The Myth of Invariance: The Origin of the Gods, Mathematics, and Music from the Ṛg Veda to Plato

244 Pages·1978·4.97 MB·English

by  Ernest G. McClain

oa Ernest G. McClain

THE MYTH OF
INVARIANCE

THE MYTH OF INVARIANCE

ERNEST G. McCLAIN
THE MYTH OF INVARIANCE
The Origin of the Gods, Mathematics and
Music from the Rg Veda to Plato
Introduction by Siegmund Levarie
Edited by Patrick A. Heelan
SHAMBHALA
Boulder & London 1978
Shambhala Publications Inc.
1123 Spruce Street
Boulder, Colorado 80302
© 1976 by Nicolas Hays Ltd.
ISBN 0-87773-118-7
LCC 77-90879
Distributed in the United States by Random House
and in Canada by Random House of Canada Ltd.
Distributed in the Commonwealth by Routledge
and Kegan Paul Ltd., London and Henley-on-Thames.
Printed in the United States of America.
This Child is Augusta’s
Let us with tuneful skill proclaim these
generations of the Gods,
That one may see them when these hymns
are chanted in a future age.
(Rgveda 10.72.1)
‘It was clear to me for a long time that
the origins of science had their deep roots
in a particular myth, that of invarzance.”’
(Giorgio de Santillana, Preface to HAMLET’S MILL)

CONTENTS

Acknowledgments
Introduction by Siegmund Levarie
Charts and Tables
Glossary of Terms
1. Introduction: the problem; de Nicolas’ challenge; a
musical hypothesis; procedure
Tone Mandala and Sun’s Chariot: the Hindu-Greek
diatonic scale
Musical Generation: God and Mother; Fathers and
Sons; Indra and the Asvin Pair; Indra as Dancer and
Lord of the Five Tribes
The Tonal Calendar: 360 “‘like pegs”; Vision in Long 33
Darkness
Algebraic Yantras: star hexagon and drum of Siva; the 43
holy mountain; origins of geometry
Expansion of the Tone-Number Field: the Brhaspati 6]
and Prajapati cycles of 3,600 and 216,000 years
Cosmic Cycles: the four Yugas; Kalpa and Brahma 72
cycles; the birth of Agni, incarnate savior; the chariot of
the gods; the duration of the universe
Music and the Calendar: arithmetic and geometric 95
coincidences; Ptolemy’s tonal zodiac
The Book of Revelation: the meeting of East and West; 107
New Jerusalem; the Choir of 144,000; the Holy City as
12,000?; the Divine Mother; conclusions; postscript on
Genesis
vi
CONTENTS
10. Babylon and Sumer: the Pythagorean achievement of 129
ancient Semitic cultures; sexagesimal arithmetic; God on
the Mountain; Babylonian and Hebrew floods; Old
Testament arithmology; Mayan cosmology; Mt. Meru
11. Lost Atlantis: Plato’s musical cities; Gilbert Ryle’s 161
hypothesis; the Muses’ Jest; the Plain of Atlantis; the
Islands of Atlantis; Callipolis and Ancient Athens;
Egyptian derivation; Egyptian music, Egyptian
mathematics; The Book of the Dead; the Underworld;
Khepura
12. Conclusions: the myth of invariance; a mathematical
perspective; codetta 195
Appendices
1 Conversion Tables 203
II Multiplication Tables for Numbers 5०5१ 205
III Simplified Acoustical Theory for Fretted Instruments 209