Structural Compression: Not the Elimination of Complexity, but Convergence upon the Minimal Relations Through Which Complexity Emerges

Minimalism is not an aesthetics of elimination, but an epistemology of convergence. Structural compression does not discard complexity; rather, it converges upon the minimal relations through which complexity can emerge.

In minimalist thinking, the crux lies not in deciding what to remove, but in discovering what must remain to the very end. Structural compression is less about reducing the volume of information than about extracting the recurring relations and conditions within complex phenomena to access their generative ground. Minimalism must be viewed through the lens of convergence rather than subtraction. From this perspective, it is critical to distinguish between simplicity and essence. While simplicity denotes a state of having fewer elements, essence is the threshold beyond which further removal causes the entire structure to collapse. Thus, the apex of minimalist thought consists not in possessing the least, but in reaching the minimum conditions required for a structure to constitute itself.

In conceiving music grounded in geometry, I strive to reflect aesthetically and historically upon the endeavors of the ancient Greeks. At the foundation of this process lies the essential premise of extracting the core. Simplifying a regular polyhedron into a few lines and faces is not a mere abbreviation of a geometric figure, but a compression of the relations—symmetry, angle, connectivity, and curvature—that constitute the form itself. Similarly, in music, a chord or an interval is not merely a sparse collection of notes, but a compression of tension, directionality, and spatial relations.

This connects directly to my consistent trajectory since 2018: a critique of cognition. Humans compress models to comprehend the world, but the danger lies in mistaking the compressed model for the world itself. Therefore, a genuine structural compression should not simplify and foreclose the world—building a closed worldview that severs communication—but rather reveal the minimal structure that generates the world’s complexity, restoring it to an open state.

Essence is not the simplest form, but an irreducible structure of relations.

This marks a crucial distinction from the reductionism I have long cautioned against. Where reductionism seeks to explain the whole as a mere sum of its components, structural compression seeks the conditions of the whole generated by the relations among those components. In other words, it is a mindset closer to fewer things, fewer assumptions, but more relations. This is precisely where modern science, despite its monumental achievements, occasionally reveals its helplessness or insular thinking. The whole is not the sum of its parts. The perspective that the whole is generated by inter-component relations may seem subtly different at first glance, but it demands far more complex, multi-layered thinking.

My project, <Exploring Manifolds>, is likewise not merely an investigation into geometric complexity, but an experiment in compressing the complex world into a few fundamental relations—connectivity, distance, curvature, direction, symmetry, locality, and globality—while ensuring that this compression never usurps or replaces the world itself.

While reduction and derivation may appear similar in their outcomes, their conceptual directions are diametrically opposed:

• Reduction operates by subtracting parts from the whole: $A \rightarrow A - \alpha - \beta - \gamma$

• Structural Reconfiguration proceeds by identifying the relations that constitute the whole and reactivating them under new conditions: $A \rightarrow \text{core relation } R \rightarrow \text{reconfiguration of } R \text{ under new condition } B$

Thus, the transition from Nongak (traditional Korean folk performance) to Samulnori can be understood in this light. Samulnori did not emerge by simply shrinking the spatial matrix, dance, theatrical performance, games, instruments, rhythmic patterns, and communal interactions of Nongak. Rather, it extracted the rhythmic and interactive core generated by the four primary instruments (Samul) within that complex system, reorganizing it within a new spatial medium (the stage) and new performance conditions.

Here, one must examine the scope captured by the term Nongak.

Literally translating to "farmers' music," Nongak foregrounds agricultural labor. Yet historically, these traditional practices extended far beyond agricultural work. Framing them solely as Nongak risks overlooking that they constituted an integrative performance system—interweaving village rituals (gut), rites, festivals, play, professional itinerant troupes (Namsadang-pae), fundraising performances (Geollip), open-field theatrical arts (Pangut), dance, theater, and music.

Hence, arguments emerge favoring terms like Pungmul or Pungmul-gut, which capture a broader spectrum of phenomena. Crucially, one must recognize the critique that the term Nongak was administratively institutionalized during the Japanese colonial period, effectively reducing a multi-faceted performing art to a singular agricultural function. Documentation from the Korean Culture and Arts Foundation in 1997 directly addresses this issue: it notes the awareness that Nongak was a Japanese-coined term, and points out how the public's familiarity with Nongak over Pungmul paradoxically led to Samulnori being perceived as a substitute for Nongak as a whole(<월간 문화예술>, 1997년 11월 통권 220호 - 한국문화예술진흥원발행 중: 문화예술 리뷰 (전통) 사물놀이가 대중문화 경향과 접목하여 만들어낸 또 하나의 활로 - 환퍼포먼스의 「난타: https://www.arko.or.kr/zine/artspaper97_11/19971119.htm).

The shift from Nongak to Samulnori was not an act of discarding excess, but an event in which the generative principles operating within Nongak's vast performance system were extracted and compressed to function under different conditions. What is intriguing here is that this "core" was not pre-existing as a fully formed entity waiting inside. Structural reconfiguration is simultaneously an excavation of latent essence and an act of discovering what can function as the core under new conditions.

Thus, I propose framing this as a step beyond structural compression—a concept I call structural derivation. Rather than a miniature version of Nongak, Samulnori is a form of structural reconfiguration: a translation of the structural core of diverse traditional practices into new spatial and mediatic conditions.

• Reduction: Eliminates elements.

• Extraction: Selects essential elements.

• Compression: Encodes a complex structure into a more compact representation.

• Structural Derivation: Derives generative principles from original, complex relations.

• Structural Reconfiguration: Reactivates derived principles under new conditions.

  
  

Viewed this way, Samulnori is treated not as a minimal version of Nongak, but as a new generative system forged through structural derivation. This framework synthesizes my broader trajectory into a unified methodology: regular polyhedra $\rightarrow$ musical structures, regular pentagons $\rightarrow$ curvature, and Nongak $\rightarrow$ Samulnori $\rightarrow$ compression of cognitive conditions.

Rather than simplifying complex phenomena, derive the relations that generate that complexity, and reconfigure them under new conditions.

Could this not serve as a compelling thesis statement for my overarching methodology? It lays the groundwork for developing what I call non-reductive compression, distinguishing it sharply from the reductionism I continuously guard against.

Minimalism is not the reduction of an archetype, but the extraction of the conditions required for that archetype to function.