Unsolvable: Existence, Smoothness, and the Problem of Turbulence

Unsolvable

Existence, Smoothness, and the Problem of Turbulence

Heather Marcelle Crickenberger

Designed for the Art Wall of the James B. Hunt, Jr. Library at North Carolina State University

and installed on September 5, 2025.

Project Overview

This project brings together aged water, sumi ink, and ideas drawn from the unsolved Navier–Stokes existence and smoothness problem to explore how natural materials move, change, and resist simple explanation. Through attention to flow, resistance, and disturbance, the work invites viewers to consider how complex systems behave—both in the physical world and in the human systems that shape knowledge, culture, and environment.

Aged Water

Aged water is water that has been left out over time, exposed to air, light, temperature changes, and the quiet presence of microorganisms. As it rests, it becomes a living environment rather than a neutral substance. Bacteria, algae, and other microscopic life subtly alter how the water moves as they pursue their own needs for oxygen, nutrients, and space. These changes may be invisible at first, but they reveal themselves through shifts in flow and through the water’s interaction with ink. In this project, aged water serves as a record of time and relationship, showing how even simple materials are shaped by many small forces acting together.

Sumi Ink

Sumi ink is traditionally valued for its depth, sensitivity, and responsiveness to water. In this work, it functions as both material and recorder. The ink is applied to watercolor paper and filmed outdoors, using natural light and environmental conditions rather than a controlled studio setting. As the ink spreads, pools, breaks, and settles, it responds to gravity, resistance, moisture, and chance. Rather than illustrating a predetermined image, the ink registers the behavior of the water beneath it, making visible the interaction between intention and material agency.

The Navier–Stokes Problem

The Navier–Stokes existence and smoothness problem asks whether the equations used to describe fluid motion will always continue to behave in an orderly, predictable way, or whether there are situations where they stop giving reliable answers. While deeply mathematical, the question gestures toward a broader concern shared across science, engineering, and the humanities: how far our models can carry us, and where uncertainty begins. This project approaches the problem not as something to be solved, but as a framework for reflection on continuity, limits, and what remains unresolved.

Viscosity

Viscosity describes how much a material resists movement. Thin liquids flow easily; thicker ones slow, drag, and hold form. In this project, viscosity is shaped by time, biological activity, and the interaction between water and ink. Small variations in thickness influence how marks form and how motion unfolds. Viscosity becomes a way of thinking about friction and constraint—not only in fluids, but in systems of knowledge, labor, and attention.

Turbulence

Turbulence occurs when smooth movement gives way to irregular, swirling motion. Instead of flowing along a single path, the liquid responds to multiple forces at once. In the ink and water works, turbulence appears as branching forms, interruptions, and sudden changes in direction. These patterns are not random; they are structured responses to pressure and interaction. Turbulence offers a way to think about moments when systems become unstable or difficult to predict, yet still governed by underlying relationships.

Complex Problems and Visibility

Taken together, these materials and processes point toward the nature of complex problems—situations shaped by many interacting forces that cannot be fully separated or simplified. Ecological systems, social structures, and research itself often behave this way. To make these dynamics perceptible, the work is presented at a large scale and documented using high-definition, slow-motion video. The ink movements are recorded analog, on paper, outdoors, but revealed through contemporary imaging technologies that slow time and extend perception. These displays allow human viewers to see processes that normally unfold too quickly, too subtly, or too quietly to notice—bridging material practice, scientific observation, and the shared human effort to make sense of complexity.

Click image above to PLAY the 20-minute video scheduled to run twice per day for 21 minutes on NC State's Hunt Libary Art Wall at the library entrance. The video is intended to be an installation piece, meaning that it is to be experienced more as part of the surrounding architecture than as a film to be watched.

Memory

Reflection

Anomaly

Human-AI Collaboration

This project was designed as a human-AI collaboration using OpenAI's ChatGPT as a source of thinking through the mechanics of the problem and ways to interpret the real-world physical outcomes of the sumi ink and water experiments.

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