12/14/25: “The Non-Linear and Discontinuous Dimensions of Curious Learning”
- john koenig
- Dec 14
- 3 min read
There is a book by Jonathan D. Kramer called The Time of Music where he explores how musical time (subjectively experienced) and “clock time” (objectively measured) interact in process of experiencing a musical composition. He develops a rather idiosyncratic vocabulary to discuss these concepts, but I’m mostly interested in his ideas of continuous versus discontinuous musical elements and linear progress of a composition versus non-linear progress.
For Kramer, continuous events are events that logically flow from one to the other. This is how we normally experience time and life; it is the fundamental principle of cause and effect. Discontinuous events have no relation to preceding events or following events; they are interruptions. Linearity in time is felt when we experience development in events as opposed to non-linear time which is defined by a stasis. Prime examples of these ideas in music can be heard in the music of Florence Price and Julius Eastman.
Florence Price writes music that is continuous and linear. From the first bars of her Piano Concerto in One Movement, for example, the rest of the piece logically flows. The flow and development of ideas contributes to a sense of continuity and linearity. The music of Julius Eastman grows out of a minimalist composition tradition that is non-linear and discontinuous. Take, for example, his composition Buddha. Everything about the composition is discontinuous and non-linear. The score itself, a circle which contains a few simple musical ideas, is visually non-linear, and the piece progresses in a fashion that is non-linear and discontinuous.
In our society, we identify with and value music that is closer to Florence Price’s because it reflects the way we structure our lives. We live largely based on the belief that we progress logically through time and that the events of our lives are continuous. However, this is not always how we experience time. Increasingly often, I find my educational experiences to be non-linear and discontinuous. Instead of learning new things in a logical and structed progression of educational events, things I learned 20 years ago often come back to inform something I just learned yesterday in a completely different subject or context. Instead of the events occurring right next to each other in time and organized by subject, they are often separated by decades of disparate experiences.
For example, when I got to the Hartt School in 2022, my professor, the late Glen Adsit, introduced me to T’ai Chi Chih, a form of moving meditation. Practicing T’ai Chi Chih deepened my awareness of body movement and flow of physical energy. When I was studying piano in high school (2012-2017), my teacher, Yehuda Gutman, introduced me to a way of playing based on supreme relaxation and body awareness. When I studied piano in college, my professor, Heidi Louise Williams, explained the ways that tension and relaxation interact in playing any musical instrument. These experiences in body awareness did not linearly flow from one to the other (at least not perceptibly, but Kramer addresses this idea; read his book). When I think of them, they are relatively isolated and unique experiences, though they may be connected at deeper levels (again, see Kramer’s book). However, now when I think about my approach to conducting, I am often transported across time and concept, connecting disparate experiences to create new learning and insight.
I believe the way humans learn, which is at best a mix of linear/non-linear and continuous/discontinuous experiences, is often in direct conflict with how we are subjugated to linear and continuous learning experiences. This overemphasis on linear and continuously structured learning often removes the magic of more nonlinear learning and can often defeat curiosity. I have found that knowledge and learning is reinforced when we are encouraged to be curious and allow our experiences from seemingly disparate places in our lives to connect, inform, and reinforce one another. Often this experience only happens when we allow ourselves to indulge in learning and curiosity for no other reason than we are curious about learning new things.
Julius Eastman, Buddha (Version 1):
Julius Eastman, Buddha (Score):
Florence Price, Piano Concerto in One Movement, Karen Walwyn, piano, Leslie B. Dunner, conductor:
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