Anhang: Nachrechenbare mathematische Tabellen und Ableitungen
Der mathematische Anhang versammelt Planetenperioden, Fuxi-Binärcodes, Dodekatemoria-Zuordnungen und den 78-Karten-Kombinatorikraum zur unabhängigen Nachrechnung.
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.
Anhang-Bibliografie I: Antike Astronomie und archäologische Quellen
Astronomische Referenzwerke und archäologische Quellensammlungen: Bretagnon & Francou (1988) VSOP87 Planetentheorien; Espenak & Meeus (2006) NASA Fünftausendjähriger Finsterniskanon (-1999 bis +3000); Hunger & Steele (2019) MUL.APIN: Astronomischer Text (ca. 1000 v. Chr.); Justeson & Lowry (2025) Maya-Dresdner-Kodex-Finsternistabelle (Science Advances 11(43), 69 Stationen über 1.655 Mondzyklen); Li et al. (2026) OBIMD-Datensatz für Orakelknochen-Inschriften (Scientific Data, 10.077 Abriebe); Neugebauer (1955, 1975) Astronomische Keilschrifttexte und Geschichte der antiken mathematischen Astronomie; Sivin (1969, 2009) Kosmos und Berechnung im alten China sowie Shoushi-Kalender; Steele (2000) Antike Finsternisbeobachtungen; Ptolemäus (1940) Tetrabiblos (Loeb Classical Library).
Anhang-Bibliografie II: Ostasiatische Divination, vorderasiatische Astrologie und Binärgeschichte
Vergleichende Modelle und Primärquellen: Cullen (2011) Wu xing zhan: Prognostiken der fünf Planeten aus Mawangdui (SCIAMVS 12: 193-249); Ho Peng-Yoke (2003) Chinese Mathematical Astrology (RoutledgeCurzon); Needham (1959) Science and Civilisation in China, Band 3; Pingree (1973) Mesopotamischer Ursprung früher indischer Astronomie; Sun & Kistemaker (1997) Der chinesische Himmel zur Han-Zeit; Klassische Dynastiegeschichten (Shiji, Hanshu, Yuanshi); Bouché-Leclercq (1899) L'astrologie grecque; Cauville (1997) Der Tierkreis von Dendera; Catalogus Codicum Astrologorum Graecorum (CCAG); Rochberg (2004, 2010) The Heavenly Writing & In the Path of the Moon; West (1880) Bundahischn; Leibniz (1703) Erklärung der binären Arithmetik; Ryan (1996) Leibniz' Binärsystem und Shao Yongs Yijing; Schumann (2021) Logische Vorhersagemuster in Mesopotamien.
Anhang-Bibliografie III: Tarot-Geschichte, statistische Prüfung und Präregistrierung
Historische Stichprobenmechanismen und statistische Methodik: Dummett (1980) The Game of Tarot (wissenschaftlicher Standardbeleg für norditalienische Hofursprünge des 15. Jahrhunderts); Dummett & McLeod (2004) A History of the Occult Tarot; Mathers (1888) Book T - The Tarot (Golden-Dawn-Manuskript zur astronomischen Zuordnung von 78 Karten); Bates et al. (2015) Lineare gemischte Modelle mit lme4; Cohen (1988) Statistische Power-Analyse für Verhaltenswissenschaften (gepaarter Versuchsplan: d=0,4, Alpha=0,05, Power=0,80); Knuth (1997) The Art of Computer Programming (Fisher-Yates-Shuffle); Rammstedt & John (2007) BFI-10 Persönlichkeitsinventar; Tobacyk (2004) Skala paranormaler Überzeugungen. Experimentelle Präregistrierung, CSPRNG-Audits und Chi-Quadrat-Homogenitätstests (df=77) sind transparent offengelegt.
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Häufige Fragen
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.
Quellen und weiterführende Literatur
Astronomische Positionen und Deutungsregeln dieser Seite sind gegen die folgenden Werke abgeglichen.
- Swiss Ephemeris (Astrodienst) (die Ephemeridenbibliothek hinter allen Kartenberechnungen)
- Swiss Ephemeris programmer's documentation (Rechenparameter und API-Referenz)
- Introduction to the Tetrabiblos (Skyscript)
- Hellenistic astrology (historische und technische Materialien zur hellenistischen Praxis)