In yesterday’s entry, I concluded by demonstrating the holistic synchronistic nature of the number system.
In other words a two-way mutually interdependent relationship exists as between the primes and natural numbers, which is of a holistic synchronistic nature where ultimately both number aspects are simultaneously determined in an ineffable manner.
Now the great problem with the conventional mathematical approach is that it is 1-dimensional in nature, thereby unambiguously seeking solely analytic interpretation of relationships in a one-directional manner.
So again, the conventional mathematical approach, by viewing numbers in cardinal terms, attempts to explain natural numbers solely in terms of the primes.
However, when one properly appreciates the corresponding ordinal approach to number, the relationship as between the primes and natural numbers is inverted with each prime now uniquely defined in a natural number manner.
So the position with the conventional mathematical approach is - as I have stated before – akin to one who can only identify left turns at a crossing.
So when one is travelling north up a straight road and encounters a crossing, the left turn (at this crossing) can be unambiguously identified; likewise when one travelling S from the opposite direction and again encounters the same crossing, once more the left turn can be unambiguously identified.
Therefore, through operating in an analytic manner with respect to independent polar reference frames in both cases, the two turns at the crossroads can be unambiguously identified as left!
However when we view these crossroad directions in a holistic manner (where N and S directions are simultaneously viewed as interdependent), then they are understood as directly opposite to each other. So of one turn is designated as left, then the other is thereby (relatively) right and alternatively if a turn is designated as right the other turn is then necessarily left in this context.
So analytic understanding is identified with the attempt to understand mathematical relationships in a static 1-dimensional manner (i.e. within an isolated fixed polar frame of reference).
Holistic understanding (at a minimum) entails the corresponding attempt to understand such relationships in a dynamic 2-dimensional manner (i.e. within two interacting frames of reference).
Just as we can attempt to approach the crossroads from two isolated directions (N and S) that are initially considered independent of each other, likewise we can approach the relationship between the primes and the natural numbers from two opposite directions - which I term Type 1 and Type 2 - that again are initially considered independent of each other.
However, when we attempt to view both directions in a holistic manner as interdependent, then we appreciate the purely paradoxical nature of both (analytic) sets of findings. It is at this point that we can then clearly appreciate that the ultimate relationship between both is of a purely synchronistic nature that is ineffable.
Now again with respect to the crossroads example, it is obvious how both analytic and holistic type appreciation are involved. So provided that the crossroads is approached from just one direction, we can unambiguously identify in analytic terms both left and right turns in an absolute manner.
However when we view the crossroads holistically as being approached from two directions simultaneously, what is absolutely left and right is rendered purely paradoxical. So combining both analytic and holistic appreciation, both left and right directions now have a merely arbitrary meaning depending on the relative context.
Likewise in truth it is similar with all mathematical relationships.
These can be given an - apparent - absolute interpretation within single isolated poles of reference in an analytic manner.
However, what is not properly appreciated within the present conventional approach to Mathematics is that all such absolute relationships possess a mirror image alternative explanation within an equally valid opposite polar frame of reference.
Then when both of these opposite interpretations are then properly realised as dynamically interdependent with each other, true holistic appreciation of an intuitive synchronistic nature emerges.
The most fundamental mathematical relationship relates to that as between the primes and natural numbers.
When properly interpreted in analytic terms we can approach this relationship in quantitative terms from two opposite directions (Type 1 and Type 2 respectively).
Then when we realise the dynamic interdependence of both sets of relationships, true holistic appreciation emerges of their mutual synchronicity.
Expressed in perhaps an even simpler manner, analytic interpretation relates to the quantitative aspect of mathematical relationships, which can be of either a Type 1 or Type 2 nature considered within single isolated poles of reference.
Holistic appreciation by contrast relates directly to the qualitative aspect of mathematical relationships, and arises from clear appreciation of the mutual dynamic relative interdependence of both Type 1 and Type 2, within complementary reference frames.
When one views Conventional Mathematics from this perspective, it is clearly seen - despite all its great achievements - as simply not fit for purpose.
Not alone is the vitally important holistic aspect of appreciation completely unrecognised (in formal terms) but even from an analytic perspective, the Type 2 aspect of quantitative appreciation is likewise effectively ignored.
One day it will be clearly recognised that both the analytic (quantitative) and holistic (qualitative) appreciation of all mathematical relationships are of equal importance and strictly have no meaning in the absence of each other.
And nowhere is this realisation more important than in appreciation of the true dynamic nature of the number system.