Plate IV
The Boundary of the Sayable
You cannot count to Infinity. It is seen all at once.
Engraved interactive hyperbolic plane
Drag the plate, or focus it and use the arrow keys, to travel across the hyperbolic plane toward the boundary. Tab to the caption term to read its definition in the lectern; Escape clears it.
Fig. IV - the hyperbolic plane: every step toward the boundary halves; the rim is at infinite distance. .
Design note: the disk is drawn because the form says the concept — in hyperbolic geometry the boundary circle is infinitely far from every interior point, so discourse may travel forever toward the boundary it intuits without ever reaching it. The rim and the band before it are untouched ground.