^{th}band of the overall spectrum of development (that I outlined again briefly yesterday).

Actually
this is where I would make another slight modification with respect to the
position I outlined some five years ago!.

I referred
then to this as representing the first of the radial bands of development,
where linear (rational) and circular (intuitive) modes of understanding are
comprehensively integrated in a mature manner.

However I
would now consider on reflection that this band should be referred to more
accurately as pre-radial.

Indeed
there is an interesting - and not entirely accidental - connection here with
another finding that I outlined yesterday with respect to cyclic primes.

And as this
whole episode illustrates the nature of holistic - as opposed to analytic -
behaviour well, I will relate it here.

Many years
ago when I was developing my holistic approach to number types, I began to
realise that there were strong connections as between the inherent dynamic
nature of prime numbers and the earliest stages of infant behaviour (i.e.
primitive instinctive behaviour).

Now the
very nature of such blindly instinctive behaviour is that neither conscious nor
unconscious aspects of personality have yet been properly differentiated.

This means
in effect that the infant still directly confuses the (holistic) unconscious
desire for meaning with (specific) conscious phenomena.

And when
extreme confusion is evident (as at the earliest stage of development) this means that
phenomena can enjoy no permanency but rather a very fleeting temporary
existence (which immediately becomes eroded in memory).

At a deeper
level because of the direct confusion of conscious and unconscious, the infant
cannot yet provide a dimensional background of space and time within which to
experience object perceptions.

In other
words we have a direct confusion here of qualitative (unconscious) and
quantitative (conscious) aspects of experience.

Indeed this
has intimate connections to the nature of sub-atomic particles which enjoy but
a fleeting - and ultimately undetectable - existence in space and time.

So once
again with such particles, the holistic dimensional context of their existence
becomes largely inseparable from their specific identity (as distinct objects).

Thus we
could very accurately describe such sub-atomic particles as relating to prime
spacetime (where prime is now understood in its inherent holistic dynamic
sense).

Now using
holistic mathematical notions, I could see that the essence of the prime notion in dynamic terms, entails the (ultimate) identity of both linear (specific)
and circular (holistic) notions of identity.

Coming from
this holistic perspective, I later became fascinated - as I have stated
elsewhere - with the nature of cyclical primes (where successive digits are
taken in a circular - rather than linear - manner).

So for
example in linear terms, the digits 142857 can only be traced forward in one
unambiguous manner and then backward (i.e. 758241) again in an unambiguous
manner.

However in
a circular fashion we can have 6 distinctive circular orderings of digits
i.e.

142857,
428571, 285714, 857142, 571428 and 714285. Also in this circular context forward
and backward lose their meaning.

I then
examined the possibility of numbers that could uniquely satisfy both linear and
circular notions of order.

This
entailed that they could only contain two digits.

So for
example in base 2, 01 and 10 satisfy these criteria. The two possibilities in
terms of linear definition are 01 (forward) and 10 (backward). Likewise these
are the same two possibilities in a circular manner (i.e. 01 and 10).

Finally -
to make it meaningful - I imposed the condition that in obtaining the difference
of the two possible numbers that we arrive back at our starting number.

So 10 – 01
in binary = 01 (which is our original number).

Now
interestingly no such 2-digit numbers exist in base 10 that satisfy these
requirements.

However I
then established the bases where it would be possible and discovered that in
all these cases the original number required represented the number 3 (as a
cyclic prime).

I then
found that when converted into our denary system that these numbers represented
the successive terms in the octagonal series,

1, 8, 21,
40, 65,…..

(Indeed 01
is the cyclic prime 3 expressed with respect to base 2 which in denary terms
then constitutes the first term in the series!)

So here is
an interesting mathematical result (which I have never seen mentioned anywhere)
which came about entirely from pursuing a holistic line of enquiry.

And, though
it has never been my main concern to do so, I have managed to make many other
- for me - original (though very simple) numerical discoveries directly through following holistic notions.

Now the
relevance of all this to my “map of development” is briefly as follows.

Basically
this map is framed in a holistic mathematical manner to show through the
various bands of development the relationship between linear (conscious) and
circular (unconscious) development.

Each of the
bands is dub-divided into 3 main levels (i.e. principal stages).

Thus I
delineate 21 levels in all (for the entire map).

Furthermore
the map is based on dynamic linkages within and between levels in a horizontal,
vertical and diagonal manner (in accordance with the geometrical nature of the
8 roots of unity).

Now 21 in
base 8 is 25 (which represents the cyclic prime 3 in base 8).

And course
21 is the 3

^{rd}octagonal (i.e. related to 8) number.
So it is
remarkable how the very structure of this map of development fits in so well with
subsequent numerical discoveries.

The meaning
of holistic is closely related to integrated! And this is why I have so much
confidence in the ideas that I express because they all spring naturally from a holistic mathematical manner of approach (which in formal
terms is entirely unrecognised within Conventional Mathematics).

Now there
are close similarities with the 3 levels of the 3

^{rd}band (higher) and the corresponding 3 levels of the 5^{th}band (which I now refer to as pre-radial).
In some
ways it can be likened to climbing a mountain.

In
spiritual contemplative terms the “higher” band is generally associated with
the “ascent” in a transcendent sense.

As we have
seen 2

^{nd}band is associated with the specialisation of differentiated (conscious) ability. In (linear) rational terms, Conventional Mathematics represents an extreme in such specialisation in what can be referred to as dualistic interpretation (i.e. where polar reference frames are clearly separated).
So the 3

^{rd}band represents the gradual breakdown of dualistic type understanding as one moves continually towards nondual (i.e. intuitive) type appreciation of a holistic kind. The very notion of nondual refers to the fact that polar opposites (such as objective and subjective) are now seen as interdependent and ultimately identical.
In holistic
terms the 1st level of this band relates to (algebraic) irrational type
understanding. This essentially relates to the reduction of (nondual) higher
dimensional intuitive type meaning in a
(dualistic) 1-dimensional rational manner.

So for
example 2-dimensional understanding is characterised by the holistic intuitive
fusion, from the (unconscious) recognition of the interdependence of the
opposite polarities (that condition all experience). Now (just like the square root of a number)
we can attempt to express this in a linear rational manner as the
complementarity of opposite poles which - literally - appears paradoxical
(i.e. irrational) from this perspective. .

So the main
problem with the 1st level is a persistent conflict whereby nondual meaning
becomes unduly identified with its reduced rational means of expression.

The 2

^{nd}level of the band then relates to (transcendental) irrational understanding which is of a more refined nature.
One no
longer attempts to express meaning in a reduced linear fashion but rather in a
subtler dynamic manner as the relationship between linear (conscious) and
(circular) unconscious aspects.

However
this implies a much greater transience with respect to phenomenal experience as
rigid identification with objects would imply a (reduced) merely conscious
understanding.

So by this
level understanding is very holistic indeed with all meaning seen as entailing
the interaction of conscious and unconscious.

The 3

^{rd}level (transfinite) would be largely concerned with removing remaining rigidities with respect to the dynamic interpretation of phenomena evolving (in a more purely nondual contemplative type of experience.
Then having
reached the contemplative mountain top, rather like one on the top of Mount
Everest one looks around so as to attain greater perspective from this new
vantage point.

So the 4

^{th}band (with its three extremely refined “levels”) represents the specialisation of pure holistic (intuitive) consciousness.
Now the 5

^{th}band (the pre-radial levels) represents the descent in immanent terms from the top as one gradually tries to maturely integrate dualistic type understanding with a permanent contemplative vision.
In fact I
would maintain that most of my own efforts in the last number of years
represent a preliminary pre-radial (level 1) interpretation of reality.

This
entails in psychological terms the emerging ability to express in a necessarily dualistic manner the
overall relationship throughout development as between linear (conscious) and
circular (unconscious) type reality (with its
corresponding complement in physical terms of the analytic and
holistic aspects respectively of reality.)

However I
must stress that in formal terms, science and mathematics operate from the
specialised development of merely the 2

^{nd}band (where no formal recognition of the holistic aspect exists).
So we hear
a great deal for example about analytic science (and indeed mathematical
analysis). But where is the equal emphasis on holistic science (and
mathematical holism)?

And even
more subtly, where is the emphasis on mathematics and science as necessarily
entailing a dynamic interaction as between its analytic and holistic elements?

However, in
certain respects an intense focus on the Riemann Hypothesis has led me on to the
next descent (level 2) where the dualistic implications of (algebraic)
irrational understanding become more apparent.

Quite
simply what this entails - but which only recently has become obvious to me - is
that the very means by which we enabled to make ordinal distinctions at a
dualistic level - literally - has its roots in higher dimensional
understanding.

For example
in the case of relating two objects with respect to each other, which
involves the simplest type of qualitative distinction, implicitly the holistic
interpretation of the two roots of 1 are entailed.

Now of
course, we do this automatically in experience (which is another way of saying
that we remain totally unconscious of what is holistically involved).

However the
very simplest ordinal distinction we can make relates directly to unconscious
(rather than conscious) ability. And as ordinal necessarily interpenetrates with cardinal, without such unconscious ability it would
likewise not be possible to make any cardinal distinctions (of a quantitative nature).

So once we
grasp this, we can no longer hope to conduct Mathematics in a merely
(conscious) rational manner, as this greatly distorts its true nature.

Thus the
pre-radial stages are largely concerned with now bringing the unconscious to
light in showing how it needs to be properly integrated with conscious
understanding for meaningful phenomenal interpretation of reality.

Indeed, the famed zeta zeros (which I refer to as Zeta 1)
represent the direct unconscious basis of our everyday quantitative
interpretation of objects.

However
this lies at an even deeper level to that of ordinal understanding. Therefore
the task of bringing it successfully to light (which represents the more
advanced level 3 pre-radial understanding) is much more difficult to access in
an intuitively obvious manner.

In other
words when you can intuitively recognise as fully obvious that the zeta zeros
represent the necessary unconscious infrastructure for all quantitative
distinctions (at a conscious level), then you are operating from level 3 of
pre-radial understanding.

As for
myself, though I know that this must necessarily be so, I have only yet had a
partial rather than full intuitive realisation of its obvious nature.