Pythagoræisk talmystik i Renæssancen Jesper Munk Jensen.

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1 Pythagoræisk talmystik i Renæssancen Jesper Munk Jensen

2 Pythagorærisk talmystik Alt er Tal Tetraktys 1+2+3+4=10 Harmoniske proportioner

3 Okkult Matematik Gnosticisme Menneskets indre guddommelighed Numerologi Tals mystiske betydning Bogstaver → Tal → Tværsum GematriaErstatning af ord med samme tværsum KabbalaJødisk mystisk tradition

4 Grosseteste (1168 – 1253) For Grosseteste, God was light. Understanding light meant understanding God. And since light followed the rules of Euclid, the way to light and to God was through geometry. John H. Lienhard - Biskop i Lincoln, England - Teologisk matematik

5 Agrippa (1486-1535) The Doctrines of Mathematicks are so necessary to, and have such an affinity with Magick, that they that do profess it without them, are quite out of the way, and labour in vain, and shall in no wise obtain their desired effect. Agrippa, de occulta philosophia - Tysk magiker, astrolog og alkymist - Del af en opblomstring af de hermetiske videnskaber i Europa efter genopdagelse af græske/ægyptiske skrifter - Okkult matematik

6 John Dee (1527-1608) Ifølge Tycho Brahe en af Europas to bedste matematikere Matematiker Matematiker Astronom Astronom Astrolog Astrolog Geograf Geograf Okkultist Okkultist Konsulent for Dronning Elizabeth Konsulent for Dronning Elizabeth

7 Mathematical Preface 1570 Forord til den første engelske udgave af Euklids elementer. Dee argumenterer for nødvendigheden og anvendeligheden af matematik og kæmper for at få mere matematik- undervisning indført.

8 Mathematical Preface All thinges are deemed either Supernaturall, Naturall or of a third being, … which by a peculiar name are called Thynges Mathematicall. Dee, Mathematical Preface (Three kinds of numbers): One in the creator, another in every creature and a third in Spirituall and Angelicall Mindes and in the Soule of man Dee, Mathematical Preface

9 Supernaturall Application: Ascending Magus Mathesis Thynges Mathematicall No further application Mathematician Mathematics Naturall Application: Descending Mechanican Mechanique

10 Monas Hieroglyphica 1564 Possibly the most obscure work written by an english man. Brian Vickers

11 Monas Hieroglyphica THEOREM I: It is by the straight line and the circle that the first and most simple example and representation of all things may be demonstrated, whether such things be either non-existent or merely hidden under Nature's veils. THEOREM II: Neither the circle without the line, nor the line without the point, can be artificially produced. It is, therefore, by virtue of the point and the Monad that all things commence to emerge in principle. That which is affected at the periphery, however large it may be, cannot in any way lack the support of the central point.

12 Monas Hieroglyphica THEOREM X: The Sun and the Moon of this Monad desire that the Elements in which the tenth proportion will flower, shall be separated, and this is done by the application of Fire.

13 Korsets Hemmeligheder

14 V + V + V + V = 5 + 5 + 5 + 5 = 20 L + L + L + L = 50 + 50 + 50 + 50 = 200 X X = 10 X X = 21 ( 21th letter) X L 2 + X 2 = 2500 X = 1: L: 10th letter, |LX|= 10 → 10·10 = 100 2500/(100·5 2 ) = 1 (5 first circular number 5 2 =25) Herved finder man det signifikante (significant) tal 252 = 20+200+10+21+1 samt proportionerne 1:10:100

15 Pantheus Voarchadumia Opskrift på de vises sten: 4 stadier a 24 timer inden for 36 dage 7 iterationer 7· 36 dage = 252 dage Dee: Significant number 252 Hver iteration øger kraften/renheden med en faktor 10. Dee: 1:10:100 2 2 + 2 3 + 2 4 + 2 5 + 2 6 + 2 7 = 252

16 Flere hemmeligheder L V X I korset fandt vi 5, 10 og 50 LUX: Lys

17 Tetraktys revisited Pythagoræisk Mulige permutationer: 24 (4·3·2·1) Pythagoræisk sum = 10 Sum af delene = 30 Kunstig Kontinuert multiplikation = 12 Simpel addition = 8 (1 7; 4 3) Sum af delene = 24 (som 24 karat guld)

18 Monas Afrunding I know that many other powerful numbers may be produced out of our Quaternary, by virtue of arithmetic and the power of numbers. Yet he who does not understand that a very great obscurity has by this method been illuminated by those numbers which I have drawn out which have nature and distinction amongst such a multitude, will not be able to estimate their meaning, which is obscure and not to the point. Dee Monas Hierglyphica

19 Afrunding På grænsen til renæssancens videnskabelige revolution Blanding af mange forskellige påvirkninger Søger en forklaring på ”verden” gennem matematikken