Apéndice: Tablas matemáticas recalculables y derivaciones
El apéndice matemático compila los períodos planetarios, códigos binarios de Fuxi, decanatos del tarot y el espacio combinatorio de 78 cartas para su verificación matemática.
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.
Bibliografía del apéndice I: Astronomía antigua y fuentes arqueológicas
Cálculos astronómicos de referencia y corpus arqueológicos: Bretagnon & Francou (1988) Teorías planetarias VSOP87; Espenak & Meeus (2006) Canon NASA de eclipses de cinco milenios (-1999 a +3000); Hunger & Steele (2019) MUL.APIN: Tratado astronómico babilonio (c. 1000 a. C.); Justeson & Lowry (2025) Tabla de eclipses del Códice de Dresde maya (Science Advances 11(43), 69 estaciones en ciclo de 1.655 lunaciones); Li et al. (2026) Corpus OBIMD de inscripciones oraculares en hueso (Scientific Data, 10.077 calcos); Neugebauer (1955, 1975) Textos cuneiformes astronómicos e Historia de la astronomía matemática antigua; Sivin (1969, 2009) Cosmos y cálculo en la astronomía china y calendario Shoushi; Steele (2000) Observaciones de eclipses; Ptolomeo (1940) Tetrabiblos (Loeb).
Bibliografía del apéndice II: Adivinación china, astrología del Próximo Oriente e historia binaria
Modelos comparativos y fuentes primarias: Cullen (2011) Wu xing zhan: pronósticos de los cinco planetas 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) Origen mesopotámico de la astronomía india; Sun & Kistemaker (1997) El cielo chino durante los Han; Historias dinásticas oficiales (Shiji, Hanshu, Yuanshi); Bouché-Leclercq (1899) L'astrologie grecque; Cauville (1997) El zodiaco de Dendera; Catalogus Codicum Astrologorum Graecorum (CCAG); Rochberg (2004, 2010) The Heavenly Writing & In the Path of the Moon; West (1880) Textos pahlavis: Bundahishn; Leibniz (1703) Explicación de la aritmética binaria; Ryan (1996) Sistema binario de Leibniz y el I Ching de Shao Yong; Schumann (2021) Razonamiento lógico en la adivinación mesopotámica.
Bibliografía del apéndice III: Historia del tarot, contraste estadístico y protocolo de preinscripción
Mecanismos de muestreo e investigación estadística empírica: Dummett (1980) The Game of Tarot (análisis canónico que documenta el origen cortesano en el norte de Italia en el siglo XV); Dummett & McLeod (2004) A History of the Occult Tarot; Mathers (1888) Book T - The Tarot (manuscrito de la Golden Dawn que proyecta 78 cartas en coordenadas astrológicas); Bates et al. (2015) Modelos lineales de efectos mixtos con lme4; Cohen (1988) Análisis de potencia estadística en ciencias del comportamiento (diseño emparejado: d=0.4, alfa=0.05, potencia=0.80); Knuth (1997) The Art of Computer Programming (algoritmo Fisher-Yates); Rammstedt & John (2007) Inventario BFI-10; Tobacyk (2004) Escala revisada de creencias paranormales. Preinscripción de ensayos emparejados y prueba de chi-cuadrado (gl=77).
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Consultas comunes
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.
Fuentes y lecturas complementarias
Las posiciones astronómicas y las reglas de interpretación de esta página se contrastan con las obras siguientes.
- Swiss Ephemeris (Astrodienst) (la biblioteca de efemérides que usamos en todos los cálculos)
- Swiss Ephemeris programmer's documentation (parámetros de cálculo y referencia de la API)
- Introduction to the Tetrabiblos (Skyscript)
- Hellenistic astrology (recursos históricos y técnicos sobre la práctica helenística)