaques-Dalcroze. He elevated improvisational movement for art and health to be a major foundation of his system. It was propagated in schools initially in Dresden in 1910, and later in various centres in Britain and the USA (Tingey, 1973,5), and of course also in Australia.

Emile Jacques-Dalcroze

Since that time, dance improvisation has played a prominent role in the development of many great choreographers. Many contemporary dance works include sections of improvisation (Livet, 1978,44).

Creative dance also continues to be regarded as a semi-therapeutic activity, and, for example, has been included as a subject in the New South Wales Primary School Syllabus (Farley, 1969, 9). It promotes personal explorations in the control of the body and its relationship to space and time and to other individuals. It also gives a form of controlled non-verbal expression of emotion, a release of tension, and an opportunity to create (Farley, 1969, 88).

Sadly later in the 20th Century, choreography became dominated by men again: George Balanchine and Merce Cunningham in America, Frederick Ashton and Kenneth Macmillan in the U.K., and Robert Helpmann and Graham Murphy in Australia. The reason for this is a great puzzle, for it happened despite there being a preponderance of women dance students and teachers.


In modern Western society, the ordinary individual has a limited number of outlets for creative expression. One major outlet used, and valued by people going through the traumatic period of re-adjustment called adolescence, is the dance floor. There, it is considered acceptable for anyone to move in an arbitrary fashion, restricted only by the laws of physics. Even the laws of decency are attenuated on the dance floor with the popularisation of movements such as those demonstrated in the film "Dirty Dancing".

Such freedom of creative expression in social dancing was repressed for several hundred years, and has only been regained this century. It occurred in two stages, with first men and later women being allowed to create choreography on the dance floor.


For several hundred years prior to 1910, the major common form of social dance in Western society was one in which each dancer or couple performed a prescribed sequence of movements. These movements could be performed in sets like the Quadrilles, or performed by couples in simple dances like the Waltz (Valse) or Polka, in which typically only one figure was performed: the Natural Turn. The Reverse Turn was socially unacceptable (Andrews, 1979, 81), probably because inexperienced dancers find it difficult to progress anticlockwise around the room while dancing Reverse Turns.

A Dance Program Card for the Ballarat Ball, 1867.

Around the start of the twentieth century, English Old Time sequence dances became popular (Fernandes, 1988,22). However, these, like the Quadrilles, have prescribed steps, and so there was no choreographic freedom for the dancers performing any of these dances.


This situation was changed around 1912 by Irene and Vernon Castle. They were nightclub dancers who became very popular performers in Europe and America. They danced in ballroom style, with Vernon essentially responsible for the choreography. Irene claimed that she "just fixed her eyes on the stud button of his dress shirt and followed his lead" (Castle, 1958, 57).

Irene and Vernon Castle

The Castles were extensively copied both in dance and in dress. They encouraged this by dancing for several short periods at the nightclub, and allowing general dancing in between, in which the patrons could practise emulating what they had seen the Castles perform.

In due course, Vernon started a dancing school in New York. In order to teach more effectively, he broke the dances down into short sequences of movements called 'Figures' or 'Steps' or 'Variations', each with its own name. For example his Tango was said to have 160 different Figures, but he said "for the average ballroom Tango, a knowledge of six basic Figures is quite enough" (Castle, 1914, 85). This structuring was done originally as a purely didactic device to simplify teaching (Castle, 1914, 108). His gift to posterity however was his suggestion to his students, that after they had learned a set of Figures, "you could do the Figures as they occur to you" (Castle, 1914, 108). He made the man in every social ballroom couple an instant choreographer, creating and performing dance as the couple moved.


Another 50 years passed before it was accepted that women could be creative in social dancing in Western society. Following development of the Lindy Hop in the 1930s, evolving into the Jitterbug of the 1940s, and the Jive of the 1950s, it became Rock'n Roll in the late 1950s. Its music was a descendent along the jazz line, with a simple 2/4 rhythm, and an accent on the second beat.

It brought with it a dance that was revolutionary: the Twist. In this dance, the couple ceased physical contact. As a simple result, it released both individuals to perform solo creative social dance for the first time in Western society (Andrews, 1979, 86).

Various forms of dancing had been called or described as a Twist previously. One reference dates back to 1894 (Burchfield, 1986, 1033). In the 1960s, the Twist was popularised by Ernest Evans (a one time chicken plucker, singing under the name of "Chubby Checker", an oblique reference to "Fats Domino"). The initial recording of the Twist was published under the Philadelphia label (Ward, 1986, 221) from a song written by Hank Ballard in 1959 (Nite, 1974, 24). It was said to be a dance which black adolescents had been doing to medium and up tempo music in USA, described as "round and round and up and down" (Ward, 1986, 199). The record holds the distinction as the only Single ever to hit number one on the charts in the USA at two different times in two different years (Nite, 1974, 107).

The rise in popularity of the dance coincided with the switch of social dancing from halls with live bands to the Discotheques, at which only records were played for dancing. Discos were of course much cheaper to run (Ward, 1986, 232).

The Twist swept Western society, and the media showed Liz Taylor doing it, even Jackie Kennedy doing it in the White House (Ward, 1986, 232). Indeed in April 1963, it was included in the Queen's dance at Windsor Castle to celebrate Pricess Alexandra's engagement (Rust, 1969, 113). Clearly, at last women were liberated to perform creative social dance.


The view of a set of movement sequences as an alphabet of symbols is a necessity in the sign language used by deaf people and others (Jean, 1982, xii). In a more popular form, body language has been described as a way of elucidating emotional attitudes and interpersonal relationships (Pearse, 1981, 7). This however depends on a culturally predefined alphabet of postures and movements.

The use of dance to communicate complex ideas to a non-verbal alien audience need not depend on any predefined alphabet, but can include the alphabet definition in the dance itself (Robinson, 1983, 83). The idea that a message can contain a definition of its own symbols has also been used outside dance, e.g. the plaque on the Pioneer 10 spacecraft (Sagan, 1973, 16).

The figures of a dance, as defined by Vernon Castle and his successors, may thus be mapped (arbitrarily) onto the digits of our numeral system. Thus ten Figures may be chosen from, say, the Tango (Moore, 1951, 212) and assigned to the digits 0 through 9. Having done this, the digits of some number say 22/7, may be interpreted as a dance. The number 22/7 has the decimal representation:

3.142 857 142 857 142 857 142 857 etc.

Because the decimal representation of a rational fraction (like 22/7) is either finite or has a recurring sequence of digits, the dance corresponding to a rational number will either be finite or have a recurring sequence: it will be a sequence dance.

By contrast, an irrational number has the digits occurring in an infinite non-repeating sequence. Thus the digits of PI (the ratio of the circumference to the diameter of a flat circle) are:

3.141 592 653 589 793 238 462 643 etc.

A dance based on this sequence of digits will be infinite and non-recurring.


The Tango is now an international dance, but it originated in the late 19th century as the Milonga in Argentina, in the slums of Buenos Aires.

The private Milonga.

It's importation into the upper classes of Western Society was catalysed by France's greatest music-hall star: Mistinguett, who gave the first ever demonstration in Paris in 1910 (Collier, 1995, 69). Interest in the dance rapidly exploded as a "Tangomania", initially through Paris then London and New York. The first world war did nothing to cool this interest, with Rudolph Valentino popularising the Tango further in his film "The Four Horsemen of the Apocalypse" (1921).

Rudolph Valentino and Beatrice Dominguez
Dancing the Tango in "The Four Horsemen of the Apocalypse"

A more recent film demonstration was given by Al Pacino and Gabrielle Anwar in "Scent of a Woman" (1992). A number of Sequence Tangos have been choreographed and are commonly performed socially around Australia, a popular one being the New Vogue dance called La Bomba.


As the first dance to start modern ballroom dancing, it seems appropriate to choose the Tango for a comparison of rational and irrational dancing.

A complication of choosing the Tango is that the Figures may start and/or end in either Closed Position or Promenade Position, so that actually two sets of Figures are necessary: one set starting from Closed Position and one set starting from Promenade Position. A suitable assignment of Figures to digits for the modern Tango is given in Appendix A. The corresponding dance for 22/7 is given in Appendix B.

The start of the dance corresponding to PI is listed in Appendix C.

One may thus view the innovation of Vernon Castle as heralding a change from rational (sequence) to irrational (as they occur to you) dancing.


Abromowitz, M., and Stegun, I.A., (Eds) (1972)
"Handbook of Mathematical Functions", Dover, New York (9th Printing).

Andrews, S., (1979)
"Take Your Partners", Hyland House, Sydney (3rd Edition).

Boyd, N., (1984)
"New Vogue Sequence Dancing", Boyd, Turramurra (Revised Edition).

Burchfield, R.W., (Ed) (1986)
"A Supplement to the Oxford English Dictionary", Vol. IV,
Oxford University Press, Oxford.

Castle, I., (1958)
"Castles in the Air", Doubleday, New York.

Castle, V., and Castle, I., (1914)
"Modern Dancing", Harper & Bros, New York.

Collier, s., Cooper, A., Azzi, M.S., & Martin, R., (1995)
"Tango", Thames & Hudson, London.

Farley, P., (1969)
"Teachers Guide to Creative Dance", A.H. & A.W. Reed, Sydney.

Fernandes, C., (1988)
"The Western Suburbs Courier", Vol. 104, No. 40,
Eastern Suburbs Newspapers, Alexandria.

Fonteyn, M., (1980)
"The Magic of Dance", British Broadcasting Corporation, London.

Hanna, J.L., (1988)
"Dance, Sex, and Gender", University of Chicago Press, Chicago.

Hinkley, C., (1980)
"Creative Dance", Alternative Publishing Cooperative, Sydney.

Jeanes, R.C., and Reynolds, D.E. (Eds) (1982)
"Dictionary of Australian Signs",
Victorian School for Deaf Children, Melbourne.

Kendall, E., (1979)
"Where She Danced", University of California Press, Los Angeles.

Livet, A., (Ed) (1978)
"Contemporary Dance", Abbeville Press, New York.

Moore, A., (1951)
"Ballroom Dancing", Pitman, London (6th Edition).

Nite, N.N., (1974)
"Rock On", Harper & Row, New York.

Pearse, A., (1981)
"Body Language", Camel, Sydney.

Robinson, S., and Robinson, J., (1983)
"Stardance", Tom Doherty Associates, New York.

Rust, F., (1969)
"Dance and Society", Routledge & Kegan Paul, London.

Sagan, K., (1973)
"The Cosmic Connection", Double day, New York.

Tingey, N., (Ed) (1973)
"Emile Jaques-Dalcroze", Dalcroze Teachers Union, London.

Ward, E., Stokes, G., and Tucker, K., (1986)
"Rock of Ages", Simon & Schuster, New York.


Assignment of Tango Figures to digits

 Digit   From Closed Position                       From Promenade Position

 0       Closed Telemark                            Promenade Link
 1       Fallaway Reverse Turn                      Closed Promenade
 2       Viennese Cross to Throwaway Oversway       Promenade Twist Turn
         and recovery to Promenade Position
 3       Progressive Link                           Ronde Fallaway
 4       Closed Reverse Turn                        Open Promenade Swivels
 5       Double Side Step to Left, to Throwaway     Double Natural Pivots
         Oversway & recovery to Promenade Position
 6       Right Entry                                Flat Whisk
 7       Four Step                                  Open Promenade Rocks
 8       Double Back Lock                           Chase and Back Lock
 9       Four Step with Kick                        Natural Promenade Turn


The Rational Tango 22/7

 3       Progressive Link

 1       Closed Promenade
 4       Closed Reverse Turn
 2       Viennese Cross etc

 8       Chase and Back Lock
 5       Double Side Step to Left etc
 7       Four Step

 1       Closed Promenade
 4       Closed Reverse Turn
 2       Viennese Cross etc

 8       Chase and Back Lock
 5       Double Side Step to Left etc
 7       Four Step

 1       Closed Promenade
 4       Closed Reverse Turn
 2       Viennese Cross etc

 8       Chase and Back Lock
 5       Double Side Step to Left etc
 7       Four Step



The Irrational Tango PI

 3       Progressive Link

 1       Closed Promenade
 4       Closed Reverse Turn
 1       Fallaway Reverse Turn

 5       Double Side Step to Left etc
 9       Four Step with Kick
 2       Promenade Twist Turn

 6       Flat Whisk
 5       Double Natural Pivots
 3       Progressive Link

 5       Double Natural Pivots
 8       Double Back Lock
 9       Four Step with Kick

 7       Open Promenade Rocks
 9       Four Step with Kick
 3       Ronde Fallaway

 2       Promenade Twist Turn
 3       Ronde Fallaway
 8       Chase and Back Lock

 4       Closed Reverse Turn
 6       Right Entry
 2       Promenade Twist Turn

 6       Flat Whisk
 4       Open Promenade Swivels
 3       Prograssive Link


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