Immutable Antinomy · Track 8 · middle
Ode to Gabriel's Horn
The trumpet-shaped surface generated by rotating y=1/x has finite volume but infinite surface area. You can fill it with paint but never coat its inside. An ode to the object that holds a paradox in its geometry — the surface that cannot cover itself. Torricelli discovered it in 1643 and called it Painter's Paradox.
Lyrics
Palazzo Pitti. January, 1643. The ink in the well is frozen again. Just woodsmoke and the sound of your own breathing. You are an equation scratched on rag paper. A goose-quill pen in a cold hand. y equals one over x. Evangelista Torricelli traces you out. He spins you around the line... and you are born. A trumpet for an angel who never arrives. You are a solid thing. I can hold you in my hand. I can fill you up with paint, one finite cup. But I can never coat your skin. Your surface runs forever. A thirst that can be filled but never touched. He wrote to Bonaventura Cavalieri. A solid of such a nature. Finite magnitude, infinite surface. He didn't call it Painter's Paradox then. He just saw you, impossible, under the candlelight. A perfect container for a perfect emptiness. You are a solid thing. I can hold you in my hand. I can fill you up with paint, one finite cup. But I can never coat your skin. Your surface runs forever. A thirst that can be filled but never touched. Some parts of us are like this. A volume you can know completely. A surface that recedes the closer you get. A love you can contain... but never, ever cover. The skin of it goes on forever. The candle gutters. The ink is still frozen. But you are here now. Gabriel's Horn. Resting on the page. Complete and untouchable.