Once again, by its very nature it requires going beyond the 1-dimensional standpoint of standard Mathematics where all symbols are given a merely quantitative (analytic) interpretation in absolute terms.
In the holistic approach, while symbols do preserve their independent analytic identity, they now possess a relative - rather than absolute - quantitative meaning. Most importantly they additionally acquire a new - hitherto unrecognised - qualitative identity which properly relates to interdependence with respect to relationships.
So from the holistic perspective, all symbols possess a - relative - independent identity in quantitative terms, combined with a relative interdependent identity from a qualitative perspective. And the very essence of the holistic approach is the integration of both of these perspectives!
Thus it is utterly pointless trying to judge the value of the holistic mathematical aspect from within the limited confines of what is formally accepted as valid Mathematics.
Rather I suggest that its great potential value can be better appraised through the manner, for example, that it can give a much more coherent explanation of the true nature of our number system!
I have long been fascinated by the nature of cyclic primes finding their properties quite magical!
Cyclic primes relate to the (repeating) decimal structure of the reciprocals of certain prime numbers.
Now we operate of course in a base 10 number system and not all primes are cyclic in this base. For example, 5 clearly is not cyclic. So the reciprocal of 5 is 1/5 and in a base 10 system this is .2!
However in the base 8 system for example, 5 is indeed fully cyclic with the repeating decimal sequence of 1463. Fully cyclic in this context implies that the number of digits in the repeating decimal sequence is 1 less than the number in question!
So indeed given an appropriate number base, all primes - and only primes - can be given a full cyclic sequence.
The first and best know cyclic prime in the base 10 system is 7.
So the reciprocal of 7 results in the repeating decimal sequence of the six digits 142857.
Now one of the remarkable properties of this number is that when we multiply by 2, 3, 4, 5 and 6 the same digits keep repeating with the circular order remaining unchanged.
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142
The circular nature of such numbers becomes even more remarkable when we consider the larger cyclic primes.
For example 97 is a cyclic prime. So when we multiply its 96 repeating digits by 2, 3…..96 the circular order of these 96 digits will remain fully preserved!
So there is a wonderful magical order of a circular nature involved here which we can all admire!
And this represents just one fascinating aspect of the ordered structure of such primes!
However, within Conventional Mathematics though we may indeed marvel at the unique number nature of cyclic properties, because of the lack of an accepted holistic dimension, the deeper significance of all this for the prime numbers is completely missed.
Now once again in conventional linear terms, the prime numbers (which have no constituents factors other than the numbers themselves and 1)) are treated as the most independent of all numbers, indeed as the essential building blocks of the cardinal number system!
So 7 is a prime number!
Written more fully (in a Type 1 manner) this is 71.or to spell it out even more clearly 7 + 1
Now the reciprocal of 7 can be written as 7 – 1 = 1/7.
As we have seen, holistic interpretation starts with 2-dimensional - rather than 1-dimensional interpretation - where its structure is indirectly expressed (in a quantitative manner) by the corresponding two roots of 1, i.e. + 1 and – 1.
However - and this is the very essence of holistic interpretation - corresponding to these two numbers + 1 and – 1, is a distinctive qualitative dimensional interpretation.
So as we have seen the holistic meaning of + is - literally - to posit in experience, which refers directly to conscious type recognition. However the holistic meaning of – is to (dynamically) negate (what has been posited in conscious terms). And this is the very means in experience through which unconscious recognition takes place!
So therefore when we look at prime numbers in 2-dimensional holistic terms, we recognise that by their very nature they contain two extremes.
Thus from the conscious perspective (with respect to its quantitative nature) they do indeed appear as the most independent of all numbers serving as the basic building blocks of the cardinal number system (in a linear manner).
However when we look at prime numbers from the unconscious perspective (with respect to their qualitative nature) they now appear as the most interdependent of all numbers serving as the unique basis for the ordinal number system (in a circular manner).
So the true mystery of prime numbers relates to this marked independence with respect to their cardinal identity, coupled with an equally marked interdependence with respect to their ordinal identity.
Thus the very nature of prime numbers is inherently dynamic entailing the interaction of these two extreme tendencies.
Therefore once again we cannot hope to understand the nature of prime numbers - and indeed our number system - in mere quantitative terms (based on analytic type interpretation).
Rather the true nature of prime numbers entails twin aspects that are relatively analytic (quantitatively independent) and holistic (qualitatively interdependent) with respect to each other.
When seen properly in this dynamic context, the corresponding nature of the famed zeta zeros is easy to appreciate as a set of numbers that establishes the mutual identity of both aspects (quantitative and qualitative). The Zeta 2 - which are not even conventionally recognised - uniquely establishes this within each prime number; the Zeta 1 then establishes this identity for the number system as a whole.
When I read the conventional literature on the Riemann Hypothesis, there are constant references as to how mathematicians are so surprised with its connections to the physical world of quantum theory.
Well I am not at all surprised as from my dynamic appreciation of the nature of prime numbers, I always assumed that this was necessarily the case!
Likewise we have the same surprise expressed in relation to the fact that the zeta zeros strongly resemble some spectrum relating to the vibration of physical frequencies.
Well again I am not surprised as I have long considered this to be necessarily the case.
Indeed I would go considerably further in recognising a complementary (as yet unrecognised) psycho-spiritual spectrum for all these zeros (which in the future will play an extremely important scientific role with respect to the most advanced meditation practices).
Indeed properly understood the physical nature of the zeros cannot be properly understood in the absence of their corresponding psychological appreciation (as both aspects are fully complementary).
And as to what is ultimately vibrating, the answer is simply the number system itself.
You see, the existing paradigm - based on 1-dimensional interpretation - of the number system existing in some abstract unchanging space is ultimately completely flawed.
When we look on the number system is a limited reduced manner - as we have been doing for millennia - it certainly appears to have an absolute unchanging nature.
However this is not as it truly is: in other words properly understood, in a dynamic interactive manner, number serves as the deepest inherent encoding of all physical and psychological processes in creation (in quantitative and qualitative terms).
Thus as soon as creation vibrates in its first instants, the number system itself vibrates with respect to the relationship between its quantitative and qualitative aspects (which necessarily begin to separate to a degree with the birth of phenomena in space and time)!
I have been aware for some 50 years now of the need for a massive paradigm shift with respect to Mathematics. And when I say massive, I mean massive as the whole discipline now needs to be rebuilt on completely new foundations (where holistic is fully recognised and then integrated with analytic interpretation and where the role of the unconscious in mathematical understanding is likewise fully recognised and then integrated with the conscious aspect).
Though I realised this long before becoming acquainted with the Riemann Hypothesis, growing acquaintance with this problem has only served to strongly confirm my initial diagnosis.