Friday, February 20, 2015

Number as the Theory of Everything

It should be clear that when both the quantitative and qualitative aspects are equally recognised, number thereby assumes an extraordinarily important role as the dynamic encoding of all created phenomena. So, literally everything, in both physical and psychological terms is ultimately encoded in number! 

Now, as all the great mystical traditions attest, the ultimate nature of reality is ineffable. One could equally say that the ultimate nature of number is ineffable and can only thereby assume a phenomenal identity, when some degree of separation exists as between its opposite polarities.

When attempting to approach this ineffable nature, the holistic meaning of 1 and 0 are often employed, where now both are understood as fully identical with each other.  So the Eastern traditions especially emphasise ultimate reality as a void or nothingness as potential for all form (which entails the holistic notion of 0); by contrast this ultimate reality is more often represented in Western traditions as a union of all form (entailing the holistic notion of 1). 

However in both East and West, the recognition exists (in varying degrees) that the two notions mutually imply each other, so that this reality is truly a plenum-void, where both union and nothingness i.e. as emptiness, are inseparable.

However the full realisation  of such interdependence is truly mysterious. So we can only phenomenally recognise  the holistic notions of 1 and 0, if they are already separated from each other (in some measure).

Thus we must always approach absolute meaning, without ever being capable of fully attaining it, from this phenomenal perspective (however refined in understanding).


However the importance of the mathematical symbols used here, is that they form the most refined bridge possible, as it were, as between phenomenal and ineffable reality.

So in the deepest sense, when appropriately understood, number provides the best interrmediary for scientific understanding of the nature of the wonderful creation, that we so mysteriously inhabit. The intrinsic nature of this reality is thereby encoded in number as its fundamental "genes" (once we learn how to decipher this code).

And as we have seen, the key step here is the recognition of the inherently dynamic nature of number, entailing the interaction of both its quantitative and qualitative aspects. 

So the first notion of number, i.e. with respect to the fundamental binary digits of 1 and 0, provides the most refined phenomenal partition that bridges potential reality (as void) and its corresponding actualisation (as form).

However the next major issue relates to how both the quantitative and qualitative aspects of this reality, can then be coherently distinguished in phenomenal terms, yet remain fully related in a consistent - and ultimately - incomprehensible manner.

So, at a local level, the phenomenal features of reality exhibit a distinct independent identity in both quantitative and qualitative terms; yet at the global level all such features are in truth ultimately interdependent with each other in a truly ineffable fashion.

Now the importance of the relationship between the primes and the natural numbers (and natural numbers and primes) is that remarkably, in a dynamic bi-directional manner, it provides the code, as it were, through which this key problem is universally solved.

And as we have seen, mediating this crucial relationship are two parallel sets of numbers i.e. the Zeta 1 and Zeta 2 zeros, which universally mediate in two-way fashion as between primes and natural numbers (thereby ensuring consistency of both quantitative and qualitative aspects).

Without such dynamic consistency being guaranteed in this manner, meaningful mathematical operations (in cardinal and ordinal terms) would not be possible; even more dramatically, the phenomenal world as we know it, which is dynamically encoded in such number relationships, could not exist.


So if we are to look for a meaningful "Theory of Everything", it is to be found in its purest phenomenal expression, in the relationship between the primes and natural numbers, which mutually entails the two sets of zeros that mediate each other in a fully synchronistic manner. 

Thus this relationship necessarily lies as the embedded code of all subsequent phenomena that are manifest in evolution. In effect this number code dictates how such phenomena can fundamentally relate to each other (in both quantitative and qualitative terms).

So number in this dynamic sense, potentially exists as the root source of all physical phenomena that can subsequently exist. However this meaning is only then actualised through its relationship with manifest phenomena. This then ultimately, through considerable psychological development, can lead to comprehensive appreciation of the code, as forming the final partition to the fulfillment of all evolution (in ineffable union). 

However this is very different from the present quest in physics for a TOE based on the postulated existence of strings.

There are in fact no "building blocks" of reality such as strings, which can be appreciated in mere analytic (quantitative) terms. Rather, phenomenal reality, as we know it, arises from the synchronistic relationship of opposite polarities (such as external /internal, whole/part and form/emptiness) that find their purest expression in the fundamental nature of the number system.

Therefore the much more profound quest of science, which has yet to be properly articulated, is to coherently show how conversion can take place, as it were, from the analytic interpretation of phenomena, where seemingly cause and effect operates in a linear manner (with quantitative and qualitative aspects separate), to the corresponding holistic interpretation, where all relationships are now understand as synchronistically determined (in both quantitative and qualitative terms).

And the mystery that underlies this quest, as we have seen is already implicitly encoded in the very nature of the number system 
From this perspective, the true task of evolution is the dynamic uncovering of this fundamental code that thereby contains the power to lead us eventually to the very gates of eternity! 

Thursday, February 19, 2015

The Zeta Zeros and Affective Appreciation

I wish to comment here on a further remarkable feature with respect to the nature of zeta zeros (Zeta 1 and Zeta 2).

Conventional Mathematics, which is of an analytic (quantitative) nature, is defined in terms of merely cognitive interpretation of mathematical symbols in a linear rational manner.

Though intuition of a holistic (qualitative) nature is implicitly required to fuel the dynamics of such understanding, in formal terms it remains unrecognised and thereby reduced in every context to quantitative interpretation.

So the first major breakthrough required is that realisation that both all mathematical interpretation properly entails both analytic (quantitative) and holistic (qualitative) aspects in dynamic interaction with each other.

Though once again, the holistic aspect relates directly to intuition, indirectly it can then be translated in a paradoxical rational manner that is circular in nature.

Indeed such circular rationality can in turn be further indirectly represented in an "imaginary" linear manner.

So whereas from a qualitative philosophical perspective, Conventional Mathematics is based on the real (i.e. conscious) use of reason, this more comprehensive approach is based on the complex expression of reason i.e. relating to both real (conscious) and imaginary (unconscious) aspects of understanding.


However there is a further surprise awaiting in the comprehension of the zeta zeros.

For example, one may start by attempting to appreciate the Zeta 2 zeros (which are the simpler to embrace) in a complex cognitive manner (i.e. involving both analytic and holistic aspects of interpretation).

However the corresponding attempt to then appreciate the Zeta 1 (Riemann) zeros in a corresponding complex cognitive manner will ultimately lead to failure. I know this convincingly from my own experience!

So what is remarkable - in terms of their adequate comprehension - is that when the Zeta 2 zeros are interpreted in a complex cognitive fashion, in relative complementary terms, the Zeta 1 (Riemann) zeros, will then correspond to complex affective understanding. In other words, their true nature from this perspective cannot be approached from a cognitive perspective!

However of course as in all dynamic interactive situations, reference frames can be switched.

So if the Zeta 1 zeros are now understood from the cognitive perspective, then the corresponding Zeta 2 zeros must now be approached in a complementary affective manner.

So ultimately -  which must come as a major surprise to anyone who sees Mathematics as a merely rational discipline - an approach to true comprehensive understanding of both sets of zeta zeros, requires the ability to balance cognitive and affective aspects of experience in a highly refined contemplative two-way intuitive manner.

Indeed this fits in very well with my comments yesterday, that the integration of the two sets of zeros coincides with the attainment of both top-down and bottom-up integration.

Now typically - especially with male personalities - top-down integration would be identified in psycho-spiritual terms, with the transcendent aspect of development, where "high level" cognitive is used to control "low level" affective behaviour (especially with regard to physical instinctive impulses of the unconscious).

Bottom-up integration, by contrast would represent the corresponding immanent attempt at achieving a spontaneous physical response, where "low-level" affective projections, now emptied of repressive influence, can freely integrate themselves with the cognitive aspect of mental control.

Thus to achieve an appropriate balance, in psychological terms, as between top-down and bottom-up integration, requires the corresponding ability to properly balance both the cognitive and affective functions of behaviour.

So when this state is achieved - or rather successfully approached in varying degrees - the primitive instinctive behaviour (of the unconscious) can be fully harmonised with the natural (conscious) requirements of living..

As we have seen, the task of achieving such two-way integration, directly corresponds with the two-way integration in mathematical terms of both the primes and natural numbers.

And just as psychological integration entails the marriage of both cognitive and affective aspects, likewise mathematical integration (with respect to the zeros) entails a similar corresponding marriage.


Now once again this might appear incomprehensible to one approaching Mathematics from the conventional perspective. for here the attempt is made to abstract rational understanding, in an absolute manner, from human experience (which is inherently of a dynamic interactive nature).

And as such human experience ultimately entails conscious and unconscious aspects, with respect to both cognitive and affective aspects of understanding, ultimately comprehensive mathematical understanding requires the same framework.

In other words the most comprehensive mathematical understanding can only arise, when mathematical activity is itself fully integrated with the rest of human experience.

I have already mentioned on several occasions that I viewed a comprehensive approach to Mathematics as entailing three main stages i.e. Analytic, Holistic and Radial (where Analytic and Holistic are increasingly combined).

However, so far this map was envisaged in a complex cognitive manner (entailing the aspects of reason and intuition).

However a fourth stage is now also required whereby Mathematics itself becomes increasingly integrated with both artistic and religious type experience.

So the 3 big domains of human experience centre around the Sciences, the Arts and Religion (as the embodiment of spiritual experience). These in turn can be identified most directly with the cognitive, affective and volitional aspects of human behaviour.

Mathematics may initially be seen as solely relevant to the Sciences. However as ultimately the Big 3 entail complementary aspects of human behaviour, a full experience of Mathematics entails a full experience likewise with respect to the other two aspects.

So in various contexts, the meaning of mathematical symbols will remain highly elusive, when approached in a merely cognitive manner.

Thus here, mathematical symbols may be best understood as indirect expressions of a meaning that is of an aesthetic nature (appealing  directly to artistic appreciation). And this is true to the nth degree, where the majestic intricate beauty of the zeta zeros is concerned!

Wednesday, February 18, 2015

Zeta Zeros - Psychological and Mathematical Connections

Properly understood, the task of properly grasping the true nature of the zeta zeros (both Zeta 1 and Zeta 2) cannot be divorced from the corresponding task of attaining full integration in psycho-spiritual terms.

My earliest realisation of this important fact came from the holistic insight that the notion of "prime" from a mathematical perspective is directly complementary with the corresponding notion of "primitive" as used in a psychological developmental context.

Deep reflection on the inherent meaning of "primitive" then enabled me to make valuable linkages to the true notion of prime numbers in a dynamic experiential mathematical context.

For example in early infancy, primitive instincts characterise the behaviour of a child.

This reflects the fact that as the conscious aspect of personality has not yet been properly differentiated from the corresponding unconscious aspect, that both are inevitably confused with each other.

Thus, in other words, the infant confuses holistic meaning (associated with the unconscious) directly with specific objects (properly pertaining to conscious understanding).

With the extreme manifestations of such behaviour, true object constancy is not possible in experience. This again is due to the fact that (specific) phenomena are so directly confused with the (holistic) dimensions they inhabit, that neither aspect can be properly distinguished from each other.

Therefore, because a sufficiently stable background of space and time cannot be yet provided, object phenomena enjoy a - necessarily - fleeting existence.

Indeed this also has close parallels with the nature of sub-atomic particles, which become inherently unstable at deeper levels of investigation, enjoying but a momentary existence in space and time.

This implies that there is holistic ground to physical reality (relating to the close interdependence of quantum phenomena with each other) so that at the extreme levels of investigation, it is longer even possible to distinguish such phenomena (as independent) from their background environment (as interdependent).  

Thus from  psychological and physical perspectives, earliest development is prime (i.e. primitive) in nature (reflecting the confusion of both analytic and holistic aspects of meaning).


When one carries over this dynamic interactive approach to the interpretation of prime numbers, it implies that they ultimately represent two extreme aspects of behaviour in a complementary manner.

Thus from one perspective, the primes are the most independent of numbers, representing, in cardinal terms, the prime "building blocks" of the natural number system (except 1).

However, from an equally valid perspective, the primes are the most interdependent of numbers, necessarily represented in a unique ordinal manner, by their natural number members.

So again for example, from this perspective, 3 is a prime, that is necessarily composed in ordinal terms of 1st, 2nd and 3rd members. Now strictly this latter definition refers to a qualitative relationship as between the members of a group!
Then, indirectly these ordinal members can be uniquely expressed in quantitative terms (again except 1) by the corresponding prime roots of 1!

Thus we have both quantitative (analytic) and qualitative (holistic) aspects to the primes.

So when the quantitative aspect is identified in a cardinal manner (relating to number independence) the corresponding qualitative aspect is then identified in an ordinal manner (relating to the number interdependence as between different members of a group).


Once again in earliest childhood both aspects of the primes i.e. quantitative and qualitative (relating to conscious and unconscious aspects respectively) are greatly confused with each other.

So the first task of development is to successfully differentiate the conscious aspect from the unconscious which is the task of Band 1 (on the spectrum of development).

Then the specialisation of this understanding (in a linear rational manner) occurs at Band 2.
And it is this Band with which Mathematics and Science - as we know them - are conventionally associated.

However this represents but a reduced quantitative interpretation of the primes (with no formal recognition of their distinctive qualitative nature).

Thus we cannot hope to understand the inherent dynamic nature of the primes in this reduced manner!

So before Mathematics can properly address this issue, it will need to recognise that further substantial qualitative mathematical development (of a holistic intuitive nature) is possible on the spectrum.

Traditionally this has been associated with the attainment of advanced contemplative awareness, (which is recognised by all the spiritual traditions).

However what has not been properly recognised is that such development has extremely important implications for both mathematical and scientific understanding, leading to the distinctive disciplines of Holistic Mathematics and Holistic Science respectively.

So Band 3 on the spectrum represents the unfolding of a new refined intuitive awareness (that indirectly finds expression in a circular i.e. paradoxical, rational manner).

Band 4 then represents the specialisation of this distinctive type of intuitive awareness thereby enabling true appreciation of the holistic aspect of number.

Now the further possible Bands of development on the spectrum (which I define as 5, 6 and 7) represent the mature integration of both (specialised) analytic and holistic appreciation of the primes.

And this is equally necessary in terms of achieving both full integration in psycho-spiritual terms and the corresponding full integration of the primes with the natural number system.

In fact the two sets of zeros (Zeta 1 and Zeta 2) are associated directly in psycho-spiritual terms with - what with might be referred to as - both the top-down and bottom-up integration of the psyche.

In fact, long before I ever gave attention to the Riemann Hypothesis, I had become convinced of the huge potential importance of the roots of 1 in terms of defining, in holistic mathematical terms, the dynamic structures of development.

It was only later that I realised that these corresponded directly with - what I refer to now as - the Zeta 2 zeros.

However the limitation of my approach was that these zeros essentially described a merely top-down approach to integration, where "lower level" affective are integrated through "higher-level" cognitive structures.

So for proper psychological balance, corresponding bottom-up integration would require that "higher-level" cognitive would now in turn be integrated from the perspective of the "low-level" affective structures In other words true integration would require that both the affective and cognitive functions would themselves be equally developed (with neither dominating each other).

Remarkably, I then gradually discovered that the famous Zeta 1 (i.e. Riemann) zeros perfectly described this latter form of integration.  

So true psychological integration entails a two-way process, whereby from one direction, unconscious meaning can be perfectly converted (i.e. find expression) in a corresponding conscious manner.

Equally from the alternative direction, conscious meaning needs to be perfectly converted in an unconscious manner.

Without the possibility of such perfect conversion (in both directions) it would not be possible to properly relate both conscious and unconscious (as quantitative and qualitative type meaning) in a consistent manner.


It is exactly similar in terms of the mathematical relationship of the primes and natural numbers.

From two opposite perspectives, the essential role of the zeta zeros (Zeta 1 and Zeta 2) is to enable perfect conversion as between the Type 1 and Type 2 aspects of the number system (that represent - in relative terms - their cardinal and ordinal aspects respectively).

Again without the possibility of such conversion (in two directions) it would not be possible to relate numbers consistently with each other (in cardinal or ordinal terms).

However, we are here light years away from the highly reduced quantitative notion of number as representing absolute entities of an abstract kind.

Rather, in truth, the notion of number inherently entails the continual dynamic interaction of both its quantitative and qualitative aspects.

Furthermore the full integrated appreciation of this understanding cannot be divorced from the corresponding psycho-spiritual quest for full integration.

We will address further issues arising from this realisation in the next entry.

Tuesday, February 17, 2015

Mathematical Revolution Required!

I have long emphasised how conventional mathematical interpretation of symbols is so limited with its mere emphasis on the quantitative aspect (that directly concurs with the linear use of reason).
We refer to this as the analytic aspect of interpretation.

Equally, however every mathematical symbol possesses a distinctive qualitative aspect that arises from the direct intuitive recognition of symbols (that indirectly is expressed through a paradoxical i.e. circular use of reason).
We refer to this as the corresponding holistic aspect of interpretation.

The true dynamics of mathematical experience then arise through the combined interaction of both quantitative (analytic) and qualitative (holistic) meaning.

I then have sought through these blog entries to apply this dynamic approach to interpretation of the zeta zeros.

However this quickly led to the realisation that there are in fact two sets of such zeros - equally important - that are dynamically interdependent with each other.

I refer to the first (recognised) set as the Zeta 1 zeros. These concur directly with the Riemann zeros (i.e. non-trivial zeros) of the Riemann Zeta function.

Now once again I will attempt here to highlight the holistic significance of these zeros.

We are accustomed to think of the primes (in quantitative analytic terms) as the independent "building blocks" of the natural number system (≠ 1). So from this perspective, all natural numbers can be expressed as the unique combination of individual primes.

However the unrecognised complementary counterpart to this (in qualitative holistic terms) is the view of the primes, as the corresponding interdependent connections governing the collective relationship of all primes (≠ 1) with the natural number system.

So when we allow for both the distinctive quantitative (analytic) and qualitative (holistic) aspects of the primes, we realise that in dynamic interactive terms, they combine both extreme independence and interdependence in a relative fashion.

So the Zeta 1 (Riemann) zeros from this perspective, can be holistically viewed as representing the complete set of such interdependent connections, which the primes collectively maintain with the natural number system.

In fact I have illustrated in my blog entries how the frequency of Riemann zeros bear a remarkably close relationship with natural number factors.

In other words the accumulated total number of natural number factors (of the composite numbers) up to n (on the real scale), approximates very closely to the corresponding frequency of Riemann zeros up to t (on the imaginary scale) where n = t/2π.

Therefore once again we can see the complementary relationship involved. So we start with the primes (as analytic measures of independence) and then find them related to the complementary holistic notion of interdependence (i.e. as factors of natural numbers).

Thus for meaningful interpretation, in a dynamic interactive manner, the primes and Zeta 1 zeros must be viewed - relatively - in analytic and holistic terms with respect to each other.
So therefore when we view the primes in a quantitative manner, we must then view the Zeta 1 (Riemann) zeros in corresponding qualitative fashion i.e. as an expression of interdependence, that indirectly can then be expressed in an imaginary number manner!

However the true interdependence as between the primes and the zeros is demonstrated by the fact that we can equally validly, switch reference frames, so that now the individual zeros assume a direct quantitative (analytic) meaning and the corresponding primes (with which they are complementary) a qualitative (holistic) interpretation as the collective behaviour of the prime numbers.

So in dynamic interactive terms, a mutual independence and interdependence characterises the primes and zeros (both of which are seamlessly integrated from two directions with each other).

This is just another way of stating the ultimate synchronistic nature of the number system, where neither primes nor zeros precede each other, as it were, but rather both mutually arise in a seamlessly integrated fashion (enabling the subsequent consistent relationship of number in both quantitative and qualitative terms).


The unrecognised - certainly with regard to their significance - set of zeros, relate to what I refer to as the Zeta 2 zeros. Indeed ultimately the Zeta 1 zeros can have no strict dynamic meaning in the absence of the Zeta 2 zeros (and vice versa)!

In some ways these zeros are in fact much easier to understand than the recognised Riemann zeros.

However the insight as to what they represent comes from ordinal rather than cardinal understanding.

As we have seen we typically start by viewing the primes in an individual cardinal manner as quantitative "building blocks" to establish their quantitative relationship with the overall natural number system (again in cardinal terms).

The zeta (i.e. Riemann) zeros then emerge to show that there is something seriously missing with this approach, by providing what in effect is a shadow system of collective holistic relationships (that must meaningfully be interpreted in a complementary qualitative manner).

However, one can also start by attempting to see each individual prime as already necessarily composed of natural numbers (in an ordinal manner). So instead of each natural number being defined quantitatively as the product of cardinal primes, alternatively, in reverse fashion, we define each prime as already ordinally composed in a unique manner by its natural number members.

So for example, 3 is a prime which is uniquely defined (from this perspective) by its 1st, 2nd and 3rd members. Now indirectly we can represent this (in quantitative terms) by obtaining the corresponding 3 roots of 1!

Significantly, when we obtain the prime roots of any number, all of these roots (again ≠ 1) representing its ordinal members, will be unique for this prime .

So the Zeta 2 zeros simply express this unique representation for each prime of its ordinal number members. And this feature of behaviour represents the complementary ordinal counterpart to the established fact that every natural number (≠ 1) in cardinal terms is uniquely composed of prime factors.

So here we start with the qualitative notion of each prime, as representing a shared group (of ordinal number members).

Then the Zeta 2 zeros arise as the indirect quantitative expression (through the prime roots of 1) of this (inherent) qualitative nature.

So once again, we can see an important complementarity here with the Zeta 1 zeros, where the set of zeros - by contrast - carry a qualitative holistic significance.

However as before the frame of reference can be switched, so that the prime (representing dimension) carries a quantitative meaning, while the collection of its ordinal members (represented by roots) is qualitative.  In fact this is simply illustrated by the fact that the sum of roots = 0, implying - literally - that their combined nature carries no quantitative significance!


So within each number and throughout the number system as a whole, we have the two-way interaction of both prime and natural number behavior (in quantitative and qualitative terms).

Thus numbers as individual members and composite groups, contain particle and wave aspects. The particle aspect refers to numbers is both cardinal and ordinal terms, while - relatively -the wave aspect relates to both Zeta 1 and Zeta 2 zeros, which dynamically keep interchanging with each other - ultimately - in a purely relative manner!

Then the inherent nature of number, from this informed dynamic perspective, approaches pure synchronicity (as between its analytic and holistic aspects) in a merely relative manner. This is mediated through the two-way relationship of both prime and natural number aspects.

The great poverty of Conventional Mathematics - in refusing to give any formal recognition to the qualitative (holistic) nature of number - is that it cannot possibly appreciate, within its greatly limited framework, this true dynamic nature of the number system.

So quite simply, nothing short of the most radical revolution possible with respect to Mathematics is now urgently required.

If you are a mathematician reading this, I urge you to wake from your slumbers and bring the "good news" to your colleagues - which unfortunately they may initially see as "bad news" - that our true mathematical journey has scarcely begun!

Thursday, February 5, 2015

Slight Modification

I have commented several times on the true significance of the zeta zeros.

Now once again from my own perspective, there are in fact two complementary sets of these zeros which I term Zeta 1 and Zeta 2. So Zeta 1 refer to the Riemann (non-trivial) zeros. The Zeta 2 by contrast refer to the various roots of unity (excluding 1, which is common to all roots.

Now once again the significance of these roots is that enable seamless conversion as between the Type 1 and Type 2 aspects of the number system.

As we have seen when the Type 1 is associated with the quantitative (analytic) aspect of number behaviour, the Type 2  is then associated, in complementary fashion, with the qualitative (holistic) aspect.

So essentially the zeta zeros enable us to convert from Type 2 to Type 1 format, and equally from Type 1 to Type 2 format.

Without this facility we would have no reason the believe in the consistency of number operations from either the (recognised) quantitative or (unrecognised) qualitative perspectives.

However rather like the state in physics, which conveniently breaks down into macro (relativistic) and micro (quantum) aspects, it is similar in the consideration of numbers.

So from one perspective, we can view each prime as composed of a unique group of natural number members (in ordinal terms).

From the other perspective, we can view the natural numbers as composed of unique groups of prime members (in cardinal terms) .

So from the first perspective we examine the micro nature of each prime (through its natural numbered ordinal members).

From the second perspective we view the macro nature of the natural number system (through its cardinal prime members).

Now from one perspective (where base numbers are viewed in Type 1 terms as quantitative and dimensional numbers as - relatively - in Type 2 terms as qualitative) , the Zeta 2 zeros provide the means of expressing each prime representing a dimension (in Type 2 terms) indirectly in a Type 1 manner.

In this way we are enabled to convert the ordinal members of each prime (as Type 2 qualitative)  indirectly in a Type 1 (quantitative) manner.

Equally, we can convert the cardinal nature of the natural numbers as a whole (as Type 1 ) quantitative, indirectly in (a Type 2) qualitative manner through the Zeta 1 zeros.

From this perspective, the Zeta 2 can be represented as the means of conversion from the Type 2 to Type 1 aspect and the Zeta 1 as the means of conversion from Type 1 to Type 2 aspect respectively.


However when we reverse the frame of reference so that the base numbers are identified in qualitative, and the corresponding dimensional numbers in - relative - quantitative terms, these connections are reversed.

So the Zeta 2 zeros can then be represented as the means of conversion from Type 1 to Type 2 aspect and the Zeta 1 zeros as the corresponding means of conversion from Type 2 to Type 1 aspect.

Thus therefore, depending on perspective, both sets of zeta zeros play a two way role in terms of converting between Type 1 and Type 2 (and Type 2 and Type 1) respectively.

Remember that we can use both the additive and multiplicative approaches to derive numbers.

In terms of the additive approach, each prime number can be defined as the unique sum of its natural number members (in ordinal terms).

In terms of the multiplicative approach, each natural number can then be defined as the unique product of prime number factors (in cardinal terms).

So the Zeta 2 zeros relate directly here to the additive approach and the the Zeta 1 to the multiplicative.

However ultimately all these are derived in a synchronous manner (where relationships are merely relative with everything dependent on everything else).

Thus to conclude the  Zeta 1 and Zeta 2 zeros play an equally important - and truly vital - role in enabling the seamless two-way conversion of number as between its quantitative (analytic) and qualitative (holistic) aspects.