Note 1 - Nature of Holistic Mathematics
I term this dynamic new interpretation of mathematics symbols - which then serves as the indispensable tool for Integral Science - as Holistic Mathematics.
To properly appreciate its nature we need to recognise that the Spectrum of Development contains many distinct levels with which are associated unique intellectual interpretations of reality.
What is conventionally known as Mathematics represents just one interpretation that is based on the highly differentiated rational understanding of the middle of this Spectrum.
Put in general terms this understanding uses an either/or logic based on the clear separation of opposite poles (e.g. interior/exterior, whole/part, finite/infinite) in development.
This leads to an interpretation of symbols that is analytic, unambiguous and static.
The analytic aspect derives from the discrete interpretation of symbols, which gives them a definite partial identity. So numbers for example can be divided (and sub-divided) into parts with a separate (numerical) identity.
The unambiguous aspect refers to an absolute type interpretation of symbols.
Thus with reference to the binary digits, 1 and 0 are understood as clearly separate. So therefore, by definition 1 is not equal to 0; likewise 0 is not equal to 1.
Also a proposition is viewed as being either true or false (so that the one thereby excludes the other).
The static aspect arises due to the separation of opposite poles.
So for example though the actual experience of a mathematical symbol such as a number necessarily entails the dynamic interaction of subject and object (and object and subject), in actual interpretation this is ignored. Therefore the number is assumed to have an objective validity (that is unaffected through interaction with mind).
In this sense in conventional understanding mathematical symbols have a merely static absolute identity.
However this specialised interpretation - based on the intellectual understanding of the middle of the Spectrum - represents just one possible valid interpretation of mathematical symbols.
Associated with each of the higher levels is an intellectual understanding that is increasingly based on a both/and logic and is bi-directional in nature.
This leads to an alternative interpretation of symbols that is by contrast holistic, paradoxical and dynamic.
Whereas in the former interpretation, opposite poles are interpreted as largely separate, by contrast here, their - necessary - interaction is explicitly recognised.
We will illustrate the holistic aspect of symbols with respect to 1 and 0.
In analytic terms they are clearly separated; in holistic terms they are inextricably linked. So 1 in holistic terms represents the generalised notion of unity (or form) which is interdependent with its complementary notion of nothingness (or emptiness).
The relationship between these two aspects is inherently paradoxical.
We cannot conceive unity i.e. form (1) in the absence of nothingness i.e. emptiness (0).
Likewise we cannot conceive of nothingness (0) in the absence of form (1).
This paradox can only be properly appreciated in dynamic terms.
Thus we now see all processes in reality as representing the ceaseless interaction of form and emptiness i.e. 1 and 0 (and emptiness and form i.e. 0 and 1).
So in the broadest terms we have two fundamental interpretations of mathematical symbols.
1) The static analytic approach which is the indispensable tool for scientific asymmetric type understanding.
2) The dynamic holistic approach which equally is the indispensable tool for a proper scientific integral approach.
The potential implications here are truly enormous for what it entails is that every mathematical symbol and relationship - regardless of how abstruse - with a partial meaning in a (static) analytic context, equally has a corresponding integral meaning from a (dynamic) holistic perspective.
What I am presenting is a preliminary - though fundamental - investigation of such integral symbols and relationships.
I hope that it will provide some insight into - what are - truly vast new terrains of unexplored territory.