# Dancing algorithms and algorithms for dance apps

Browsing through teaching material a few years ago, I had stumbled upon dancing algorithms, which illustrate common algorithms in computing using dance [1] and couldn’t resist writing about since I used to dance folk dances. More of them have been developed in the meantime. The list further below has them sorted by algorithm and by dance style, with links to the videos on YouTube. Related ideas have also been used in mathematics teaching, such as for teaching multiplication tables with Hip Hop singing and dancing in a class in Cape Town, dancing equations, mathsdance [2], and, stretching the scope a bit, rapping fractions elsewhere.

That brought me to the notion of algorithms for dancing, which takes a systematic and mathematical or computational approach to dance. For instance, the maths in salsa [2] and an ontology to describe some of dance [3], and a few more, which go beyond the hard-to-read Labanotation that is geared toward ballet but not pair dancing, let alone a four-couple dance [4] or, say, a rueda (multiple pairs in a circle, passing on partners). Since there was little for Salsa dance, I had proposed a computer science & dance project last year, and three computer science honours students were interested to develop their Salsational Dance App. The outcome of their hard work is that now there’s a demonstrated-to-be-usable API for the data structure to describe moves (designed for beats that counts in multiples of four), a grammar for the moves to construct valid sequences, and some visualization of the moves, therewith improving on the static information from Salsa is good that counted as baseline. The data structure is extensible to other dance styles beyond Salsa that have multiples of four, such as Bachata (without the syncopations, true).

In my opinion, the grammar is the coolest component, since it is both from a scientific and from an engineering perspective the most novel aspect and it was technically the most challenging task of the project. The grammar’s expressiveness remained within a context-free grammar, which is computationally still doable. This may be because of the moves covered—the usual moves one learns during a Salsa beginners course—or maybe in any case. The grammar has been tested to cover a series of test cases in the system, which all worked well (whether all theoretically physically feasible sequences feel comfortable to dance is a separate matter). The parsing is done by the JavaCC parser, which carries out a formal verification to check if the sequence of moves is valid, and it even does that on-the-fly. That is, when a user selects a move during the planning of a sequence of moves, it instantly re-computes which one(s) of the moves in the system can follow the last one selected, as can be seen in the following screenshot.

Screenshot of planning a sequence of moves.

The grammar thus even has a neat ‘wrapper’ in the form of an end-user usable tool, which was evaluated by several members of Evolution Dance Company in Cape Town. Special thanks go to its owner, Mr. Angus Prince, who served also as external expert on the project. Some more screenshots, the code, and the project papers by the three students—Alka Baijnath, Jordy Chetty, and Micara Marajh—are available from the CS honours project archive.

The project also showed that much more can be done, not just porting it to other dance styles, but also still for salsa. This concerns not only the grammar, but also how to encode moves in a user-friendly way and how to link it up to the graphics so that the ‘puppets’ will dance the sequence of moves selected, as well as meeting other requirements, such as a mobile app as ‘cheat sheet’ to quickly check a move during a social dance evening and choreography planning. Based on my own experiences goofing around writing down moves, the latter (choreography) seems to be less hard to realise [documenting, at least] than the ‘any move’ scenario. Either way, the honours projects topics are being finalised around now. Hopefully, there will be another 2-3 students interested in computing and dance this year, so we can build up a larger body of software tools and techniques to support dance.

Dancing algorithms by type

Sorting

– Quicksort as a Hungarian folk dance

– Bubble sort as a Hungarian dance, Bollywood style dance, and with synthetic music

– Shell sort as a Hungarian dance.

– Select sort as a gypsy/Roma dance

– Merge sort in ‘Transylvananian-Saxon’ dance style

– Insert sort in Romanian folk dance style

– Heap sort also as in Hungarian folk dance style

There are more sorting algorithms than these, though, so there’s plenty of choice to pick your own. A different artistic look at the algorithms is this one, with 15 sorts that almost sound like music (but not quite).

Searching

– Linear search in Flamenco style

– Binary search also in Flamenco style

Backtracking as a ballet performance

Dancing algorithms by dance style

European folk:

– Hungarian dance for the quicksort, bubble sort, shell sort, and heap sort;

– Roma (gypsy) dance for the select sort;

– Transylvananian-saxon dance for the merge sort;

– Romanian dance for an insert sort.

Latin American folk: Flamenco dancing a binary search and a linear search.

Bollywood dance where students are dancing a bubble sort.

Classical (Ballet) for a backtracking algorithm.

Modern (synthetic music) where a class attempts to dance a bubble sort.

That’s all for now. If you make a choreography for an algorithm, get people to dance it, record it, and want to have the video listed here, feel free to contact me and I’ll add it.

References

[1] Zoltan Katai and Laszlo Toth. Technologically and artistically enhanced multi-sensory computer programming education. Teaching and Teacher Education, 2010, 26(2): 244-251.

[2] Stephen Ornes. Math Dance. Proceedings of the National Academy of Sciences of the United States of America 2013. 110(26): 10465-10465.

[3] Christine von Renesse and Volker Ecke. Mathematics and Salsa Dancing. Journal of Mathematics and the Arts, 2011, 5(1): 17-28.

[4] Katerina El Raheb and Yannis Yoannidis. A Labanotation based ontology for representing dance movement. In: Gesture and Sign language in Human-Computer Interaction and Embodied Communication (GW’11). Springer, LNAI vol. 7206, 106-117. 2012.

[5] Michael R. Bush and Gary M. Roodman. Different partners, different places: mathematics applied to the construction of four-couple folk dances. Journal of Mathematics and the Arts, 2013, 7(1): 17-28.