Torus clock

Each body has two angles, its place in the zodiac and its place in the houses. Two angles make a torus, and this one lives on a sphere in four dimensions.

Drag to orbit. The bright ring is this instant.

Select a body to find it on both instruments.
Body	Longitude	House	Per day

Time

Run backwards

Go to

Fourth dimension

Turn 0°

Past 45° the torus opens through infinity and closes with zodiac and houses exchanged.

Place

Latitude Longitude east

The ascendant and houses depend on where you stand. Times are shown in your browser's time zone.

The torus

Coloured rings round the tube mark the signs and their decans, by element. Pale rings the long way round are house cusps; the outer equator is the eastern horizon, the inner one the western. Whatever rides the upper half is above the horizon.

The bright ring

House is longitude minus ascendant, so at any instant the whole sky lies on one diagonal of the torus. In four dimensions that diagonal is a great circle, a fibre of the Hopf fibration, so it always projects to a true circle. The Earth's turning sweeps it from fibre to fibre.

The dial

The zodiac is the circle at infinity of a hyperbolic plane, and aspects are its straight lines: red for squares and oppositions, blue for trines and sextiles. Drag to move your vantage point. The part of the zodiac you approach opens up, which pulls tight clusters apart.