group theory is the study of
symmetry, where a group is a set of elements combined with an operation that satisfies certain rules
let's play with the idea of applying
high-level concepts from group theory to astronomical configurations, as a lens for exploring patterns within
chart(s)
a basic framework
1️⃣ elements in the group are the luminaries, planets, asteroids, lots, etc. (which are themselves divided into
subgroups)
2️⃣ operations in the group are the
aspects: the angular relationships
between two elements, corresponding to
symmetries on the circle
(a conjunction is 0°; an opposition is 180° — a reflection or C₂; quintile is 72°; a trine is 120° — a rotation
symmetry of a triangle or C₃)
3️⃣ there are 12 constellations, each with 30 degrees of arc (also called "houses") — where each degree has a
different significance (e.g., 0° is very different from
29°)
4️⃣ the four qualities and the
three modalities create distinct
(sub)groupings and symmetries
property I: closure ➡️ if you combine any two elements in the group, the result is still an element within that
same group
if you merge the
archetypes associated with two
constellations, the result remains interpretable within the archetypal framework
if you apply an aspect (a group
operation) between two objects, the result is still an aspect within the system
property II: associativity ➡️ (a⋅b)⋅c = a⋅(b⋅c)
consider a complex planetary configuration, say a
t-square with three objects
the overall astrological interpretation of that t-square's influence remains consistent, regardless of the order
in which the objects are considered
property III: identity ➡️ there is an element that leaves other elements unchanged when applied through the group
operation
for example, consider a simple rotation group: scorpio (8) + 5 → aries (1), because 8 + 5 = 13 ≡ 1 mod 12
this operation: is closed (always lands on another constellation), has an identity (rotates by 0), has an inverse
(rotates backward), and is associative (the order of rotating doesn't matter)
another example of identity in relation to modalities or qualities can be extrapolated from the
constellation in which an object is
exalted or in its domicile, as
this may be seen as representing its identity state
property IV: inverse ➡️ every element has an inverse that, when combined through the group operation, produces the
identity
following the same logic, the constellation where an object is in detriment can be seen as the inverse of its
exalted state
to be continued...
meanwhile... can you guess the
prompts and the
styles
for this fellow gemini's birthday celebration?
