Annexe : Tables mathématiques recalculables et dérivations
L'annexe mathématique rassemble les périodes planétaires, les codes binaires de Fuxi, les décans du tarot et l'espace combinatoire des 78 cartes pour vérification ouverte.
Introduction to Recomputable Tables and Mathematical Auditability
Scientific research demands transparency, auditability, and independent recomputability. This appendix brings together the foundational constants, algebraic permutation matrices, combinatorial probability figures, and algorithmic lookup tables referenced throughout the monograph. Every table includes clear derivation methods and citations, ensuring third-party researchers can replicate all calculations.
Table A-1: Five Planets: Periods and Classical Chinese Correspondences
Constants determined from NASA Planetary Fact Sheets: Mercury (Chenxing / Water) sidereal period 88 days, synodic period 116 days; Venus (Taibai / Metal) sidereal 225 days, synodic 584 days; Mars (Yinghuo / Fire) sidereal 687 days, synodic 780 days; Jupiter (Suixing / Wood) sidereal 11.86 years, synodic 399 days; Saturn (Zhenxing / Earth) sidereal 29.46 years, synodic 378 days. Sidereal periods lock chronological cycles, while synodic periods pace observational omen windows.
Table A-2: Bagua Three-Bit Binary Values (Fuxi Order)
Following the Bouvet-Leibniz binary interpretation (yang = 1, yin = 0, read top-down): Qian 111 corresponds to decimal 7, Dui 110 to 6, Li 101 to 5, Zhen 100 to 4, Xun 011 to 3, Kan 010 to 2, Gen 001 to 1, and Kun 000 to 0. Shao Yong's circular and square arrangements illustrate ascending and descending binary progressions, proving 64 hexagrams exhaust the 6-bit state space.
Table A-3 and A-3b/c: Book T Tarot Correspondences and Thirty-Six Decans
Sourced from the 1888 Hermetic Order of the Golden Dawn Book T manuscripts: 0 Fool corresponds to Aether/Air, 1 Magician to Mercury, 2 High Priestess to Moon, 3 Empress to Venus, 4 Emperor to Aries, through 21 World to Saturn. Egyptian thirty-six decans divide the zodiac into 10-degree intervals, providing a recursive 3x12 subdivision identical to astronomical timekeeping practices across Persia and Hellenistic Greece.
Table A-4a/b/c: Tarot 78-Card Combinatorial State Spaces and Permutations
Across 78 cards with independent upright/reversed orientations: 1-card draw yields 156 states; 3-card spread yields 456,456 permutations (3,651,648 with orientations); 5-card spread yields 2,533,330,800 permutations (8.10x10¹⁰ with orientations); 10-card Celtic Cross spans 4.67x10²¹ states. Popular literature erroneously applying combinations underestimates spread complexity by 3,628,800-fold (10!). Exact probabilities: 3-card contains major arcana: 63.56%; 5-card: 81.91%; 10-card: 97.17%.
Figure A-1: Liuren Cosmic Board Information Flow and Modular Lookup
The ancient Chinese Liuren cosmic board maps celestial mechanics through rotating heaven and earth plates. The derivation executes modular arithmetic: solar month plus hour establishes the heaven plate; Four Lessons identify elemental relationships; Three Transmissions extract initial, middle, and final pivots. The algorithm functions as a deterministic finite state machine with zero random sources.
Figure A-2: Sexagenary Sixty-Cycle Congruence Generation Rule
Ten heavenly stems (mod 10) and twelve earthly branches (mod 12) pair via i ↦ (i mod 10, i mod 12). Because gcd(10, 12) = 2 and lcm(10, 12) = 60, the pairs remain distinct across steps 0 through 59, closing precisely at step 60. This simple algebraic rule demonstrates the mathematical inevitability of the sixty-year calendrical cycle without arbitrary empirical intervention.
Bibliographie de l'appendice I : Astronomie antique et sources archéologiques
Calculs astronomiques fondamentaux et éditions de sources archéologiques : Bretagnon & Francou (1988) Théories planétaires VSOP87 ; Espenak & Meeus (2006) Canon NASA des éclipses sur cinq millénaires (-1999 à +3000) ; Hunger & Steele (2019) Traité astronomique babylonien MUL.APIN (vers 1000 av. J.-C.) ; Justeson & Lowry (2025) Table des éclipses du Codex de Dresde maya (Science Advances 11(43), 69 stations sur 1 655 lunaisons) ; Li et al. (2026) Corpus OBIMD d'inscriptions sur os oraculaires (Scientific Data, 10 077 estampages) ; Neugebauer (1955, 1975) Textes cunéiformes astronomiques et Histoire de l'astronomie mathématique antique ; Sivin (1969, 2009) Calculs astronomiques dans la Chine ancienne et réforme du calendrier Shoushi ; Steele (2000) Prédiction des éclipses ; Ptolémée (1940) Tétrabiblos (Loeb).
Bibliographie de l'appendice II : Divination chinoise, astrologie proche-orientale et histoire binaire
Modèles comparés et éditions textuelles : Cullen (2011) Wu xing zhan : prognostics des cinq planètes de Mawangdui (SCIAMVS 12: 193-249) ; Ho Peng-Yoke (2003) Chinese Mathematical Astrology (RoutledgeCurzon) ; Needham (1959) Science and Civilisation in China, vol. 3 ; Pingree (1973) Origine mésopotamienne de l'astronomie indienne ; Sun & Kistemaker (1997) Le ciel chinois sous les Han ; Textes dynastiques officiels (Shiji, Hanshu, Yuanshi) ; Bouché-Leclercq (1899) L'astrologie grecque ; Cauville (1997) Le zodiaque d'Osiris ; Catalogus Codicum Astrologorum Graecorum (CCAG) ; Rochberg (2004, 2010) The Heavenly Writing & In the Path of the Moon ; West (1880) Textes pehlevis : Bundahishn ; Leibniz (1703) Explication de l'arithmétique binaire ; Ryan (1996) Le système binaire de Leibniz et le Yijing de Shao Yong ; Schumann (2021) Logique booléenne divinatoire en Mésopotamie.
Bibliographie de l'appendice III : Histoire du tarot, validation statistique et protocole d'enregistrement
Histoire des mécanismes d'échantillonnage et méthodologie statistique : Dummett (1980) The Game of Tarot (référence académique attestant l'origine princière en Italie du Nord au XVe siècle) ; Dummett & McLeod (2004) A History of the Occult Tarot ; Mathers (1888) Book T - The Tarot (manuscrit du Golden Dawn ancrant 78 cartes dans les coordonnées célestes) ; Bates et al. (2015) Modèles linéaires à effets mixtes avec lme4 ; Cohen (1988) Puissance statistique en sciences du comportement (dispositif apparié : d=0,4, alpha=0,05, puissance=0,80) ; Knuth (1997) Algorithmes semi-numériques (mélange de Fisher-Yates) ; Rammstedt & John (2007) Échelle BFI-10 ; Tobacyk (2004) Échelle révisée des croyances paranormales. Préenregistrement de l'expérience appariée et test du chi-carré (ddl=77).
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Questions courantes
Why must positional tarot spreads use permutations (P) instead of combinations (C)?
Because spread positions (such as past, present, future) possess distinct contextual definitions. Drawing the exact same cards in a different sequence produces an entirely different interpretive outcome, making order decisive.
Why does the sixty-year sexagenary cycle terminate at 60 steps rather than 120?
Because 10 and 12 share a greatest common divisor of 2. By the Chinese Remainder Theorem and elementary number theory, their least common multiple lcm(10, 12) equals 60, after which the modular sequences necessarily repeat.
How does the Liuren cosmic board connect to modern computing concepts?
The Liuren system is a geometric finite state machine. Plate rotations correspond to modular 12 addition, and extracting transmissions corresponds to strict conditional branching and matrix lookup, without supernatural randomness.
Sources et lectures complémentaires
Les positions astronomiques et les règles d'interprétation de cette page sont vérifiées sur les ouvrages ci-dessous.
- Swiss Ephemeris (Astrodienst) (la bibliothèque d'éphémérides utilisée pour tous les calculs)
- Swiss Ephemeris programmer's documentation (paramètres de calcul et référence d'API)
- Introduction to the Tetrabiblos (Skyscript)
- Hellenistic astrology (ressources historiques et techniques sur la pratique hellénistique)