Table Of ContentCollection copyright © 2010 by Wooden Books Ltd
Sacred Number copyright © 2005 by Miranda Lundy
Sacred Geometry copyright © 2001 by Miranda Lundy
Platonic & Archimedean Solids copyright © 2002 by Daud Sutton
Harmonograph copyright © 2003 by Anthony Ashton
The Elements of Music copyright © 2008 by Jason Martineau
A Little Book of Coincidence copyright © 2001 by John Martineau
Appendix pages from Ruler and Compass © 2009 by Daud Sutton
All rights reserved. No part of this book may be used or reproduced in any manner
the four classical liberal arts of
whatsoever without written permission from the publisher except in the case of
brief quotations embodied in critical articles or reviews. For information please
address Wooden Books Ltd, Red Brick Building, Glastonbury BA6 9FT. number, geometry, music, & cosmology
Simultaneously published in 2010
in the UK by Wooden Books Ltd, Glastonbury
and in the US by Bloomsbury USA, New York.
This eBook version published in 2020.
A CIP catalogue record for this book is available from the British Library.
ebook ISBN: 978-1-912706-24-1
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QUADRIVIUM
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NEW YORK • LONDON • OXFORD • NEW DELHI • SYDNEY
“The Tao gives birth to the One,
the One gives birth to the Two,
the Two gives birth to the Three,
the Three gives birth to the Ten Thousand Things.”
Lao Tzu [605-531BC]
Contents
Editor’s Preface 1
Foreword 3
Keith Critchlow
Book I Sacred Number 7
Miranda Lundy
Book II Sacred Geometry 59
Miranda Lundy
Book III Platonic & Archimedean Solids 127
Daud Sutton
Book IV Harmonograph 181
Anthony Ashton
Book V The Elements of Music 237
Jason Martineau
Book VI A Little Book of Coincidence 291
John Martineau
Appendices & Index 355
The four subjects concerned with number which comprise the Quadrivium: Arithmetic (top left), Geometry
(top right), Music (bottom left), and Astronomy (bottom right). From the Margarita Philosophica,
Strasburg, Germany, 1503, by Gregor Reisch [1467-1525]. Courtesy of the Warburg Institute, London.
Editor’s Preface
T
he volume you are holding is a treasure chest of old, once secret,
and always useful things. It is immortal—it will never go out of
date. And it is universal—a magical passport between cultures, sacred
and scientific, provincial and foreign, ancient and modern.
Six books from the Wooden Books series have been combined to
produce Quadrivium, plus 32 new pages for good measure. Geometry
and music are each covered as two books, hence the six. We have
tried to minimize repetition due to overlap in the original books but a
few instances remain here and there. Also, since this is a transatlantic
edition, we have opted for a mixture of English and American spelling
and punctuation. If this upsets some readers, we apologize.
A volume of this scope involves bringing together many people.
Thanks to Sally Pucill, Richard Henry, Adam Tetlow, John Michell,
John Neal, Dr Paul Marchant, Robin Heath, David Wade, Dr Khaled
Azzam, Malcolm Stewart, Polly Napper, Geoff Stray, Dr Moff
Betts, Prof Scott Olsen, Richard Heath, Matt Tweed, Mark Mills,
Prof Robert Temple, Stephen Parsons, Nathan Williams and Tracey
Robinson for their help and contributions.
Thanks to the additional Wooden Books series editors, George
Gibson of Walker & Bloomsbury in New York, and Daud Sutton in
Cairo. Thanks finally to Prof Keith Critchlow for the foreword, and to
the authors themselves, Miranda Lundy, Daud Sutton, my grandfather
Anthony Ashton, and Dr Jason Martineau in Berkeley.
John Martineau
1
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2
Foreword
E
lements of the Quadrivium were taught by Pythagoras as the
Tetraktys around 500bc, in a community where all were equal,
materially and morally, including women and men. A thousand years
later, Boethius and the early European schools which followed began to
hone education down to seven essential subjects—the seven liberal arts.
The word ‘education’ comes from the Latin educere meaning ‘to
lead out’, pointing to the central doctrine that Socrates, under Plato’s
pen, elucidated so clearly—Knowledge is an inherent and intrinsic
part of our soul structure. The Trivium of language is structured on
the cardinal and objective values of Truth, Beauty and Goodness. Its
three subjects are Grammar, that ensures the good structure of language,
Logic for finding truth, and Rhetoric for the beautiful use of language
in expressing truth. The Quadrivium arises out of the most revered of
all subjects available to the human mind—Number. The first of these
disciplines we call Arithmetic, the second is Geometry or the order of
space as Number in Space, the third is Harmony which for Plato meant
Number in Time, and the fourth is Astronomy, or Number in Space
and Time. All these studies offer a safe and reliable ladder to reach the
simultaneous values of the True, the Good, and the Beautiful. This in
turn leads to the essential harmonious value of Wholeness.
Our soul, which is proven to be immortal by Socrates in the
Phaedo, comes from a position of complete knowledge prior to being
born into the body. Re-membering—the point of education—
literally means putting the separate members back into a wholeness.
3
The goal of studying these subjects was to climb back (up) to Unity
through simplification based on the understanding gained by engaging
in each area of the Quadrivium. The goal lay in finding their source
(traditionally this was the sole purpose of the search for knowledge).
In his discussions on the ideals of education, Socrates reveals his
model of the continuity of consciousness. This was as a ‘line’ drawn
vertically reaching from the beginnings of conscious knowledge in
Estimations right up to the climax of consciousness as Noesis, which is
Unified Understanding. Beyond this is the indescribable and ineffable.
There are, significantly, four stages (another Quadrivium or Tetraktys)
given by Socrates’ division of the ‘Ontological line’. The first and
fundamental division is between the Intelligible and Sensory world,
between Mind and Matter. Next, each of these is divided, Estimations
from Opinions. In the sensory world even correct opinions are still
based on sensory experience, while above the first divided line, in the
Intelligible world of the Mind we find ourselves in the ‘truth-bearing’
realm of the Quadrivium, true and objective knowledge. The final
topmost division of the intelligible is Nous or Pure Knowledge itself
where the knower, the known, and the knowing become One. This is
the goal and source of all knowledge. Thus, time and wisdom tested,
the Quadrivium offers the sincere seeker the opportunity to regain
their own inner understanding of the integral nature of the universe,
with themselves as an inseparable part.
Turning now to the ‘four ways’ in more detail, Arithmetic has
three levels: the materially Numbered; Mathematicians’ Number
(indefinite); and Ideal or Archetypal Number (complete at 10).
4
