What is drama therapy?

Kathryn Farley obtained her PhD from Northwestern University in performance studies in 2007. After almost a decade working in that area, she has just started a Master’s program at New York University in a related field called drama therapy (DT).

I thought today I would talk about the math aspects of DT.

Okay so why should I report on DT here? It seems to have nothing in common with our usual topics. But I claim that it does, and I would like to make the case that it is an example of a phenomenon that we see throughout mathematics.

So here goes. By the way—to be fair and transparent—I must say that I am biased about Dr. Farley, since she is my wonderful wife. So take all I say with some reservations.

The whole point is that understanding what DT is hard, at least for me. But when I realized that it related to math it became much clearer to me, and I hope that it may even help those in DT to see what they do in a new light. It’s the power of math applied not to physics, not to biology, not to economics, but to a social science. Perhaps I am off and it’s just another example of “when you have a hammer, the whole world looks like a nail.” Oh, well.

DT

I asked Kathryn for a summary of DT and here it is:

Drama therapy uses methods from theatre and performance to achieve therapeutic goals. Unlike traditional “talk” therapy, this new therapeutic method involves people enacting scenes from their own lives in order to express hidden emotions, gain valuable insights, solve problems and explore healthier behaviors. There are many types of DT, but most methods rely on members of a group acting as therapeutic agents for each other. In effect, the group functions as a self-contained theatre company, playing all the roles that a performance requires—playwright, director, actors, stagehands, and audience. The therapist functions as a producer, setting up the context for each scene and soliciting feedback from the audience.

Math View Of DT

Kathryn’s summary of DT is clear and perhaps I should stop here and forget about linking it to math. But I think there is a nice connection that I would like to make.

Since Kathryn is a student again, and students are assigned readings—there is a lot of reading in DT—you may imagine that she has been sharing with me a lot of thoughts on her readings and classes. I have listened carefully to her, but honestly it was only the other day, in a cab going to Quad Cinema down on 13th St., that I had the “lightblub moment.” I suddenly understood what she is studying. Perhaps riding in a cab helps one listen: maybe that has been studied before by those in cognitive studies.

What I realized during that cab ride is that DT is an example of a generalization of another type of therapy. If the other therapy involves ${N=2}$ people–including the therapist—then DT is the generalization to ${N>2}$. We see this all the time in math, but it really helped me to see that the core insight—in my opinion—is that DT has simply moved ${N}$ from ${2}$ to ${3}$ or more.

We this type of generalization all the time in math. For example, in communication complexity the basic model is two players sending each other messages. The generalization to more players creates very different behavior. Another example is the rank of a matrix. This is a well understood notion: easy to compute and well behaved. Yet simply changing from a two-dimensional matrix to a three-dimensional tensor changes everything. Now the behavior is vastly more complex and the rank function is no longer known to be easy to compute.

An Example

Here is an example of how DT could work—it is based on a case study Kathryn told me about.

Consider Bob who is seeing Alice who is Bob’s therapist. Alice is trained in some type of therapy that she uses via conversations with Bob to help him with some issue. This can be very useful if done correctly.

What DT is doing in letting ${N}$ be ${3}$ or more is a huge step. We see this happen all the time in mathematics—-finally the connection. Let’s look at Bob and Alice once more. Now Alice is talking with Bob about an issue. To be concrete let’s assume that Bob’s issue is this:

Bob has been dating two women. His dilemma is, which one should he view as a marriage prospect? He thinks both would go steady with him but they are very different in character. Sally is practical, solid, and interesting; Wanda is interesting too but a bit wild and unpredictable. Whom should he prefer?

The usual talk therapy would probably have Alice and Bob discuss the pros and cons. Hopefully Alice would ask the right question to help Bob make a good decision.

The DT approach would be quite different. Alice would have at least one other person join them to discuss Bob’s decision. This would change the mode from direct “telling” to a more indirect story-line. In that line it might emerge that Bob’s mother is a major factor in his decision—even though she passed away long ago. It might come out that his mom divorced his dad when he was young because he was too staid and level-headed. Perhaps this would make it clear to Bob that his mother was really the reason he was even considering Wanda, the wild one.

What is so interesting here is that by using more that just Bob, by setting ${N = 3}$, Alice can make the issues much more viivid for Bob.

${N}$ is the Root

The more I think about it, the idea of ${N \geq 3}$ people involved is the root. Naturally anything with more than two people transits from dialogue to theater. So the aspect of `drama’ is not primordial—it is emergent. Once you say ${N \geq 3}$, what goes down as Drama Therapy in the textbooks flows logically and sensibly—at least it does to me now.

This is accompanied by a phase change in complexity and richness. As such it parallels ways we have talked about mathematical transitions from the case of ${2}$ to ${3}$ on the blog before. Maybe DT even implements a strategy I heard from Albert Meyer:

Prove the theorem for ${3}$ and then let ${3}$ go to infinity.

Open Problems

Does this connection help? Does it make any sense at all?

It was just Ken’s birthday

Kenneth Regan’s birthday was just the other day.

I believe I join all in wishing him a wonder unbirthday today. Read more…

A new approximation algorithm

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Ola Svensson, Jakub Tarnawski, and László Végh have made a breakthrough in the area of approximation algorithms. Tarnawski is a student of Svensson at EPFL in Lausanne—they have another paper in FOCS on matchings to note—while Végh was a postdoc at Georgia Tech six years ago and is now at the London School of Economics.

Today Ken and I want to highlight their wonderful new result.

Svensson, Tarnawski, and Végh (STV) have created a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). This solves a long-standing open problem and is a breakthrough of the first order. Read more…

A gathering this Labor Day in Rochester

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Joel Seiferas retired on December 31, 2016 and is now a professor emeritus in the University of Rochester Computer Science Department.

Today Ken and I wish to talk about his party happening this Labor Day—September 4th.

A topical look at Norbert Blum’s paper and wider thoughts.

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Thales of Miletus may—or may not—have accurately predicted one or more total solar eclipses in the years 585 through 581 BCE.

Today we discuss the nature of science viewed from mathematics and computing. A serious claim of ${\mathsf{NP \neq P}}$ by Norbert Blum has shot in front of what we were planning to say about next Monday’s total solar eclipse in the US. Update 9/2/17: Blum has retracted his claim—see update at end.

A surprising theorem about differential equations

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Olivier Bournez and Amaury Pouly have proved an interesting theorem about modeling physical systems. They presented their paper at ICALP 2017 last month in Warsaw.

Today Ken and I wish to explain their theorem and its possible connections to complexity theory. Read more…

Including debt to Marina Ratner, 1938-2017

Maryam Mirzakhani won the Fields Medal in 2014. We and the whole community are grieving after losing her to breast cancer two weeks ago. She made several breakthroughs in the geometric understanding of dynamical systems. Who knows what other great results she would have found if she had lived: we will never know. Besides her research she also was the first woman and the first Iranian to win the Fields Medal.

Today we wish to express both our great sorrow and our appreciation of her work.