Statement: Quantum Art Festival Special Exhibition "Alternative Computations: Worlds Otherwise Calculated"

Text: Ryuta Aoki

Gunpowder can become either a weapon or fireworks.

I have long sought to explore "firework-like technology." Technology turns violent when play and festivity are lost. When calculation becomes fixed as an apparatus solely for efficiency and accuracy, fluctuation and deviation are eliminated, and the world converges toward a singular worldview. Today, as technology permeates every domain of society, this convergence accelerates at an unprecedented pace.

Calculation is not a technology invented by humans. It is a phenomenon that constantly occurs in the natural world; life itself is calculation. Mathematics serves as an interface for understanding this phenomenon and engaging with the world, while simultaneously functioning as an invisible structure that reflects how we frame and perceive reality. In other words, like language, mathematics itself constitutes a way of seeing the world. The totality of human practices surrounding the use and treatment of calculation and mathematics—this exhibition terms "cultures of calculation."

This exhibition interrogates "cultures of calculation" through three works. The large-scale installation Alternative Computations, sharing its title with the exhibition, stands at its center. Referencing wasan (traditional Japanese mathematics) as a lost culture of calculation and East Asian cosmology, it assumes the lineage of sculpture while inaugurating a festive space. Alongside this central work, the series Phantom Realities reinterprets contemporary mathematical formulas through the lens of wasan, visualizing the "parallel worldness" inherent in mathematics as an invisible structure. New Rousseau Machine (2021) materializes social calculation—voting and aggregation. It reveals how identical votes can yield different outcomes depending on aggregation rules, demonstrating that social decision-making is itself a form of contingent calculation.

These three works illuminate from different angles how calculation is not merely a tool for optimization, but a cultural practice that shapes worldviews, generates relations, and constitutes society.

Alternative Computations

Technology is not universal. As philosopher Yuk Hui argues through the concept of "cosmotechnics," technology can take diverse forms rooted in different cultures and cosmologies. Japan once possessed its own distinctive mathematics called wasan. In the 17th century, Takakazu Seki independently discovered the concept of determinants and derived sequences equivalent to Bernoulli numbers before the West, developing highly sophisticated algebra and geometry in a context entirely independent of Western mathematics. Yet the essence of wasan lies beyond mere mathematical achievement. It was a practice that cultivated thinking through relationships with things, rather than converging toward a single solution.

The playful and festive acts through which wasan generated fields and relations constituted a cultural practice alongside haiku and chanoyu (the Japanese tea ceremony). The "festivity" I speak of here refers to the deviation from everyday efficiency that Roger Caillois discussed in Man, Play and Games, and the quality of time-space that permits the excess Georges Bataille called "dépense" (expenditure). The custom of sangaku—dedicating mathematical problems and their solutions to shrines and temples—embodied precisely this festivity. Sangaku were not merely records of mathematical proofs but beautifully decorated offerings to deities, sometimes generating competitive exchanges and forming spaces for intellectual exchange within local communities. They testify to a "culture of calculation" in which mathematics was intertwined with economy, art, and religion.

Mathematics, like language, has developed distinctively within each cultural sphere. As the Sapir-Whorf hypothesis suggests regarding language, mathematics too influences thought and shapes human perception of the world. However, during Japan's Meiji-era modernization (late 19th century), wasan and this culture of calculation were eliminated from the educational system by the government, replaced by Western mathematics introduced nationwide. Just as the utility of English as an international lingua franca does not justify the replacement of all other languages, the loss of diversity in mathematics constitutes immeasurable damage to humanity.

This work does not nostalgically recreate a lost culture of calculation. It attempts to spatially manifest in the present the festivity that wasan possessed—the affirmation of excess beyond the logic of productivity and utility, and the playful practice of generating fields and relations.

Sculpture has transformed from material mass to relationships of light and space, and then to systems and information. Meanwhile, Mono-ha presented the "encounter" between material and observer as sculpture itself, following a path distinct from Western systems theory. What is sculpture, and how far can its materials and conditions of existence be extended? This work takes up these questions while referencing East Asian cosmology, attempting sculpture as a "field" that temporarily emerges through fluctuation and relationality. If Social Sculpture extended into human thought and will, and if Bio Art moved toward life as material, this work treats calculation—an invisible structure, a way of seeing the world itself—as sculptural material, seeking to restore festivity and playfulness to it.

In traditional East Asian astronomy, the celestial sphere is divided into the Twenty-Eight Mansions (nijūhasshuku)—lunar stations that map the heavens into four quadrants, each associated with a mythological creature and governing cosmic order and time. In the installation's celestial space, twenty-eight sangi (calculating rods used in wasan) hang in a circle, symbolizing these mansions and undulating like celestial movements. Light enters from the direction of Dou (the Dipper), the first mansion of the Northern Genbu (Black Tortoise) quadrant—the stellar lodge marking the origin of the calendar and cosmic order—endowing the space with time and orientation.

Below lies a yojōhan (four-and-a-half tatami mat) floor. In chanoyu, the four-and-a-half mat room represents a microcosm: four mats for the four seasons, half a mat for doyō (the transitional periods between seasons). It is a place where one sits, composes the spirit, and faces the world. The surrounding reeds evoke Ashihara no Nakatsukuni (the Central Land of Reed Plains)—in Japanese mythology, the earthly realm between the heavens and the underworld. The sound of rain pervades the space—water that nurtures life, fluctuation itself. The presence and behavior of viewers become incorporated into the state of the field, and each time a different universe emerges. The same universe never appears twice.

In this work, the bodily protocols performed by dancer Erika Fuki and tea master Souryo Matsumura are not ancillary events but essential components of the work. From the countless possibilities latent within the installation, their bodily gestures "observe" and temporarily actualize a specific universe. The gestures of temae (the ritualized procedures of preparing tea) in chanoyu, the trajectories of bodies in dance, impose order upon space, mark intervals in time, activate and then suspend the field. This resonates with how sangaku dedication in wasan became a "culture of calculation" only through the bodily and ritual act of offering, not through mathematical action alone.

Alternative Calculations, Alternative Worlds

What this exhibition presents is neither correct answers nor optimal solutions. It presents the possibility that through calculation and mathematics, the world might emerge otherwise—that beyond the worldview we have accepted as given, alternative cultures of calculation can indeed exist.

The three works differ in form and material, yet each attempts resistance to convergence—embracing fluctuation, maintaining diversity, and restoring festivity.

To dwell in the "in-between" before convergence. To present the playfulness and festivity inherent in calculation as an invisible yet experienceable structure. This is the endeavor of "Alternative Computations: Worlds Otherwise Calculated."