Partner Dance Permutations

An Odd Eureka! How to Greet Everyone in Partner- Shifting Dances, such as Dances of Universal Peace

Some embodied spiritual practices include partner dances, consisting of two circles of participants, where the people of the inner circle face those of the outer circle, and one circle 'moves over one person' for each round of a chant or ritual gesture. One property of such dances is that each person ritually encounters the people from the other circle, but none from that person's own circle. With a 'line dance', as described below, each person may encounter everyone else in the group, not just half of the group.

In the line dance I have in mind, there are two lines of dancers, facing each other. The following diagrams show how five people in such a line dance can progress through five rounds of a chant or ritual gesture. Of course, the lines of people could be wavy, but for the sake of easy illustration they  are here depicted as straight. Person '1' in the diagrams below is highlighted, in order to help more clearly to illustrate how the dancers shift positions for each round of the dance.

The progression through a dance would work similarly with any odd-numbered set of dancers. Also, one can deduce that, with any odd number of dancers, e.g., five, it takes exactly that number of (e.g., five) rounds of the dance for each person to encounter each other. Note, however, that each person also has one round of non-encounter. The diagrams below show how Person 1 encounters, in order, Persons 5, 3, (no-one), 4, and 2. Similarly, the other four dancers also encounter each of their compatriots over the course of this dance.

1 5 2 4 3

5 4 1 3 2

4 3 5 2 1

3 2 4 1 5

2 1 3 5 4

The above sort of line dance maximizes the number of encounters, but it turns out that this full set of encounters occurs only with an odd number of dancers. With an even number, each person encounters only half of the group, making such an arrangement no more 'friendly' than dances that use the familiar pair of circles. E.g., in the following progression around the line, with six dancers, each person encounters only three others, and sees each of them twice during the one progression. Specifically, in this example, Person '1' encounters Persons 6, 4 and 2, but no others.

1 6 2 5 3 4

6 5 1 4 2 3

5 4 6 3 1 2

4 3 5 2 6 1

3 2 4 1 5 6

2 1 3 6 4 5

How then to handle the case where there is an even number of dancers? If one is leading such a dance and wants to maximize the number of (distinct) encounters, then one can ensure that an odd number of people are participating in the dance by either joining the group or remaining out of the group, depending on which choice makes the total number of dancers an odd number. Alternatively, with an even number of dancers, two of the dancers could cluster together, acting as one as they progress around the line. These two could then have one special round at the very end (or beginning) to encounter each other.

Thus, whether we have an even or an odd number of dancers, there are ways to make use of a line dance so that we maximize the encounters between dancers. If we want our ritual dances to let each person encounter each other person, then I recommend the use of the 'odd line dance' formation indicated above!

Akiva and Colleagues Visit the Garden

The Talmudic tradition (e.g., Tosefta, Yerushalmi and Bavli: Chagigah, Chapter 2) relates a story of four sages who journey mystically to the supernal 'Orchard' or 'Garden'.  Rabbi Akiva seems to be the only one of the four who has a successful journey. In fact, in the Bavli version, Akiva even offers helpful advice to the others before the journey. However, despite any advice, the other three do not fare so well. They either die, go insane or fall into apostasy.

An obvious lesson of this story warns us of the risks attendant upon advanced mystical or psycho-spiritual practices. One must be careful and strong, and of course, well-prepared, in order to withstand the intense experiences that such practices invite or produce.  

While noting the risks of these practices, we might also agree that the purpose or benefits of such practices extend beyond 'merely surviving' the experience. That is, presumably (or ideally) one undertakes such a mystical journey in order to grow, deepen, contribute to the God-field, or accomplish some other good.

We read that Akiva both entered and left the Garden in 'shalom', presumably meaning something like wholeness and peace. Did he also gain anything or accomplish anything during the journey, or as a result of the journey? Given a sympathetic, 'traditionally mainstream' reading of the story, it may be implicit or 'too obvious for the masters to have stated', that Akiva's journey brought him (and/or the world) to some deeper, higher spiritual state.

However, on a simplistic reading, he merely survived the journey. So from the perspective of deeper accomplishment, a radical assessment of Akiva's survival might suggest that his journey failed to achieve anything.

The other three sages clearly were deeply affected by the journey. If Akiva alone was unaffected by his mystical visit to the Garden, then we might consider his spiritual mastery, or his spiritual openness, to be even less than that of the other three sages. One could argue as follows: They, at least, were affected, albeit in apparently negative ways, by the journey. We see elsewhere, e.g., with Moshe Rabbeinu, that with higher spiritual status or accomplishment comes a higher standard of responsibility. Analogously, it also seems apparent that with a higher level of sensitivity and openness comes a higher level of vulnerability.

Irrespective of any speculation about 'what else' happened to Akiva, or about ranking the Garden sages, we may glean another lesson by reading this story: Sometimes we dare a bold, or even not-so-bold adventure. And sometimes a bold adventure befalls us whether we dare or not. In all these cases, we have an opportunity both to reach a goal, a destination, a discrete outcome; and to grow and contribute along the way. Ideally, we complete our adventures both by 'showing up' at the 'other end' and also by growing along the way.