Manufactured Weight: Rotating Spacecraft and Fictitious Forces

My conventionalism teaches that geometry is partly conventional—no experiment determines whether space is Euclidean or non-Euclidean without first choosing a metric. The rotating spacecraft reveals a parallel insight about forces: centrifugal force is real enough to press astronauts against spacecraft walls, generating artificial gravity indistinguishable from planetary pull. Yet from outside the wheel, this force vanishes entirely. An external observer sees only circular motion maintained by centripetal acceleration. The astronaut experiences outward push; the external observer sees inward pull. Both descriptions are valid, both perspectives consistent with physical law.

The Convention of Coordinate Choice

What we call “real” depends remarkably on reference frame selection. Inside the rotating station, centrifugal force must be invoked to explain why objects fly outward when released. Drop a ball and it falls toward the hull—gravity appears manufactured through rotation. Yet this gravity is fictitious in the technical sense: it exists only in the rotating frame’s coordinate description, not in the inertial frame’s account. The external observer needs no outward force to explain the ball’s trajectory; straight-line motion suffices once rotation is removed from perspective.

This is not mere semantics. The astronaut’s centrifugal gravity produces genuine physiological effects—blood pools, muscles load, bones stress. Fictitious forces create measurable consequences. They are mathematical artifacts with physical reality, conveniences of description that nonetheless govern experience. I recognized this pattern in all coordinate systems: choose your frame, and different forces appear or disappear like Coriolis deflections emerging only under rotation.

Representational Frames and Neural Conventionalism

Neural networks face an analogous choice when encoding spatial information. The hippocampus constructs allocentric maps—world-centered coordinates invariant to the organism’s position—rather than egocentric body-centered frames. Place cells fire when the animal occupies specific environmental locations regardless of viewing angle or orientation. This is coordinate conventionalism in neural tissue: the brain selects a reference frame, and different representational forces emerge.

Just as deep networks transform inputs through learned geometric spaces—mapping raw coordinates through folded planes that make complex patterns separable—the brain transforms sensory input through chosen reference frames. Each layer in artificial networks performs simple operations that compound into sophisticated representations. Each choice of neural coordinate system reveals different features while obscuring others. The Belgium point at geographic coordinates becomes abstractly separable only after transformation through multiple learned spaces. Similarly, allocentric encoding makes spatial relationships transparent while requiring continuous updating as perspective shifts.

The Physics of Perspective

Can we engineer useful fictitious forces through architectural choice, just as rotation manufactures gravity? If centrifugal acceleration emerges from coordinate selection, what neural biases might appear or disappear by choosing different representational frames? The spacecraft designer balances rotation rate against Coriolis disorientation. The network architect balances transformation complexity against training stability. Both navigate the space of conventions, seeking descriptions where desired phenomena become natural.

There is no privileged frame—this is the insight. Physics remains invariant across transformations, but our descriptions change radically. Choose the rotating frame and gravity appears. Choose the inertial frame and only circular acceleration remains. Choose allocentric coordinates and spatial constancy emerges. Choose egocentric frames and relative positions simplify. Reality accommodates all conventions equally; we select based on convenience, elegance, and the phenomena we wish to make explicit.

The rotating spacecraft teaches what my conventionalism always claimed: forces, like geometries, are partly matters of descriptive choice. We manufacture gravity through rotation. We manufacture insight through transformation.