Where does syzygy collide?

A nearly straight-line arrangement of three or more celestial bodies, most often the Sun, Earth, and Moon, which produces events such as eclipses and the new and full phases of the Moon. Greek astronomers named this configuration, and it is set out in Ptolemy's Almagest (composed around 150 CE) as the moment when the Sun and Moon share the same or opposite position along the sky. Meeus's 1998 Astronomical Algorithms gives the modern methods for computing the exact times of these alignments. Here the word names a geometric line-up of bodies in space, not a dependency among algebraic quantities or a pairing of opposites in the mind.[1][2]

Unit

One line-up of three or more bodies falling on a near-straight line, dated to a moment in time

Recovery means

Not applicable

Measured by

Computed from orbital positions as the times when two bodies share the same or opposite ecliptic longitude

A relation among the generators of an algebraic object: a combination of them, with polynomial coefficients, that sums to zero and so records a dependency among them. James Joseph Sylvester introduced the word into mathematics in the early 1850s, using it in his 1853 study On a theory of the syzygetic relations of two rational integral functions. David Hilbert's 1890 Ueber die Theorie der algebraischen Formen gave it its modern form through the syzygy theorem, which bounds how far the chain of relations, and relations among those relations, can run. In this meaning the word names an algebraic dependency, not a line-up of bodies in space or a pairing of opposites in the mind.[3][4]

Unit

One polynomial relation among generators that sums to zero

Recovery means

Not applicable

Measured by

Found by computing the kernel of the map from free generators onto a module, for example with a Groebner basis

A pairing of opposites, in particular the union of the anima (a man's inner feminine image) and the animus (a woman's inner masculine image) as complementary figures of the unconscious. Carl Jung set out this meaning in the chapter 'The Syzygy: Anima and Animus' in his 1951 Aion, taking the word from Gnostic writing, where paired emanations were themselves called syzygies. For Jung the pairing is an archetype of wholeness that joins masculine and feminine elements of the psyche. Here the word names a coupling of psychic opposites, not an alignment of bodies in space or a dependency among algebraic quantities.[5]

Unit

One archetypal pairing of complementary opposites in the psyche

Recovery means

Not applicable

Measured by

Approached qualitatively through the analysis of dreams, myths, and projections rather than by numeric scoring