THE CATHARTURGY CORPUS
The Projection of Gravity
The dimensional graph of a fall — the velocity axis added
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The first Earth — stationary at the origin; its worldline the time axis The first object — the curved worldline of the fall, on the plane The second Earth — traveling directly up the z axis The second object — the linear diagonal, meeting the second Earth at (0, 0, 140) The change of velocity — graphed linearly against time on the z axis wall The straight chord — the same fall at constant velocity, for contrast

The Flat Graph

The first act is unchanged: in the [x, −y] plane the Earth is stationary at the origin, its worldline the time axis itself, and the object is released at (1000 m, −14.29 s), traveling in the positive y direction while its distance closes under g = 9.8 m/s², its curved worldline arriving exactly at the origin. The meeting of object and Earth is the origin of the graph.

The Velocity Axis

A z axis is then raised at (0, 0, 0), and upon it the change of velocity is graphed linearly: v = g·t, a straight line against time on the wall of the axis, running from zero at release to exactly 140 m/s at impact — for √(2·9.8·1000) = 140 precisely. The curvature of the flat worldline and the straightness of the velocity line are the same fall, read on different axes.

The Second Pair

A second Earth and a second object travel the straightened worldlines of the higher dimension, on the same clock as the fall itself — the two accounts of the one event unfold simultaneously. The second Earth rises directly up the z axis, and because the change of velocity is linear, its height at every moment is exactly the fall’s current velocity. The second object travels the single linear diagonal from the release point to (0, 0, 140 m/s), and the two meet there exactly, at the very instant the first pair meets at the origin — at the impact position, at the impact moment, at the height of the final velocity. Below them the first pair still traces the curved account of the same event: on this view, the bent worldline of the plane and the straight convergence above it are one fall, and the curvature belongs to the projection rather than to the higher figure. The companion piece, The Spiral of the Year, shows the same principle at the scale of orbit.