The Number Paradigms

                                                             The Number Paradigms   There is a dynamic number system in Holistic Mathematics which exactly complements the quantitative system in (conventional) mathematics. The Number Paradigms - written circa 1995 - is an original work which translates all the levels and stages of psychological development in this qualitative mathematical fashion giving an unexpected yet highly precise mapping of the Spectrum of Consciousness.  The application of this approach leads to a radical reinterpretation of the most fundamental scientific notions. The full text of this book is now online. THE NUMBER PARADIGMS The Remarkable Complementarity of Mathematics and Transpersonal Psychology   CONTENTS       Introduction Binary Beginning  Primal Con...

                                                                     INTRODUCTION     Basic Outline     In my earlier "Transforming Voyage", I outlined the manner in which the various structures of personality, conscious and unconscious emerge at different stages of development. I concluded there, that the most complete level of development involves the integration of the fully differentiated conscious (rational) and unconscious (intuitive) processes. Though reason and intuition are seen at lower levels as separate - and largely unrelated - processes of understanding, at higher levels they become complementary and indeed ultimately identical. Thus for example, at lower levels, psychology and mathematics are treated as very separate areas. Psychology, is understood as rel...

                                                         BINARY BEGINNING QUALITATIVE NUMBERS: BINARY Introduction   In all that follows, it is important to remember that numbers have dual aspects which are complementary. Numbers have - in direct terms - a horizontal or rational interpretation as mathematical quantities. This is the manner in which numbers are conventionally understood. Equally, numbers have a vertical or intuitive interpretation - in direct terms - as psychological qualities. In other words, each number type represents a distinctive manner of viewing reality i.e. a paradigm. Though this latter understanding was very important in earlier times e.g. among the Pythagoreans, it was subsequently ignored, with the result that mathematics and esoteric psychology have developed as almost entirely separate...

                                                              PRIMAL CONFUSION   QUALITATIVE NUMBERS: PRIME   Quantity and Quality Prime numbers, are the fundamental building blocks of the natural number system. A prime number has no factors other than itself and 1. So, for example, 7 is a prime number, as it has no other factors other than 7 and 1. Now, bearing in mind that in dynamic terms numbers have dual aspects both as quantities and qualities, we will define prime numbers in a likewise manner. Thus we can list on a horizontal scale the set of prime numbers 2, 3, 5, 7, 11 ..... , and also on a vertical scale the same set 2, 3, 5, 7, 11 ..... . The first set represents numbers as quantities, all defined within the same dimension (i.e. number as quality). This is always taken - where not oth...

                                                           EMERGING REALITY     QUALITATIVE NUMBERS: NATURAL   Composite Understanding I have defined this first composite stage as that time, where conscious phenomena achieve a degree of constancy and can therefore be clearly identified. A remarkable transformation in psychological understanding is necessary to achieve this, which involves the ability to separate quantitative from qualitative characteristics (i.e. to separate partial object phenomena from holistic dimensional experience). In other words for the first time the child is able to clearly locate objects in an environment of space and time. This crucial change represents a degree of differentiation of conscious structures, enabling more creative interaction with the unconscious. The child n...

                                                                   FRAGMENTATION   QUALITATIVE NUMBERS: RATIONAL   (A) Concrete Stages   Positive Direction In psychological terms, we have seen how concrete operational ability involves a new transformation in understanding, whereby a child acquires the ability to rationally control physical objects in the environment. What this in turn involves is a growing clarity in terms of whole and part distinctions. This requires a sufficient degree of conscious specialisation so as to enable (implicit) unconscious operations to be reduced to, and interpreted within the rational linear approach. The child can now break objects into parts, which preserve a distinct independent identity. These parts can then be related back to the wholes f...

                                                                   SELF DISCOVERY   QUALITATIVE NUMBERS: INTEGERS     Negative Existence   As I have stated elsewhere, a child initially believes that objects only exist, when immediately present in experience. Thus though able to recognise objects, they still enjoy a somewhat fleeting existence. They are quickly forgotten when not in the present field of experience. The next advance in understanding, involves an ability to separate the two directional poles, whereby the child is more easily able to distinguish the (subjective) self from the (objective) world. What this in turn entails, is the implicit recognition that these poles are opposite to each other. Switching from the external world to the internal self in experien...

                                                    THE WHOLE PROBLEM   COMBINED STAGE: INTEGRATION There is an attempt in Western psychology, to represent integration of all specialised structures of the linear level, in a final combined stage, sometimes referred to as the centaur level. This, as I have argued is only possible in a very limited sense. The linear level by definition is not geared towards true integration. It is heavily based on the conscious process which favours differentiation of structures. True integration involves considerable specialisation of unconscious understanding which requires going beyond the linear level. Now, when we confine numbers to the rational set, there is no great difficulty in achieving integration of the number system. All numbers thus encountered, prime, natural, negative integers and fr...