We address here the holistic mathematical reason as to why the Riemann zeros are postulated to lie on the imaginary line through .5!
So far we have concentrated on the dynamic relationship between whole and part
i.e. in the manner in which number keeps switching - relatively - as between
its quantitative and qualitative (and qualitative and quantitative)
However there is another dynamic interaction that necessarily applies to all
numbers with respect to both external and internal aspects.
Therefore when one refers to a number as existing "out there" in
an objective manner, the - relatively - external aspect of number is involved.
However when one then refers to a number "in here" as a subjective
mental perception, then the corresponding internal aspect is involved.
Now in conventional mathematical terms, the internal aspect is effectively
reduced in terms of the external in an absolute static manner.
So a mathematician - if pressed - might reluctantly concede that one's
actual experience of number entails both the objective notion of number
together with its subjective (mental) interpretation.
However, such dynamics will then be quickly forgotten with number in formal
terms treated as enjoying an absolute objective existence in an external
Therefore it is vital to appreciate that - properly understood - number
represents a dynamic interaction as between both its external and internal
aspects, which in holistic mathematical terms are positive and negative with
respect to each other.
Now the key to such balanced dynamic understanding of number is the realisation
that both conscious and unconscious aspect of understanding are equally
Thus the actual positing of number with respect to its external direction
takes place in a (rational) conscious manner.
The corresponding dynamic negation of this aspect then occurs in an (intuitive)
unconscious manner, which causes a switch in the direction of experience.
So now, the actual positing of number takes place in a corresponding internal
direction as mental interpretation (again in a conscious manner).
And then once more, dynamic negation with respect to this aspect occurs in
an unconscious manner causing another switch in direction.
In this way, one keeps alternating in a balanced manner as between both
external and internal aspects of number appreciation (with both understood in a
So this refined rational appreciation of number - where neither external nor
internal aspect attains dominance - coincides with a corresponding highly
refined intuitive appreciation.
In other words, both the conscious and unconscious aspects of mathematical
appreciation are then brought fully into harmony with each other.
Now once again with respect to the Riemann Hypothesis the non-trivial zeros
are all postulated to lie on the line 1/2 + it (and 1/2 – it) respectively.
These complex numbers refer to
dimensional powers with respect to the natural numbers!
Now when we raise the first number
i.e. 1 to 1/2 i.e. 11/2, we get – 1.
The clue here then in holistic
mathematical terms is that the proper appreciation of the Riemann Hypothesis
(i.e. in a dynamic interactive manner) requires that both unconscious
(holistic) and conscious (analytic) interpretation be equally involved.
The requirement that all the zeros lie on the line through .5, points directly to the fact that in dynamic interactive terms, ultimately number is equally both physical and psychological in nature i.e. as representing both (objective) fact and (subjective) mental interpretation respectively.
In fact when one is able to
appreciate this necessary dynamic balance as between the external and internal
aspects of all numbers then the pure intuitive nature of numbers, as energy
states, can be directly appreciated in a psycho spiritual manner. This then
complements the corresponding realisation coming from comparison of the zeros
with quantum chaotic states in physics that the zeros represent (physical)
The deeper implications of all this
is that properly understood, number is already always inherent in phenomena
(with respect to their most fundamental encoding) in both physical and
psychological terms. Thus the supposed abstract existence of numbers –
that has dominated mathematical thinking now for millennia – represents but a fundamentally
Therefore for one to approximate experientially
as close as possible to the truth enshrined in the Riemann Hypothesis, then it
is necessary that both conscious (analytic)) and unconscious (holistic) modes
of understanding be employed in the most refined and balanced manner.
This relates firstly to both the
external and internal aspects of all number phenomena; secondly it also relates
to the quantitative and qualitative aspects (with respect to whole/part interactions)
of the same number phenomena.
Such understanding - at its most
refined level - then forms the thinnest partition possible as between the
(manifest) world of form and the (unmanifest) ineffable origins of all
So number - when appropriately
understood - most perfectly bridges this mysterious gap that divides (phenomenal)
form from (spiritual) emptiness.