Comprehensive Study Notes – 40 Terms & Concepts for Exam

Cosmological Models and Astronomy

Armillary sphere (screensaver in lecture)
- Physical model of the cosmos composed of nested rings.
- Medieval/Renaissance versions normally show the Ptolemaic system – $\text{Earth}$ fixed at the centre with all heavenly bodies revolving in perfect circles.
- Instructor stresses BOTH elements of the old model are wrong today:
- Centre is the Sun (Copernicus, 1543, De Revolutionibus).
- Orbits are elliptical (Kepler, $1519$ formulation → published 1609 in Astronomia Nova).
- Popular teaching instrument through the Renaissance; survives as a symbolic “screensaver.”

Key Egyptian Concepts & Deities

The Ennead (spelled "Aeneid" in lecture)
- Nine primeval creator-gods: Atum (Amon) and four male–female pairs: ${\text{Shu,Tefnut};\,\text{Geb,Nut};\,\text{Isis,Osiris};\,\text{Seth,Nepthys}}$ .
- Birth order forms a triangular/pyramidal hierarchy mirrored by the Pythagorean Tetractys (1+2+3+4 dots = 10 (\leftrightarrow) Horus as 10th god).
- Conceptualised as a series of coincidentia oppositorum – wet/dry, earth/sky, life/death.
Hermes Trismegistus (Thoth)
- “Thrice-Great Hermes”; Egyptian god of wisdom, inventor of hieroglyphs, recorder of the judgment of the soul.
- Renaissance scholars treated the Corpus Hermeticum as the primordial source of all philosophy.
- Root of the terms hermetic / hermeticism → “sealed, occult, hidden.”
Hermetic/Occult Principle
- Ultimate origins are inaccessible; Amon can be represented only via the solar disk (unseeable light).
- Physical analogues: sealed chambers in temples/palaces; undeciphered hieroglyphs before 1800.
Book of the Dead (funerary papyri & wall texts)
- Describes subterranean journey: weighing of the heart vs. feather of Ma’at.
- Anubis (jackal-headed) guides; Thoth records; Ammit (crocodile-hippo-lion) devours the wicked; Horus escorts the justified to Osiris.
- Iconography: Osiris enthroned, mummified; Isis & Nephthys behind; lotus holding the Four Sons of Horus (canopic jars: liver, lungs, stomach, intestines).
Hieroglyphs
- Simultaneously pictographic and alphabetic → yields a dense, multivalent language.
- Deciphered by J-F Champollion from the Rosetta Stone (3 scripts: Greek, Demotic, Hieroglyphic) after Napoleon’s 1800 invasion.

Numerical & Geometric Systems

Pythagorean Tetractys $\begin{matrix} & & \bullet & & \ & \bullet & & \bullet & \ \bullet & & \bullet & & \bullet \end{matrix}$
- Ten points in rows 1–4.
- Ratios embedded: $2:1$ (octave), $3:2$ (fifth), $4:3$ (fourth).
- Links mathematics → musical harmony → architectural proportion → cosmic order (pyramids, Renaissance plans).
Fibonacci Series $1,1,2,3,5,8,13,21,34,\dots$
- Each term = sum of two previous; ratio of successive terms → $1.618\ldots$ (golden ratio $\varphi$ ).
- Observed by Leonardo Fibonacci in plant phyllotaxis; retroactively ascribed to Egyptian practice.
- Golden ratio pervades Egyptian → Greek → Roman → Medieval → Renaissance → bioconstructivist design (natura naturans).
Platonic/Atomic Solids (Timaeus)
- Earth $\to$ cube; Fire $\to$ tetrahedron; Air $\to$ octahedron; Water $\to$ icosahedron; all inscribable in a sphere.
Grosseteste’s Geometry of Creation
- Two lights: lux spiritualis (uncreated) → lumen (physical).
- Matter precipitates via geometrical figures: straight, curved, refracted rays; cones; vault-like surfaces.

Mythic Narratives Inspiring Architecture

Cretan Cycle
- King Minos (son of Zeus & Europa) builds palace & labyrinth via Daedalus.
- Pasiphaë + Poseidon’s bull → Minotaur; labyrinth represents womb/tomb/passages beneath bull horns (labrys = double-axe).
- Theseus slays beast through Ariadne’s thread (root of “arachnid”; weaving parallels architectural making).
- Daedalus: archetypal architect; wooden cow, wax wings (Icarus), Sicilian works.
- Labyrinth = metaphor for eternal return, cyclical time, coincidence of opposites.

Architectural Archetypes & Tropes

Trope (Greek “twist”)
- Rhetorical figure; 14 types per Aristotle. Key four: metaphor, metonymy, synecdoche, irony.
- Buildings themselves can be rhetorical signs (Vitruvius’ signum/significatum).
Catechism (re-defined)
- Any three-dimensional model of knowledge; pre-printing buildings = principal “books” of culture (pyramids, Gothic portals, string-theory diagrams).
- Related terms: edify/edifice/edificium – to build & to instruct.
Hypostyle Hall (Egyptian temple type)
- Forest of columns; high centre lit by clerestory → blooming papyrus capitals; dark aisles → bud capitals.
- Pylons flank entry (Isis & Nephthys). Floor rises/ceiling drops toward sanctuary → metaphor for spiritual intensification.
- Morphs into Roman basilica → Christian basilica archetype.
Tabularium Motif (Roman)
- Structural Etruscan arch + ornamental Greek column.
- First seen on the Tabularium (state archive) at Forum’s west end; propagated to basilicas, Colosseum, Theatre of Marcellus, Bramante’s Vatican Cortile, US Capitol, etc.
Vitruvian Canon
- Vitruvian Man (circle = divinity, square = earth; man mediates).
- Triad: $\text{Firmitas}$ (firmness/structure), $\text{Utilitas}$ (function), $\text{Venustas}$ (beauty/delight). English: firmness, commodity, delight.
- Lecturer adds fourth necessity: conveyance of metaphysical idea (architecture as art, not mere engineering).

Classical Philosophical Foundations

Plato
- Timaeus: first written cosmology; Demiurge shapes four elements via mathematical ratios (Pythagorean, golden mean).
- Republic: politics; distrust of democracy & artists; allegory of the cave → perceptible realm as shadows; true forms (archetypes) apprehended by nous.
- Symposium: “ladder” of love; ascent from bodily lust → Platonic love (Marcello Ficino coinage); progressing from particular → universal through noesis (non-sensory intellect).
Aristotle (contrast)
- Empiricism; knowledge through sense-data only; far less architectural influence historically.

Medieval Scholastic Synthesis

Scholasticism
- Intellectual method (≈ 1100-1350 CE); writing form = Summa (comprehensive synthesis).
- Goal: reconcile Christian theology with Greco-Roman philosophy (“great synthesis”).
- Leading figures: Thomas Aquinas (Summa Theologica); Albertus Magnus; Robert Grosseteste (earlier English precursor).
Seven Liberal Arts
- Trivium (higher, noetic): Grammar, Rhetoric, Logic → align with $\text{virtus intellectiva}$ .
- Quadrivium (lower, discursive): Arithmetic, Geometry, Music, Astronomy.
- Cathedrals embody these arts physically; Erwin Panofsky: Gothic Architecture & Scholasticism.
Robert Grosseteste (c. 1175–1253)
- First Chancellor of Oxford University; Bishop of Lincoln.
- Cosmologies: De Luce (On Light) & De Lineis Angulis Figuris (geometry of matter).
- Postulated Big-Bang-like expansion: lux → lumen → matter.
- Translated Aristotle; commented on Pseudo-Dionysius; “father of natural philosophy.”
- Influenced unprecedented geometries in Lincoln Cathedral.

Gothic Architectural Innovations (England-centred)

Structural Vocabulary
- Springer Pole: vertical shaft carrying ribs from arcade through triforium/clerestory.
- Rib Types:
- Main transverse/diagonal ribs (structural).
- Tierceron (“third-order”): springs from springer but stops short of crossing vault.
- Lierne (“binder”): non-springing short rib joining other ribs (purely decorative/“handwriting”).
- Handwriting Concept: ornamental geometry without structural role (Pevsner) or cosmological coding (lecturer).
Crazy Vault (Saint Hugh’s Choir, Lincoln)
- Master Mason: Geoffrey de Noyer (assistant of William of Sens).
- Asymmetrical, first-ever ridge rib, first tiercerons; three lancets per bay; “scissor” pattern with bosses masking junctions.
- Read as catechism of Grosseteste’s light geometry.
Later English Developments
- Net vault (Wells), pendant vault (Divinity School, Oxford), fan vault (Gloucester by Thomas of Cambridge), elaborate lierne patterns (St Mary Redcliffe) – all evolutions of Lincoln’s experimental ribs.

Metaphysical & Epistemological Terms

Coincidentia Oppositorum
- Unity of contraries; surfaces in Ennead, labyrinth, day/night dichotomy, language with dual meanings (Latin altus = high/low; sacer = sacred/profane). Freud studied this phenomenon.
Chthonic vs Olympian Religion
- Chthonic: earth-bound forces, snakes/owls, mounds, tree-wrappings; pre-temple shrines in Crete.
- Olympian: anthropomorphic gods dwelling aloft; Plato’s preferred “rational” worship.
Noûs Poietikos / Virtus Intellectiva
- Higher, non-sensory intellect enabling grasp of intelligible forms (eidê) and metaphysical ideas.
Specios Apprehensibilis (eidos) vs Specios Sensibilis (morphê/hylê)
- Perception requires mental pre-construction (a priori intuition; Kant). Mind’s eye (oculus mentis) illuminated by lux spiritualis.
Natura Naturans vs Natura Naturata (Plotinus)
- Creating nature (dynamic generative principles) vs created nature (finished forms). True art imitates the former – e.g., using golden ratio rather than copying leaves.

Historical Shifts in Media of Knowledge

Architecture as primary text → Era of the Book (post-printing, $\text{c. 1540}$ ) → Era of the Internet (present).
Implication: architects must now rely on syntax/space rather than literal iconography to carry metaphysical content; ethical duty remains to foster intellectual ascent.

Summary of Key Numerical Ratios & Formulae Mentioned

Pythagorean Harmonics: $2:1\;(\text{octave}),\;3:2\;(\text{fifth}),\;4:3\;(\text{fourth})$ .
Golden Ratio: $\varphi \approx 1.618 \approx \frac{F{n+1}}{Fn}$ .
Fibonacci Recurrence: $F{n}=F{n-1}+F{n-2},\;F1=1,\,F_2=1$ .

Practical Exam Guidance (from Instructor)

40 terms supplied; 20 will appear on exam.
Required response: five-part definition + four-minute essay in paragraphs, complete sentences.
Overlap among terms encouraged; external sources acceptable but verify lecturer’s intended meaning (e.g., “catechism”).
Use lecture, review material, and these notes for examples, metaphors, numeric data, philosophical links, and real-world relevance.