Pythagoræisk talmystik i Renæssancen

Jesper Munk Jensen

Pythagorærisk talmystik

• Alt er Tal

• Tetraktys 1+2+3+4=10

• Harmoniske proportioner

Okkult Matematik

• Gnosticisme Menneskets indre guddommelighed

• Numerologi Tals mystiske betydningBogstaver → Tal →

Tværsum

• Gematria Erstatning af ord med samme tværsum

• Kabbala Jødisk mystisk tradition

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

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

John Dee (1527-1608)

Ifølge Tycho Brahe en af Europas to bedste matematikereIfølge Tycho Brahe en af Europas to bedste matematikere

• MatematikerMatematiker• AstronomAstronom• AstrologAstrolog• GeografGeograf• OkkultistOkkultist• Konsulent for Dronning ElizabethKonsulent for Dronning Elizabeth

Mathematical Preface 1570

Forord til den første engelske udgaveaf Euklids elementer. Dee argumenterer for nødvendigheden og anvendeligheden af matematik og kæmper for at få mere matematik- undervisning indført.

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 creatureand a third in Spirituall and Angelicall Mindes and in the Soule of man

Dee, Mathematical Preface

SupernaturallApplication:

AscendingMagus

Mathesis

Thynges Mathematicall

No further application

Mathematician

Mathematics

NaturallApplication:

DescendingMechanican

Mechanique

Monas Hieroglyphica 1564

Possibly the most obscure work written by an english man.

Brian Vickers

Monas HieroglyphicaTHEOREM I:THEOREM I:It is by the straight line and the circle that the first It is by the straight line and the circle that the first and most simple example and representation of all and most simple example and representation of all things may be demonstrated, whether such things things may be demonstrated, whether such things be either non-existent or merely hidden under be either non-existent or merely hidden under Nature's veils. Nature's veils.

THEOREM II:THEOREM II:Neither the circle without the line, nor the line Neither the circle without the line, nor the line without the point, can be artificially produced. It is, without the point, can be artificially produced. It is, therefore, by virtue of the point and the Monad that therefore, by virtue of the point and the Monad that all things commence to emerge in principle. all things commence to emerge in principle.

That which is affected at the periphery, however That which is affected at the periphery, however large it may be, cannot in any way lack the support large it may be, cannot in any way lack the support of the central point.of the central point.

Monas Hieroglyphica

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

Korsets Hemmeligheder

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)

XL2 + X2 = 2500

X = 1: L: 10th letter, |LX|= 10 → 10·10 = 1002500/(100·52) = 1 (5 first circular number 52=25)

Herved finder man det signifikante (significant) tal 252 = 20+200+10+21+1samt proportionerne 1:10:100

Pantheus

VoarchadumiaOpskrift 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• 22 + 23 + 24 + 25 + 26 + 27 = 252

Flere hemmeligheder

L V X

I korset fandt vi 5, 10 og 50

LUX: Lys

Tetraktys revisited

Pythagoræisk

Mulige permutationer: 24 (4·3·2·1)Pythagoræisk sum = 10Sum af delene = 30

Kunstig

Kontinuert multiplikation = 12Simpel addition = 8 (1 7; 4 3)Sum af delene = 24 (som 24 karat guld)

Monas AfrundingI 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

Afrunding

• På grænsen til renæssancens videnskabelige revolution

• Blanding af mange forskellige påvirkninger

• Søger en forklaring på ”verden” gennem matematikken