# One door closes, another one opens

So I asked:

"Five elements. Two versions of each element. How many possible combinations are there?"

The question arose out of seeing Cunningham's *Split Sides* at BAM last night. The final NY performance of the world's most celebrated dance company was bittersweet - profound and earthy, mysterious and straightforward - in typical Merce style.

Split Sides is one of the more popular later works, partly because of the collaboration with Radiohead and Sigur Rós on the music score, and partly because of the way that the chance operations that were so fundamental to Merce's approach are brought right out on stage. The official video is available on Netflix and Amazon, and contains several possible sequences. It works like this: the sequence of the dance, the music, the costumes, the sets, and the lights is determined just before the dance starts by five tosses of a die. In other words, when the die is thrown for the dance, and even number means the 'A' portion of the dance goes first, and an odd result means that the 'B' portion goes first. And so forth for the sequence of the rest of the elements.

The program told us that 32 possible combinations existed, but we didn't have the math skills to prove this out, so I asked for help from people who actually might understand the math. Henry punted [it was Saturday night after 11 pm, after all] and Robert responded at 3:00 in the morning with a series of cogent questions, pointing out how incomplete my framing of the question actually was:

1. *How many elements per "combination"? 2? And saying five elements with two versions of each is really just saying 10 elements, mathematically speaking.*

* **2. Also, is element1 + element2 counted as a different combination from element2 + element1?*

* **3. Also, can two of the same element together be considered a combination?*

To be fair, Henry actually responded later with the correct mathmatical formulation of the problem, which is *2^5, or 2 to the fifth power. *Seems so simple when you know what to ask. Robert has graciously pointed out that I should be embarrassed that I could not put 2 and 2 together, as it were. He's right, of course, but I'm profoundly glad that my son is smarter than me. I probably learned this in 8th grade algebra and promptly forgot it. Use is or lose it.

Since I was losing sleep over the question, I got up early and spent a couple of hours working it out visually for those of us who are slow learners. Below is a picture of the 32 possible combinations [click to enlarge]. By the way, other than Robert Swinston's failure to take the bow he so deserves, the version that we experienced last night seemed absolutely perfect. The Cunningham legacy will live on, thanks in no small measure to the way he opened the eyes and ears of so many people around the world. Always looking ahead to see the future before the rest of us could even imagine it. Always living in the present. Always listening carefully to the sound of silence.