POINT OF INFINITY
San Francisco
2023
2023
Art that is selected, or given, rather than made. This idea of Marcel Duchamp is increasingly important in my creative output of recent years. The starting point for my proposal for the Treasure Island Arts Master Plan was not to “make” a sculptural shape but to ask myself what should be “given” to this very specific place. There is such a thing as place memory. Treasure Island was the site of the 1939 World’s Fair. The Bay Bridge, which connects San Francisco with Treasure Island, Yerba Buena Island, and Oakland, was completed in 1936. Going further back in time, there was the Great San Francisco Earthquake of 1906, the gold rush of 1848, and the arrival of the Spanish settlers in 1769. Beyond that, humans first spread from the Eurasian to the American continent fifteen thousand years ago.
My task, I feel, is to delve into humanity’s memories and revisit the actual place where human consciousness was born. Its origins are shut away in the primordial darkness of eternity. Humanity’s destination, meanwhile, seems to extend into the future as far as infinity. I therefore felt that the challenge I had been “given” by this place was that of a hyperbolic curve that would suggest both infinity and eternity: two converging curved lines, getting closer and closer but never meeting, whose shape is expressed by the following cubic function.
𝑥 = cos 𝑢
cosh 𝑣
𝑦 = sin 𝑢
cosh 𝑣
𝑧 = 𝑣 − tanh 𝑣
( ０ ≤ 𝑢 < ２π , ０ ≤ 𝑣 < ∞)
Surface of revolution with constant negative curvature
The concept of infinity is a human invention. The point of infinity is a paradox, but should it exist in the natural world, it must be in a faraway place beyond the edge of the universe—or maybe it is no more than an illusion born inside the human brain. Nonetheless, ever since its birth, the human race has persisted in seeing this illusion. We call it art.
In the material world, it is physically impossible to make a point that reaches all the way to infinity. What I can do, however, is suggest infinity by making an approximate point that can exist in the material world, as a twenty-one-meter-high mathematically modeled structure with a twenty-one-millimeter-wide tip. This mathematical model, to be placed on Yerba Buena Island in the center of San Francisco Bay, will act as a monumental sundial. From the longitude and latitude of its position, I can calculate where the tip of the shadow of the tower will fall at noon on the spring and autumn equinoxes. A stone will be placed at that particular spot with vertical grooves carved into its polished flat surface for precise observation of the position of the noon shadow. Rather like a rotating top, the Earth’s axis is actually wobbling very slightly. Five thousand years from now, that wobble will reach its greatest magnitude. Ten thousand years from now, however, I predict that the axis will revert to where it is today. This tower will allow future civilizations to observe these changes. The creation of the pyramids is shrouded in mystery. By contrast, this tower will act as a symbol expressing humanity’s yearning for the infinite even fifty centuries in the future.
Hiroshi Sugimoto
Collection of the Treasure Island Development Authority.
My task, I feel, is to delve into humanity’s memories and revisit the actual place where human consciousness was born. Its origins are shut away in the primordial darkness of eternity. Humanity’s destination, meanwhile, seems to extend into the future as far as infinity. I therefore felt that the challenge I had been “given” by this place was that of a hyperbolic curve that would suggest both infinity and eternity: two converging curved lines, getting closer and closer but never meeting, whose shape is expressed by the following cubic function.
𝑥 = cos 𝑢
cosh 𝑣
𝑦 = sin 𝑢
cosh 𝑣
𝑧 = 𝑣 − tanh 𝑣
( ０ ≤ 𝑢 < ２π , ０ ≤ 𝑣 < ∞)
Surface of revolution with constant negative curvature
The concept of infinity is a human invention. The point of infinity is a paradox, but should it exist in the natural world, it must be in a faraway place beyond the edge of the universe—or maybe it is no more than an illusion born inside the human brain. Nonetheless, ever since its birth, the human race has persisted in seeing this illusion. We call it art.
In the material world, it is physically impossible to make a point that reaches all the way to infinity. What I can do, however, is suggest infinity by making an approximate point that can exist in the material world, as a twenty-one-meter-high mathematically modeled structure with a twenty-one-millimeter-wide tip. This mathematical model, to be placed on Yerba Buena Island in the center of San Francisco Bay, will act as a monumental sundial. From the longitude and latitude of its position, I can calculate where the tip of the shadow of the tower will fall at noon on the spring and autumn equinoxes. A stone will be placed at that particular spot with vertical grooves carved into its polished flat surface for precise observation of the position of the noon shadow. Rather like a rotating top, the Earth’s axis is actually wobbling very slightly. Five thousand years from now, that wobble will reach its greatest magnitude. Ten thousand years from now, however, I predict that the axis will revert to where it is today. This tower will allow future civilizations to observe these changes. The creation of the pyramids is shrouded in mystery. By contrast, this tower will act as a symbol expressing humanity’s yearning for the infinite even fifty centuries in the future.
Hiroshi Sugimoto
Collection of the Treasure Island Development Authority.
