Time & Measurement

The Torquetum as an Inter-Frame Transformation Engine

Period and origin

Medieval Europe and the Islamic world, thirteenth century onward

What it was built to do

To measure or represent a celestial direction in one reference frame and read it in another, composing the local horizon, the celestial equator and the ecliptic in a single articulated instrument.

How the mechanism works

Nested, mutually inclined plates stand for the three principal planes of positional astronomy. Sights, graduated arcs and rotating rules hold a direction fixed while its coordinate representation changes. Latitude, obliquity and local sidereal angle enter as frame-orientation parameters.

Input

A celestial direction, either sighted or set, plus the observer’s latitude and the local sidereal orientation.

Transformation

Composition of rotations between horizon, equatorial and ecliptic frames, performed by the physical articulation of the plates.

Output

The same direction expressed in the requested frame, read from the graduated arcs.

What is evidenced

Deduction: mathematically forced, or nearly forced, by the evidence.

What it demonstrates

That changing the description of something and changing the thing itself are different operations - the instrument exists to keep a direction invariant while everything said about it changes.

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