Science Between Space and Counterspace

by Nick Thomas

Reviewed by Ron Jarman

This book contains the results of research into the Science of the Spirit as illumined by the methods of modern projective geometry. In his scientific lecture courses of the early 1920s Rudolf Steiner developed the qualitative path of 7 stages leading from Earth through Water, Air, Warmth, Light and Chemistry to Life. The individual characteristics of each of them (elements and ethers) have to be grasped through medi-tative thinking. This is what Nick Thomas has undertaken. Without meditative (i.e. clear) thinking the reader will find it difficult to understand his book. Also he stresses that the re-search described is by no means complete and invites anyone who can to join in further research. We no longer live in an age when scientific riddles are solved by single people. Co-operative efforts are needed in scientific progress just as much as they are in social progress generally.
The contrast between centric and peripheral forces is a vital theme in the book. Rudolf Steiner remarked in his "Light Course" that what exists in Nature (including inorganic na-ture) can never be explained by centric forces alone. Save for artificial things made by human beings, cosmic (or peripheral) and centric forces are always flowing together. Steiner went on to assert that such a truth was profoundly clear to Goethe.
Today we can be enheartened by new impulses in Goethean-ism, for example by the efforts of Margaret Colquhoun and the Life Science Trust in which the essential Imagination is de-veloped; also by the fine book "How the leopard changed its spots" by Brian Goodwin. But a further step is needed (Inspiration) - capital I's refer to the spiritual technical terms of Steiner - to pursue the 7 elements-ether path. It was also in the "Light Course" that Steiner declared "We are not credu-lous believers in the physics of today, nor need we be of Go-ethe. Goethe died in 1832. What we now seek is a further evolution and development of what he brought." The rose cross meditation described in Steiner's "Occult Science" also has 2 stages. In the second (Inspiration) stage the hard won living pictures of the first (Imagination) stage have to be sac-rificed and washed away before the new experience sounds through us, when not mental pictures but pure concepts supply the ground above which one builds.
Naturally in a penetrating presentation at this deeper level the author has to assume that many of the elementary facets of projective geometry are familiar to the reader, although refer-ences are given whereby the reader may acquire this familiar-ity. He needs to be sure, for example, of how statements can develop like the following: (i) A line and a point not on it de-termine a unique plane, (ii) If two distinct planes have a point in common, they also have in common a unique line through that point, (iii) If the unique line is without position (a line at infinity) in positive space the planes are parallel, (iv) If the unique point is without position in negative space, the planes and line are infinite elements in that negative space.
Often advanced mathematics is used to express the clarity required (e.g. some tensor calculus), but there is still much that the layman can grasp through inspired imagination. One could wish for several large coloured geometrical drawings in the book to illustrate the way of thinking needed to become at home with the behaviour of this or that element or ether. Quite apart from the much increased price the book would then have to carry, this task is also for the motivated reader to provide either on paper for his physical eyes or in his representations for his mind's eye.
A brief survey of some of the main themes of Nick Thomas' book is given below.
Radically different ways of thinking about the world are needed today free of the standard Euclidean metric; scientists like Bohm and Penrose support this. The unsatisfactory nature of models and the Copenhagen interpretation of Quantum theory are discussed.
Collineations, correlations and cross ratios in space and counterspace are focused upon. Area and volume are shown to be quite independent concepts. The 4 stages or types of ge-ometry called pure projective, affine, special affine and Euclidean are shown to relate first to the 4 elements (Warmth down to Earth) and then in their polar geometrical (cosmic,peripheral) aspects to the 4 ethers (going upwards to Life ether). The polar counterparts of area and volume are developed.
Everything is affected by both positive and negative space, giving rise to "strain", which in turn leads to active "stress". So, for example, affine stress varies directly as the rate of change of affine strain. The concepts of "turn" and "shift" are introduced, the former a vector, the latter not. Surprisingly perhaps we find that time is inversely proportional to radial turn. This awakened for me the memory that atomic weight is inversely proportional to specific heat and one wonders if yet deeper relationships may be discoverable at the purely Intui-tive level.
Gravity, both at the Newtonian and Einsteinian level are gone into but whereas gravity only applies to crystalline and other homogeneous bodies, different concepts apply above that state and the idea of black holes would seem in need of drastic revision.
Special chapters are given to heat (not as simple and predict-able as may be thought from first considerations of the prime 7 states - elements and ethers), chemistry, light and life. Phe-nomena of reflection, refraction, interference etc. are looked at anew and where life is concerned the author declares that it certainly is not merely a product of the laws governing sub-stances but is integral to an organism ab initio. What makes an organism is that its presence is inside every cell where counterspace is concerned.
Nick Thomas' book is certainly difficult for those unfamiliar with modern maths and projective geometry. It is a book which could be of considerable interest to a modern physicist or biologist and could be recommended or given as a birthday present to friends of that ilk. It is a high ranking piece of sci-entific research. Ron Jarman, 11 Feb 1999

Science Between Space and Counterspace by Nick Thomas, New Science Books (Temple Lodge Publications), January 1999, ISBN 0 902636 02 3, 17.95