Spectrum of Development

Perhaps the most startling implication of this holistic mathematical understanding of the number "4" is that it leads to a completely new interpretation of the nature of space and time (which is now understood in an inherently dynamic interactive manner). In this holistic understanding, space and time simply represent the manner in which the two fundamental polarity sets (external/internal and whole/part) - which necessarily condition all phenomenal reality - interact. So just as in number terms, we can maintain that the four roots of 1 (representing the reduced 1-dimensional expression of 4 as representing a dimensional number) are real and imaginary with positive and negative directions respectively, equally we can maintain the same with respect to space and time. Thus from one valid perspective, we can say that the 4 dimensions contain  two real dimensions of space  (1 positive and 1 negative) and 2 imaginary dimensions (again 1 positive and 1 negative). And becaus

For a long time since the late 60's, I was aware of the fact that all phenomenal reality is conditioned by two key sets of polarities. The first of these relates to external and internal (which we have already briefly discussed). As we have seen in dynamic interactive terms, these two poles - constituting now 2 holistic dimensions of experience, are, relatively, + 1 and  – 1 with respect to each other. The second polarity set relates to whole and part, which can also express itself as general and particular, collective and individual, qualitative and quantitative and so on. I was studying Economics at University in Dublin at the time and was considering then a new dynamic methodology for the discipline that would involve these two sets of polarities. So from one perspective all external economic events entail an internal psychological aspect of behaviour (that is dynamically inseparable from such events). Likewise a key dynamic interaction characterises the relation betwee

In yesterday's blog entry, I attempted to outline succinctly the holistic mathematical nature of "2" (as representing a dimensional number). This in turn is directly related to the unfolding of the various stages of Level 1 (Band 3). What happens here is that one's former dualistic vision of reality becomes steadily eroded, through a marked acceleration in unconscious development, where phenomena become - literally - negated to a considerable extent. This then leads to a more spiritually refined intuitive worldview, where the dynamic relative nature of all phenomena can be readily appreciated. In my own account, Level 1 is largely concerned with - what I refer to as - the horizontal polarities of external and internal (which are relatively + 1 and – 1 with respect to each other) , which necessarily condition the experience of all phenomena. And in holistic mathematical terms, this culminates in the coherent vision of the nature of 2-dimensional - as opposed to

Even as a small child I was fascinated with the nature of number and the fundamental mathematical operations of addition and multiplication. This led me on at the age of about 5 to the discovery of my own system of logs (based on the power of 2) whereby multiplication of numbers could be conveniently "converted" into a simple operation involving addition. Then about 5 years later, I made a much more important and life-changing discovery, when I clearly came to realise that every act of multiplication inevitably involves a qualitative as well as quantitative transformation. However the qualitative aspect is then completely edited out of conventional mathematical interpretation. This initially arose from consideration of the area of rectangular fields. So if a field is of length 80 metres and width 60 metres, the area, 80 * 60 = 4800 sq. metres. So though the initial measurement of length and width are both 1-dimensional, the resulting area now represents 2-dimensional un

Perhaps at this stage I should offer further clarification on the nature of Band 5 on the spectrum, which I have referred to as the “Spiritual Descent". In truth the dynamics are a little more complex that I had previously suggested. Now in terms of my own classification system, I associate Band 2 with the specialisation of linear type understanding. So this represents the ground level of the personal stages, in the conscious understanding of the world of everyday dual phenomena. Then I characterised Band 3 as an ascent through transpersonal stages representing increasingly more refined intuitive understanding   towards an ultimate spiritual reality of a nondual ineffable nature. However because of the inherent complementarity, in a dynamic interactive manner, of transpersonal and prepersonal stages, this equally requires an underground journey back into the deep recesses of earlier development as one comes to encounter ever more starkly the primitive instinctive r

It is a while now since I contributed new material to this blog. When I last posted, I was dealing with the refined cognitive development relating to Band 5 (Level 2) which in my account was intimately related to the unravelling of the mysterious nature of the number system. For I was now beginning to see clearly the remarkable implications, which the qualitative behaviour of the primes hold for psychological development. In conventional mathematical terms, the primes are seen as the basic “building blocks” of the natural number system (in quantitative terms). However a key realisation of this stage is a growing recognition that all mathematical symbols (such as number) can be given both quantitative (analytic) and qualitative (holistic) interpretations! So this leads to an inherently dynamic appreciation of the number system, where both primes and natural numbers interact with each other in a bi-directional fashion.   When the great German mathematician David Hilbert w