Indeed as
the true implication of the Riemann Hypothesis are so fundamental and far
reaching for Mathematics, in effect the present has been used in many
respects to overlap with material covered in that latter blog.

Though in
some senses a bit vague, the word “spectrum” is now widely used in physics to
refer - in any context - to a variety of related phenomena,

Perhaps its
best known use is in connection with the “spectrum of light” whereby in
passing through a prism, the various wavelengths of natural light can become manifest as
different colours. And of course the colours of the rainbow produce a beautiful
natural example of this phenomenon!

Then when
it was realised that natural light represented just one small band with respect
to electromagnetic energy, this spectrum notion was widened to include all its
possible bands from very high frequency gamma radiation at one end to extremely
long frequency radio waves at the other.

The
notion of light in physical terms invites comparison with the corresponding
notion of light in a psycho-spiritual context so that human development itself
represents a spectrum of all possibilities with respect to the capacity for
enlightenment.

Such
enlightenment is directly related to the holistic aspect of intuition.

As we have
seen mathematical activity itself, in dynamic terms, necessarily entails an interaction
between reason and intuition. Indeed it will be readily admitted by mathematicians,
that where especially creative work is involved, that intuition necessarily
plays an important role.

However in
formal terms, mathematical results are then presented in a merely reduced
rational manner (with the important holistic aspect of intuition edited
completely out of the story).

What is not
readily recognised however is in a somewhat complementary manner to the
electromagnetic spectrum, that the full range of intuitive possibilities allowed
by the psycho-spiritual spectrum is much greater than generally imagined.

Indeed just
as natural light forms just one small band of the electromagnetic energy
spectrum, likewise - what we might call - natural intuition (that supports the linear
use of reason in Conventional Mathematics) comprises just one small band of the
full range of intuitive possibilities available.

Detailed explorations
of higher intuitive states have been undertaken in all the major spiritual contemplative
traditions.

However
what has been almost completely missing has been the attempt to study the
relevance for Mathematics of such psycho-spiritual development.

So from a
very early age, I could somehow see this area as my special goal in life, i.e. to marry the
holistic possibilities opened up through spiritual contemplation, to the mapping
of a new mathematical understanding (consistent with such development).

I then
realised that inherent in the very notion of number, is a marvellous way of
precisely detailing all possible stages of development in a holistic
mathematical manner.

Some 20
years ago I wrote an online book “The Number Paradigms” that basically
outlines my earlier findings on this matter.

What struck
me forcibly at the time is this!

From a quantitative
perspective, they are now indeed many recognised number types that play a huge
role in Conventional Mathematics.

So I
outlined firstly what I termed the original numbers 1 and 0. Next on the list
we have the primes, then the natural numbers and the integers (positive and
negative).

These are
followed by the important rational numbers.

Then we move
on to irrational number (algebraic and transcendental), the imaginary and
complex nos. and the transfinite.

Now this is
the key point!

In
conventional mathematical terms all these are understood within what may be correctly referred to - qualitatively speaking - as the rational paradigm.

So, while we
recognise a wide range of number types in quantitative analytic terms, we
recognise just one i.e. rational in a qualitative holistic manner. And as I
have repeatedly stated in my blog entries the very nature of this rational
paradigm is to reduce all qualitative meaning in merely quantitative terms!

Thus we have
sectioned off just one very small restricted band of possible development
(relating to specialised rational understanding) and defined Mathematics
exclusively in terms of this band.

It is
quite akin to sectioning off the small band corresponding to natural light and refusing to recognise the validity of
all other energy wavelengths on the electromagnetic spectrum!

Indeed the parallels
are very striking! It would be extremely difficult for one identifying
exclusively with the present mathematical paradigm to even appreciate what is
being said here.

When one
literally “sees” exclusively in accordance with the natural intuition that
informs conventional mathematical understanding, any appeal to different types of mathematical reality (based on holistic intuition
relating to other bands on the spectrum) literally has no resonance.

Though my
thinking on these matters have become considerably more refined in the
last 20 years or so, I still would see the basic position taken in “The Number
Paradigms” as fully sound.

Putting it
simply, when we adopt a true holistic (i.e. qualitative) mathematical
perspective, then all of human development - and in complementary terms physical
evolution - can be fruitfully seen as representing a number spectrum.

So giving a
brief outline we have firstly the lower stages of development.

The
basic point here is that these are marked by confusion as between conscious and
unconscious processes.

So the
first task is to successfully differentiate conscious from unconscious
understanding. The earlier number types mentioned, original, prime, natural and
integers in qualitative holistic terms are then associated with these stages.

The middle stages
represent the specialisation of differentiated conscious understanding (free
of holistic unconscious confusion). Conventional Mathematics - par excellence
- represents an extreme in terms of this understanding which of course in
qualitative terms is associated with the rational numbers.

The higher
stages then represent the process of now developing in a mature way the
unconscious holistic aspect of understanding, which is qualitative terms is associated
with irrational (algebraic and transcendental) and imaginary numbers.

One of the interesting
findings I made at the time was that the most refined form of holistic
understanding (where phenomena are now of a highly transparent and fleeting
nature) are associated with transcendental structures of an imaginary
nature.

As these
directly relate to the very nature of the Zeta 1 (non-trivial) zeros, let me
briefly elaborate.

Imaginary
in a qualitative holistic sense, refers to the indirect expression (in a refined
conscious) manner of what pertains directly to unconscious meaning.

So when we
are understanding in a refined imaginary manner we can quickly recognise all phenomenal
projections (though invested in consciously recognised objects) as directly expressive
of holistic (unconscious) meaning.

Transcendental
refers to a highly refined form of
understanding where objects are neither interpreted exclusively in a linear (conscious) nor circular (unconscious) manner, but in terms of
the common relationship - which is ultimately ineffable - as between both.

So the
ability to immediately interpret projections (as imaginary) in a
transcendental manner, requires the most refined spiritual development possible
(consistent with experience in the phenomenal realm).

Now the significance
of this is that the zeta zeros necessarily unfold in the very first instants of phenomenal
creation.

When number
is appropriately understood in a dynamic interactive manner, it is no longer
considered in abstract (merely rational) terms, but rather as the most intrinsic
encoding of all phenomena (both in physical and psychological terms).

Without
this encoding, enabling both quantitative and qualitative aspects of reality to
coherently interact, no phenomena could ever become manifest.

Thus to
properly appreciate what is - literally most primitive or prime - with respect
to earliest creation, requires ultimately the most developed spiritual
experience possible.

In the
truest sense the zeta zeros come closest in the phenomenal realm to serving as
the first bridge from the nothingness preceding physical evolution.

Therefore
their mature understanding likewise requires reaching as close as possible to
that final spiritual bridge to the ineffable.

The zeta zeros
in fact represent the holistic (unconscious) counterpart to the analytic (conscious)
aspect of the primes.

We look on
the primes as perhaps the most rigid and immutable in absolute terms.

In fact, as is the nature of all experience,
they cannot be totally absolute, though yet coming closest in the phenomenal
realm to reaching this standard.

However as the
zeta zeros represent the holistic (unconscious) shadow of the primes, they approximate closest at the opposite extreme to the most purely relative - and
inherently dynamic - expression possible of the number system.

So the
number system is the original and most important spectrum (with respect
to both physical and psychological aspects). And of course it is an inherently
dynamic spectrum that necessarily vibrates through the medium of physical and psychological interactions)..

The idea
that this system is some fixed abstract entity frozen in space and
time is just the product of a false and limited type of understanding.

In fact the
number system represents all the possibilities for the evolution of phenomenal
creation (as its inherent encoding in quantitative and qualitative terms).

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