Here are four new dances I have written since A Group of Calculated Figures appeared:   "Autumn Moon" (tune by Rebecca King) and "Silver Lining" and "Forget Me Not" (tunes by Debbie Jackson), and "It's a Draw" (tune by Greg Allen).   There are recordings for the first three dances on our new CD, Good Friends" (and the fourth one will no doubt be on our next CD).   Great music for all four dances, as you will see.
Autumn Moon
Silver Lining
Forget Me Not
It's a Draw


A Group of Calculated Figures contains three dances that deserve special comment.  They are four-couple dances in which every dancer is in a different place with a different partner every time through the dance.   Based on my informal surveys of English, Scottish, and Square dance leaders, there are few, if any, four-couple dances with this characteristic (in fact, I have not found a single one).   I had been trying for sometime to write such a dance but had given up, until I showed the problem to Michael Bush, Assistant Professor of Mathematics at Smith College.   He helped me analyze it using a body of mathematics called group theory.   Group theory is the mathematical study of symmetry.   With Michaelís help, I discovered that there are a limited number of combinations of moves that will do the trick.   Perhaps most important, the theory showed me how to identify the combinations of moves (the vast majority, in this case) that will never work. *

Michael and I have written two versions of a paper on this topic.   The first one is a careful mathematical statement of how we figured things out.   The second paper tries to motivate the key ideas from the first paper without being too rigorous about it.   It is addressed to people with some mathematical knowledge (but not too much) and an interest in dancing.   The arguments in the second paper are relatively easy to follow, but it may not always be obvious why they are true.   To get that part, you probably need the first paper.

                              First Paper          Second Paper

DP/DP dances all have one important property in common:   The figures in the dance are almost the same all four times through, BUT in each one, there is at least one place where the figures done the 1st and 3rd times through are slightly different from the figures done the 2nd and 4th times through.   (The mathematics says that this is what has to happen to get the DP/DP progression.)

It should be emphasized that DP/DP dances, to be any good, still need to be fun, make sense, and be rememberable.  I know from experience that what is conceptually possible is not necessarily enjoyably danceable.   I will appreciate feedback from those who have a chance to try this dance.

* In addition to Michael Bush's help in solving this puzzle, I want to acknowledge the members of the informal ECD Society of Dancing Mathematicians, who saw my query on the ECD List about the existence of such dances and sent me valuable comments and ideas.   Al Blank and Robert Messer were particularly enthusiastic about helping me figure things out.


Occasionally, there is a dance of mine that I wish I could tinker with and re-release.  Also, I sometimes think of a way I could have made the instructions for a dance clearer.   The changes I have wanted to make are all pretty small, but I offer them here anyway for your consideration.

Cadgers' Caper
Charlene's Celebration
Coming and Going

Designing Woman

Far Away

Henry's Hornpipe

Honeysuckle Cottage

Laisteridge Lane

The Matching Pair

Mevagissey Car Park

Mr. Chopin's Waltz

Mr. Roodman's Fancy

Promise of Spring



Here are some minor typographical and musical-notation errors that have snuck into my books.  There are probably others I have not found yet, but here are the ones I know about.
Alexander's Birth Day
(tempo marking)
Designing Woman
Far Away
Helene('s Gavotte)
(name change)
A Quick Romp in the Hey
Ramblin' Rosie
Social Symmetry
(measure numbers)
Woodlands Waltz
(measure numbers)