Studies on Infinity

Contact Quarterly 1986English
Contact Quarterly Vol. 11 No. 2 (Spring/Summer, 1986): 19-21.

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Contextual note
This text is excerpted from a talk between Lisa Nelson and Danny Lepkoff in Vermont in August, 1985.

Lisa: How did you make the decisions to structure the sound score for your performance "Studies on Infinity"?

Danny: It pretty much happened all of a sudden sitting down with a tape recorder by myself. I think the major thing was that I had a goal of proving, demonstrating, to an audience that there are two different kinds of infinities. So, with that goal in mind I figured out what I thought was the most accessible way of doing that; what was necessary in terms of background to introduce people who didn't know anything about the subject. That's what gave me the idea that I should define a 'set', and that I should define what 'number' is. And define what it means for two infinite sets to be equal. And I gave examples of using those definitions so it would be seen how they work in different situations. And then I just went into the proof. So I think my understanding of the subject matter and wanting to teach it motivated how it was structured.

Lisa: Why did you pick 'infinity' as your subject?

Danny: I picked it. You just say 'infinity' and everybody has some kind of image of what it is, of endlessness or expansiveness. So it's a real compelling concept. So in mathematics its compellingness is tamed and it's defined and it's manipulated in a completely logical way, just like adding one and one. And there's as much mystery in that way-why one and one is two, as why two infinite sets can be equal or not equal. So there's a kind of a delight in taking something that is far out and reeling it in and talking about it in a really strict way. Because of that it could inform someone of the character or flavor of mathematics. And you don't have to stop having your feelings for what infinity is because you can talk about it exactly, but it's a different way of dealing with that concept.

Lisa: Would you say that you structured the performance with a 'classically' mathematical mind?

Danny: Yeah, I think so. It was pretty straight.

Lisa: As you describe it, you were doing a proof that you knew already. You were presenting the fruit of your labor in a way to make someone else understand the 'product' of that thinking, rather than the process of that thinking.

Danny: Right. I didn't demonstrate the process. The problem that I was grappling with right there was my dancing. That was a problem that was being unravelled and that I was having to find my way through right then and there-the improvisation. 

Lisa: I wonder if there is something similar in your mathematical process and your dancing process.

Danny: Yeah, there is because it's me, engaging in a problem.

Lisa: ls there any further similarity in the way you define a problem in math and how you define a problem in your dancing? Or are you working with two different parts of yourself?

Danny: I never thought that [while I am dancing] that I am demonstrating how I work on a problem in my dancing. But in mathematics, there is a question posed and there's energy put towards resolving that question. So the structure is the question and it's a very specific question. So you end up taking a real specific path to answer that question, even though you may fish around.

Lisa: Can that question be answered in different ways?

Danny: Yeah. You find one way.

Lisa: How could you describe the contrast of that process with what you're doing when you're dancing, or making dances?

Danny: I think when I'm dancing, for some reason I resist giving myself a specific problem to work on. I think that the goal that I have in dancing is only realized after I get there, but it's not there before I start to go towards it. I'm not sure that I can say what it is that I want from my dancing but I don't feel that it's all that objective. My desires in dancing are not to objectively solve a problem. So that's why I reject having an objective problem in the first place. But I'm looking for some kind of resonance of my being through movement radiating from me to the audience and reflecting back from the audience to me. And the one dynamic that I knew was that I was bringing together two very different parts of myself and that would make some kind of energy dynamic interplay in the juxtaposition of me with a highly specific articulated knowledge of a technical language and me as a kind of soft body of feeling and image, sort of undifferentiated, trying to differentiate itself in the moment. Those two parts of me being brought together. And there's a crossover between those two, a crossover that there is some feeling-fulness, feelingful energy, emotional energy that goes into pushing through to solving a mathematical problem. And then there's also maybe some mental detachment and abstraction that plays in me as an improvisor.

Lisa: You talked about the emotional energy that goes into the solving of a math problem. I'm curious if there's an awareness of that emotional energy while you're doing a proof, or maybe it's an effort, an awareness of an effort that is also present when you 're dancing. Do you feel that there's an effort in dancing to create a logic? or a point of view?

Danny: Yeah. At least when things aren't working. I'm conscious that there's an effort to compose or to make something concrete, to get a reflection off of. It's a similar kind of effort as when there's a math problem and it's not being solved. Until it's solved, all the time that you worked on it doesn't add up to anything. And that feels somewhat the same.

Lisa: During the performance that I saw, there was a section where you were talking and dancing, see-sawing back and forth, seeming to interrupt yourself from each activity. It appeared to me that you were showing an effort involved in staying on a train of thought, making it linear. There were points where your speech fractured into wordlessness which extended into stuttering movement of your whole body, somewhat like you 're describing now about what happens when you're trying to think through a problem and don't know yet what the answer is. This section seemed to bring the two processes closer together.

Danny: Yeah, that was pretty successful. But I definitely wanted to juxtapose two things, not make the dancing anything like the mathematics. It's been suggested to me that I could apply computer programming to dance. I don 't respond to that as interesting, because programming is programming. It's so much more convenient to program a computer, it's built for that, so why program a human body?



This final section is the crowning glory of our argument. We shall demonstrate that we can with all logical consistency talk about orders of infinity. In fact, given any infinite set we can always find another of a higher order. Why this is true I really do not know. All we will attempt to do tonight is to find a set with a higher order than the counting numbers. This argument is tedious at best, but what we will have accomplished at the end of this evening is an understanding hopefully of a mathematical fact which is beyond the normal intuitive understanding of the world. This is one of the fascinating aspects of mathematics, in that following our logical senses we have created structures which do go beyond our own intuitive concepts of the world at large.