The Holistic Nature of the Number System (11)

In this entry, I will once again attempt to communicate in an intuitively accessible manner the true startling nature of our number system.

Firstly, when properly understood i.e. in a dynamic interactive manner, number is directly related to human experience with two complementary aspects that are physical and psychological with respect to each other.

In other words the long accepted notion of number as absolutely existing in some abstract mathematical space is but a fiction arising from a reduced interpretation of its true nature.

More correctly, number is inherent in all processes (physical and psychological) as their most fundamental nature. So from this perspective, we cannot abstract number from either physical reality (or its corresponding psychological interpretation) as - by their very nature - these are dynamically encoded in number.

All the surprise that is being now expressed regarding intimate connections as between the Riemann zeros and chaotic quantum states thereby reflects the reduced existing interpretation of number. If number was properly understood i.e. in a dynamic interactive manner, no such surprise would occur!

 

As well as twin physical and psychological aspects (reflecting the necessary human interaction as between opposite polarities that are internal and external with respect to each other) number equally expresses the necessary dynamic interaction as between quantitative and qualitative aspects (reflecting in turn the relationship between wholes and parts).

There is huge confusion in present Mathematics with respect to this issue. Because of its merely quantitative bias in formal terms, the qualitative aspect is thereby reduced and distorted (from every perspective) in quantitative terms.

The cardinal and ordinal notions of number relate to the quantitative and qualitative aspects of the number system respectively.

This means in effect - because of reduced quantitative nature - that no coherent interpretation of the ordinal aspect of number can be given within Conventional Mathematics. (And because of their necessary interdependence, no coherent interpretation can likewise be given of  the cardinal aspect)! 

This Mathematics is solely geared to the analytic type appreciation of relationships (as independent). This corresponds in psychological terms with a merely (conscious) rational interpretation.

However when appropriately understood, the ordinal aspect of number relates to the holistic type appreciation of number relationships (as interdependent).

This likewise entails that such appreciation relates directly to  understanding of an (unconscious) intuitive rather than (conscious) rational nature.

The clear implication therefore is truly revolutionary in that the understanding of our number system and indeed all mathematical relationships (in a coherent fashion) requires a radical new paradigm with analytic and holistic type appreciation both recognised - though (conscious) reason and (unconscious) intuition respectively - as equal partners.

In a dynamic context, sole emphasis on the prime numbers (as the building blocks of the number system) is seen to be in error.

Rather what is now emphasised is the dynamic two-way relationship as between the primes and the natural numbers (and the natural numbers and the primes) through which both the quantitative (cardinal) and qualitative (ordinal) aspects of the number system are mediated.

When looked at in a dualistic manner (through separate reference frames) the direction of causation as between both seems directly in conflict. Thus from the cardinal perspective, the primes appear as the building blocks of the (composite) natural numbers; however equally from the (unrecognised) ordinal perspective, the natural numbers appear as the building blocks of each prime!

Thus from the linear (quantitative) perspective, the primes appear as the most independent of all numbers; however equally from the circular (qualitative) perspective, the primes now appear as the most interdependent!

 

So when one properly appreciates this paradox with respect to the primes, the true fundamental requirement is then to establish the ultimate consistency of both quantitative and qualitative aspects.

And when properly understood, this is what the Riemann Hypothesis is truly about!

The zeta zeros relate directly to this mysterious identity in the number system with respect to both cardinal (quantitative) and ordinal (qualitative) aspects.

Again - when appropriately understood in a dynamic interactive manner - two complementary sets of these zeros can be seen to exist (which I refer to as Zeta 1 and Zeta 2).

The Zeta 2 zeros (which are the simpler to intuitively grasp) relate within each prime number (representing a group of members) to how ordinal identity - which is qualitative in nature -  can be coherently expressed (indirectly) in a quantitative manner. Therefore, though ordinal identity relates directly to the interdependence nature of a number group, as this is of a merely relative nature, indirectly it likewise has an independent identity!

The Zeta 1 zeros then relate to the corresponding issue of how ordinal identity with respect to the number system as a whole (arising from the combination of prime number factors) can likewise be coherently expressed through an unlimited set of numbers. In reverse manner, though cardinal identity directly relates to the independent nature of each individual number, again because this is of a merely relative nature, indirectly it likewise has an interdependent ordinal identity with respect to the number system as a whole (which is what the Zeta 1 zeros represent). 

 

What is crucial to understand is that both of these sets of zeros relate directly to the holistic - rather than analytic - interpretation of number (i.e. to the interdependence of both quantitative and qualitative aspects).

This likewise implies that their true appreciation can only come from the specialised development of the intuitive unconscious in higher dimensional contemplative experience of reality. However indirectly such intuitive appreciated can be given circular rational expression in a paradoxical manner.

And this cannot be provided through Conventional Mathematics, which by its very nature is defined in a linear (1-dimensional) conscious format!

Rather, from a comprehensive mathematical perspective, 3 - rather than at present 1 - relatively distinct areas are required:

1) The Type 1 aspect geared to traditional analytic appreciation in a quantitate manner. However crucially all relationships would now be interpreted in a relative - rather than absolute - manner.

This aspect of Mathematics is rational in a linear (i.e. 1-dimensional) fashion based on isolated polar reference frames.


2)  The Type 2 aspect geared to the (formally) unrecognised holistic appreciation in a qualitative manner. Typically, I have referred to in the past as Holistic Mathematics.

This aspect of Mathematics crucially entails viewing the polar reference frames (which condition all mathematical experience) as interdependent in a dynamic interactive fashion. In direct terms it is of an intuitive nature which indirectly can be expressed in a rational manner (which appears paradoxical in terms of linear reason).

So this aspect of Mathematics is rational in a circular manner (in all dimensions ≠ 1). However its simplest expression in 2-dimensional terms - based on the direct complementarity of opposite poles such as internal/ external and whole/part - in an important sense serves as a prototype for all other higher dimensional interpretations.

Since my late teens, I have been in the process of developing this completely neglected qualitative aspect of Mathematics (which rightly should be seen as an equal partner with its quantitative counterpart).

In particular I have spent many years using it to show that human development - with respect to the entire spectrum of its possible structures - can be scientifically best appreciated in a holistic mathematical manner.


3) The Type 3 aspect - which I formerly referred to as Radial Mathematics - is geared to the two-way comprehensive integration of both Type 1 and Type 2 aspects.
Of course, this Type 3 aspect cannot have meaning in the complete absence of formal recognitiont of the Type 2 (holistic) aspect of Mathematics.

In a very preliminary manner, I have been demonstrating in recent years on this blog how this Type 3 aspect is crucially necessary for coherent interpretation of the Riemann Hypothesis (and its many fundamental consequences).

Therefore, when correctly interpreted in a more comprehensive manner, the most important implication of the Riemann Hypothesis is the truly inadequate state of existing Mathematics.
Indeed continued failure to prove the Riemann Hypothesis may well serve to eventually act as the catalyst for a much needed new vision of Mathematics.
  

So underlying our common sense conscious interpretation of number (in analytical terms) is a deep unrecognised unconscious appreciation (of a truly holistic nature).

This holistic unconscious appreciation represents the great unrecognised shadow of Mathematics.

As it stands, our present formal appreciation of Mathematics is totally lacking a holistic integral perspective (which requires explicit recognition of the role of the unconscious). In other words our understanding of Mathematics at present is hugely unbalanced.

Though it may seem highly rigorous and specialised to many, present Mathematics is in fact based on greatly reduced - and thereby greatly confused - assumptions. This means in turn that accepted notions of science (which are intimately based on Mathematics) thereby suffer from the same reductionism and confusion.

If we cannot provide a coherent account of the number system (on which everything else is based) well then we cannot offer in truth a coherent account of anything!

 

Though I would expect that what I have said here will simply be ignored by practicing mathematicians, I write with a great conviction as one who already began to recognise the highly reduced nature of mathematical assumptions at an early age.

Now, after 50 years of on-going reflection, I am utterly confident of the position outlined here and that what I say here will eventually be accepted in the years to come.

Make no mistake about it! When it is clearly realised what is at stake here i.e. the true nature of Mathematics, will set the stage for by far the greatest revolution yet in our intellectual history. All previous developments simply pale by comparison.