What excited me so much about discussion on the "integral" forums, is that I had strong conviction that I had found the underlying holistic mathematical rationale of integration.
Now, I must stress once more that this certainly does not represent the standard analytic mathematical approach applied to development (which would represent a gross form of reductionism), but rather an entirely distinctive mathematical appreciation that is primarily dependent on authentic intuitive insight before its concepts can become meaningful.
So undoubtedly this was the biggest problem I faced all the time on the forums, as even those participants with genuine good will for my endeavours tended to approach ideas with their conventional mathematical training still firmly in place.
Therefore perhaps it always was somewhat ambitious in thinking that I could start an intellectual revolution with these ideas (even though I think this will inevitably happen through someone else offering a similar approach in future).
For some considerable time in the 80's I shared a strong resonance with the works of C.J Jung.
As is well known, Jung had pointed to the importance of certain mandalas as important archetypes of integration.
The ones that he especially emphasised were those that involved the division of circular patterns - often in a highly artistic and ornate manner - into symmetrical four-fold and eight-fold patterns.
Now the 4 and 8 roots of unity are respectively represented in geometrical terms through a circle equally divided into four quadrants and eight sectors respectively.
So through exploring the true nature of these respective roots, I realised that I was in fact providing the deeper holistic mathematical rationale (artistically represented through the mandalas) that underlie integration with respect to all processes of development.
Therefore, though I was always ready to engage in any of the specific topics of interest on the forums, my real purpose was to use discussion of these issues to demonstrate the central importance of the holistic mathematical notions (underlying all integral processes). And this inevitably entailed the understanding of reality inherently in a dynamic interactive manner!
I have also frequently referred to the revealing quote by Marie-Louise Von Franz "Jung devoted practically the whole of his life's work to demonstrating the vast psychological significance of the number four".
Now in this context she was clearly referring to the (circular) holistic - rather than the (linear) analytic - meaning of 4.
And just as 4 is so important in analytic terms in out understanding e.g. of a world existing in four dimensions of space and time, 4 is equally important in a holistic sense in leading to an entirely new appreciation of the dynamic interactive nature of these dimensions in experience.
So in dynamic interactive terms we now have two real and two imaginary dimensions (each with positive and negative directions) with respect to space and time that intimately underlie phenomenal experience of reality.
And these dimensions in turn reflect the very manner in which whole/part and internal/external interaction dynamically takes place with respect to all developmental processes.
However I would now be anxious to stress, while admitting the great central importance of the holistic notions of 2, 4 and 8 (with respect to integral development) that every number has its own unique holistic mathematical significance (with direct application to development).
Indeed it leads to an extremely important aspect of the holistic mathematical approach. Because it is directly based on the dynamics of experience, this means that every mathematical notion - when given its appropriate holistic interpretation - thereby has an important relevance for developmental processes (physical and psychological).
So the implications here are truly mind-boggling, as sometime in our future human evolution, we will be readily able to intuit the true significance of even the most arcane mathematical notions for the understanding of reality!
The great limitation of the conventional treatment of Mathematics and Science - and indeed with respect to present intellectual discourse generally - is that - in holistic terms - it clearly represents a 1-dimensional approach (i.e. where unambiguous dualistic understanding occurs through adopting isolated polar reference frames). This inevitably leads therefore to gross reductionism, i.e. where the internal pole is reduced in terms of the external and where the whole pole is reduced in terms of the part.
This leads to the fallacy of truth expressed as mere objective enquiry (with the whole in any context quantitatively reduced to its parts).
Though this indeed is initially valuable in terms of the differentiated appreciation of the various aspects of development, it is totally unsuited to understanding of their corresponding integration.
We are living in a world which is fast becoming dangerously fragmented in social, political and economic terms.
No proper solution to this problem can emerge until we change the very nature of our thinking in a true holistic manner. This will however require the greatest revolution yet in our intellectual history.
Now, I must stress once more that this certainly does not represent the standard analytic mathematical approach applied to development (which would represent a gross form of reductionism), but rather an entirely distinctive mathematical appreciation that is primarily dependent on authentic intuitive insight before its concepts can become meaningful.
So undoubtedly this was the biggest problem I faced all the time on the forums, as even those participants with genuine good will for my endeavours tended to approach ideas with their conventional mathematical training still firmly in place.
Therefore perhaps it always was somewhat ambitious in thinking that I could start an intellectual revolution with these ideas (even though I think this will inevitably happen through someone else offering a similar approach in future).
For some considerable time in the 80's I shared a strong resonance with the works of C.J Jung.
As is well known, Jung had pointed to the importance of certain mandalas as important archetypes of integration.
The ones that he especially emphasised were those that involved the division of circular patterns - often in a highly artistic and ornate manner - into symmetrical four-fold and eight-fold patterns.
Now the 4 and 8 roots of unity are respectively represented in geometrical terms through a circle equally divided into four quadrants and eight sectors respectively.
So through exploring the true nature of these respective roots, I realised that I was in fact providing the deeper holistic mathematical rationale (artistically represented through the mandalas) that underlie integration with respect to all processes of development.
Therefore, though I was always ready to engage in any of the specific topics of interest on the forums, my real purpose was to use discussion of these issues to demonstrate the central importance of the holistic mathematical notions (underlying all integral processes). And this inevitably entailed the understanding of reality inherently in a dynamic interactive manner!
I have also frequently referred to the revealing quote by Marie-Louise Von Franz "Jung devoted practically the whole of his life's work to demonstrating the vast psychological significance of the number four".
Now in this context she was clearly referring to the (circular) holistic - rather than the (linear) analytic - meaning of 4.
And just as 4 is so important in analytic terms in out understanding e.g. of a world existing in four dimensions of space and time, 4 is equally important in a holistic sense in leading to an entirely new appreciation of the dynamic interactive nature of these dimensions in experience.
So in dynamic interactive terms we now have two real and two imaginary dimensions (each with positive and negative directions) with respect to space and time that intimately underlie phenomenal experience of reality.
And these dimensions in turn reflect the very manner in which whole/part and internal/external interaction dynamically takes place with respect to all developmental processes.
However I would now be anxious to stress, while admitting the great central importance of the holistic notions of 2, 4 and 8 (with respect to integral development) that every number has its own unique holistic mathematical significance (with direct application to development).
Indeed it leads to an extremely important aspect of the holistic mathematical approach. Because it is directly based on the dynamics of experience, this means that every mathematical notion - when given its appropriate holistic interpretation - thereby has an important relevance for developmental processes (physical and psychological).
So the implications here are truly mind-boggling, as sometime in our future human evolution, we will be readily able to intuit the true significance of even the most arcane mathematical notions for the understanding of reality!
The great limitation of the conventional treatment of Mathematics and Science - and indeed with respect to present intellectual discourse generally - is that - in holistic terms - it clearly represents a 1-dimensional approach (i.e. where unambiguous dualistic understanding occurs through adopting isolated polar reference frames). This inevitably leads therefore to gross reductionism, i.e. where the internal pole is reduced in terms of the external and where the whole pole is reduced in terms of the part.
This leads to the fallacy of truth expressed as mere objective enquiry (with the whole in any context quantitatively reduced to its parts).
Though this indeed is initially valuable in terms of the differentiated appreciation of the various aspects of development, it is totally unsuited to understanding of their corresponding integration.
We are living in a world which is fast becoming dangerously fragmented in social, political and economic terms.
No proper solution to this problem can emerge until we change the very nature of our thinking in a true holistic manner. This will however require the greatest revolution yet in our intellectual history.
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