Boston Medical Library 8 The Fenway Digitized by the Internet Archive in 2010 with funding from Open Knowledge Commons and Harvard Medical School http://www.archive.org/details/geometricalpsychOOcook r/l/~ 0' £p GEOMETRICAL PSYCHOLOGY OR THE SCIENCE OF REPRESENTATION AN ABSTRACT OF THE THEORIES AND DIAGRAMS OF BETTS B. W. LOUISA COOK S. LONDON GEORGE REDWAY rORK STREET COVENT GARDEN 1887 CONTENTS. .......... PAGE Preface 5 PART I. SECTION I. Subject proposed 9 SECTION II. .11 Scheme of Evolution . . . . . . SECTION III. The Great Duality. Evolution through Polarity, etc. . 14 ...... SECTION IV. Principles ofRepresentation 16 SECTION Y. The Polar-Opposite forms and the Mean form of Sense- Consciousness. The Ond, Onde, and Onden figures 26 . SECTION VI. The three kinds of Numerical Progression, Arithmetical, Geometrical, and Harmonical, and their equivalent in Consciousness. Eurther explanation of the me- chanica.l wor.king.of t.he Di.agra.ms .. .. ....31 SECTION VII. Variation 37 Scales for the Angular Measurement ofthe Diagrams 50 . PART II. SECTION I. Negative Morality and its Mathematical Equivalent . . 53 SECTION II. — The Evolution of the Higher Morality Philanthropy or — .56 Altruism Its principles of Representation . . 4 CONTENTS. PAGE SECTION III. The Polar-Opposite forms of the third ground. The Ond and Onde Corollas .58 . . . . . . SECTION IV. Variations of the third standing-ground. Horn Corollas. Bi-axial Corollas . . 64 SECTION V. Speculations on a fourth Dimension in Space . . .71 SECTION VI. .... The fourth standing-ground ofLife 76 SECTION VII. ...........80 The fifth standing-ground ofLife . . . . Appendix 89 DIAGRAMS. Part I. The Onden. Figs. 1, 2, 3. The Ond. Figs. 4, 5, 6, 7. The Onde. Figs. 8, 9, 10, 11. Variations ofthe Ond and Onde. Figs. 12 to 17. Further variations of the Ond and Onde. Figs. 18 to 23. Part II. The Ond and Onde Corolla. Figs. 1, 2. Foliated Ond and Onde Corollas. Figs. 3, 4. Varieties ofFoliated Corollas. Figs, 5, 6. Furthervarieties of Foliated Corollas. Figs. 7, 8. Horn-shaped Ond Corolla. Fig. 9. Horn-shaped Onde Corolla. Fig. 10. Another example ofHorn-shaped Ond Corolla. Fig. 11. Another example ofHorn-shaped Onde Corolla. Fig. 12. Bi-axial Onde Corolla. Fig. 13. fBi-axial Ond Corolla. Fig. 14. \Perspective appearance of Ond Corolla. Fig. 14. Bi-axial Onde Corolla (same scale as Fig. 14). Fig. 15. Elevation ofOnd Corolla. Fig. 16. The Sphere and its counterpart form. Fig. 17. The Ond Corolla ofthe Solar Universe. Fig. 18. Plan of the Ond Corolla ofthe Solar Universe. Fig. 19. PREFACE. Benjamin Betts was born in the year 1832. He was educated in England as an architect, and showed considerable promise of success but no system of ; architecture not fully based on mathematics could satisfy him, and he felt that decorative art should not be altogether arbitrary and conventional, nor yet a slavish reproduction of natural forms, but should be executed with understanding according to sound prin- ciples of scientific conventionalisation. His mind turned towards the study of internal truth, and he resolved to quit his intended career in order to think out his philosophy oflife. He went abroad to secure the quiet and freedom from distraction which the abstruse nature of his studies required, but the solitude inwhich hehaslived, while aiding his spiritual conceptions, has proved a hindrance when he wished to give out the result of his thought to the world, for having lived so much apart from men it has become very difficult for him to make his ideas intelligible to others. After spending some time in India and the East, he obtained a post in the Government Civil Service, at Auckland, NewZealand, as Trigonometrical Computer 6 PREFACE. of the Survey Department. From this* he draws a modest income which enables him to devote all his leisure time to the metaphysical studies he delights in. The study of internal truth by degrees connected itself in his mind with ideas of form, which combi- nation was probably the result of his early training in Decorative and Architectural Art. An analogy used by Fichte in "The Science of Knowledge," of the correspondence of the line and the circle with modes of consciousness, led to his conception of the idea of developing a Scienceof Representation. Heperceived with Leo Grindon that " all forms are representative, and their significance is the science of sciences." When he had succeeded in developing the plane forms which are his symbols of sense-consciousness, he sent them with a letter to Mr. Ruskin, but Mr. Ruskinfailed to perceive the intention of the diagrams, and replied that Art must be spontaneous, and could not be made mechanical, supposing that Mr. Bettswas attempting some new departure in Art, not in meta- physical science. Later, when Mr. Betts had also developed the corolla forms, he sent the series of diagrams to his sister, with a manuscript in which he attempted to explain them to her. For, practically as well as theoretically, Mr. Betts holds the opinion that for all true work a union of the male and female mind is required. Miss Betts, though sincerely anxious to help and sympathise with her brother in his studies, had not the mathematical and metaphysical training which might have enabled her to be of service to * Since the above was written Mr. Betts has relinquished his Government Post.