I have mentioned before the
nature of 2-dimensional interpretation which in holistic mathematical terms
defines the various structures (cognitive and affective) that unfold during
Band 3 (Level 1).

Again this means that external and internal aspects of understanding are seen increasingly as complementary (and ultimately identical with each other).

Firstly we have the unfolding of the supersensory structures i.e. where 2-dimensional understanding is posited with respect to the more superficial concrete structures.

Then we have the corresponding negation of such structures (where rigid phenomenal attachment is eroded) leading to a purer nondual contemplative experience.

Then we have the unfolding of the suprarational structures where 2-dimensional understanding is now posited with respect to the deeper formal structures.

Finally we have the "dark night of the soul" which represents the negation of rigid attachment to 2-dimensional structures at both the conceptual formal and empirical sense levels, culminating in much purer (internal) intuitive type experience.

Now in the Functional Equation of the Riemann Zeta Function a direct connection is made as between ζ(s) and ζ(1 – s). This means that when s (as dimensional number) is – 2, 1 – s = 3.

It is fascinating that psychological experience follows a similar dynamic pattern with the "dark night" representing dimensional experience holistically conforming to – 2, now slowly gives way to a new type of experience (that represents the holistic expression of s = 3).

In other words the transition period, that I was referring to in the last two entries, is now followed by - what in fact conforms to - the holistic mathematical interpretation of 3-dimensional experience.

Now remember we are referring to dimensions in their qualitative holistic sense and not in the reduced quantitative manner that is employed in conventional scientific terms!

The holistic nature of the 3 dimensions is indirectly expressed by the 3 roots of 1.

So these 3 roots are 1, – 1/2 + .866i and – 1/2 - .866i.

Now the odd numbered roots are distinctly different from their even numbered counterparts. With the even there is always a direct complementarity of opposites in evidence i.e. where half of the roots are exactly counterbalanced by their negative expressions!

However with odd numbered roots such symmetry is not in evidence. One of the roots i.e. 1 always stands alone to an extent, with the remaining roots forming pairs that are complex conjugates of each other.

So we can see this in the case of the 3 roots in question.

The first root is 1 which stands separately. Then the other two form a pair (with the same real part in each case and the imaginary aspect alternating as between positive and negative).

Now linear activity is defined by the 1st dimension. So therefore with odd-dimensional understanding a linear (analytic) aspect is always involved.

As I stated in my own case ,this was very helpful in enabling me to readapt to the customary activities and relationships consistent with normal living.

However actual experience is never of a merely conscious (i.e. linear) nature. The unconscious is also necessarily involved in the form of projections that indirectly draw attention to the holistic nature of our desires.

Thus though we may focus on the conscious aspect e.g. in buying a new car, indirectly the very desire to purchase this item reflects a deeper holistic desire for fulfilment. So in some ways acquiring the car is therefore seen as fulfilling that purpose.

Now when our activities are conducted largely at the conscious level, we literally become blind to associated holistic (unconscious) elements.

And as we have see our conventional mathematical and scientific notions are formally interpreted in a merely real (i.e. conscious) manner.

However it is important to recognise that even here, every mathematical symbol, strictly speaking, represents an interaction as between both real (conscious) and imaginary (unconscious) aspects.

In this regard, all experience is complex (in a precise holistic mathematical sense). Thus the very pursuit of mathematical truth reflects a deeper unconscious quest for holistic meaning (which mathematical activity is seen to provide in some measure).

However the very nature of linear type activity (coming out of the "dark night") is that the direct conscious aspect has already become significantly eroded.

This therefore implies that the projections coming from the unconscious are much harder to ignore and in fact quickly become the most dominant aspect of experience.

So it is in the very nature of experience that the drive for integration (represented by even numbered stages) is directly followed by a new period of more refined differentiated activity (represented by the odd numbered stages).

Now until perfection is reached - which of course can only be imperfectly approximated in human terms - there will always be some imbalance present in this activity (i.e. where involuntary attachments arise).

If we were to be fully free of involuntary attachment, this would require that as soon as a projection arises, that it would be immediately negated. In this way projections would - like virtual particles - keep dissolving as soon as they arise in consciousness.

If this ideal was achieved with respect to the 2nd and 3rd roots of 1, i.e. – 1/2 + .866i and – 1/2 - .866i, then imaginary aspect would be immediately eroded leaving just the real part of – 1/2 in each case.

Thus when combined the sum of the real parts would be – 1, which would exactly balance with + 1.

However, in practice a considerable amount of temporary difficulties are likely to be experienced in dealing successfully with projections.

Furthermore the transcendent stance that characterised the previous stages will not be effective in coming to terms with them!

Ultimately such projections reflect a limitation in properly listening to the nature of unconscious desires (through repression). This then leads to their involuntary projection (where they become rigidly identified with conscious symbols).

In fact at a deeper level when we obtain prime numbered roots (such as 3) this number will be contained in some form in the resulting root expression.

So for example .866 (which occurs in each root of the conjugate pairing) is the value of √3/2.

What is truly remarkable is that the qualitative notion of prime numbers is very closely related to - what we might refer to as -"primitive" i.e. prime instincts.

Therefore the very mastery of such primitive impulses (emanating from the unconscious as projections) requires on-going development through the various prime numbered dimensions.

However having said this, the early prime numbers such as 2 and 3 are the most important serving as a template for all further primes.

Thus we can see that the very task of understanding the qualitative nature of prime numbered dimensions is the very means of coming to terms with primitive (involuntary) impulses emanating from the unconscious.

Again this means that external and internal aspects of understanding are seen increasingly as complementary (and ultimately identical with each other).

Firstly we have the unfolding of the supersensory structures i.e. where 2-dimensional understanding is posited with respect to the more superficial concrete structures.

Then we have the corresponding negation of such structures (where rigid phenomenal attachment is eroded) leading to a purer nondual contemplative experience.

Then we have the unfolding of the suprarational structures where 2-dimensional understanding is now posited with respect to the deeper formal structures.

Finally we have the "dark night of the soul" which represents the negation of rigid attachment to 2-dimensional structures at both the conceptual formal and empirical sense levels, culminating in much purer (internal) intuitive type experience.

Now in the Functional Equation of the Riemann Zeta Function a direct connection is made as between ζ(s) and ζ(1 – s). This means that when s (as dimensional number) is – 2, 1 – s = 3.

It is fascinating that psychological experience follows a similar dynamic pattern with the "dark night" representing dimensional experience holistically conforming to – 2, now slowly gives way to a new type of experience (that represents the holistic expression of s = 3).

In other words the transition period, that I was referring to in the last two entries, is now followed by - what in fact conforms to - the holistic mathematical interpretation of 3-dimensional experience.

Now remember we are referring to dimensions in their qualitative holistic sense and not in the reduced quantitative manner that is employed in conventional scientific terms!

The holistic nature of the 3 dimensions is indirectly expressed by the 3 roots of 1.

So these 3 roots are 1, – 1/2 + .866i and – 1/2 - .866i.

Now the odd numbered roots are distinctly different from their even numbered counterparts. With the even there is always a direct complementarity of opposites in evidence i.e. where half of the roots are exactly counterbalanced by their negative expressions!

However with odd numbered roots such symmetry is not in evidence. One of the roots i.e. 1 always stands alone to an extent, with the remaining roots forming pairs that are complex conjugates of each other.

So we can see this in the case of the 3 roots in question.

The first root is 1 which stands separately. Then the other two form a pair (with the same real part in each case and the imaginary aspect alternating as between positive and negative).

Now linear activity is defined by the 1st dimension. So therefore with odd-dimensional understanding a linear (analytic) aspect is always involved.

As I stated in my own case ,this was very helpful in enabling me to readapt to the customary activities and relationships consistent with normal living.

However actual experience is never of a merely conscious (i.e. linear) nature. The unconscious is also necessarily involved in the form of projections that indirectly draw attention to the holistic nature of our desires.

Thus though we may focus on the conscious aspect e.g. in buying a new car, indirectly the very desire to purchase this item reflects a deeper holistic desire for fulfilment. So in some ways acquiring the car is therefore seen as fulfilling that purpose.

Now when our activities are conducted largely at the conscious level, we literally become blind to associated holistic (unconscious) elements.

And as we have see our conventional mathematical and scientific notions are formally interpreted in a merely real (i.e. conscious) manner.

However it is important to recognise that even here, every mathematical symbol, strictly speaking, represents an interaction as between both real (conscious) and imaginary (unconscious) aspects.

In this regard, all experience is complex (in a precise holistic mathematical sense). Thus the very pursuit of mathematical truth reflects a deeper unconscious quest for holistic meaning (which mathematical activity is seen to provide in some measure).

However the very nature of linear type activity (coming out of the "dark night") is that the direct conscious aspect has already become significantly eroded.

This therefore implies that the projections coming from the unconscious are much harder to ignore and in fact quickly become the most dominant aspect of experience.

So it is in the very nature of experience that the drive for integration (represented by even numbered stages) is directly followed by a new period of more refined differentiated activity (represented by the odd numbered stages).

Now until perfection is reached - which of course can only be imperfectly approximated in human terms - there will always be some imbalance present in this activity (i.e. where involuntary attachments arise).

If we were to be fully free of involuntary attachment, this would require that as soon as a projection arises, that it would be immediately negated. In this way projections would - like virtual particles - keep dissolving as soon as they arise in consciousness.

If this ideal was achieved with respect to the 2nd and 3rd roots of 1, i.e. – 1/2 + .866i and – 1/2 - .866i, then imaginary aspect would be immediately eroded leaving just the real part of – 1/2 in each case.

Thus when combined the sum of the real parts would be – 1, which would exactly balance with + 1.

However, in practice a considerable amount of temporary difficulties are likely to be experienced in dealing successfully with projections.

Furthermore the transcendent stance that characterised the previous stages will not be effective in coming to terms with them!

Ultimately such projections reflect a limitation in properly listening to the nature of unconscious desires (through repression). This then leads to their involuntary projection (where they become rigidly identified with conscious symbols).

In fact at a deeper level when we obtain prime numbered roots (such as 3) this number will be contained in some form in the resulting root expression.

So for example .866 (which occurs in each root of the conjugate pairing) is the value of √3/2.

What is truly remarkable is that the qualitative notion of prime numbers is very closely related to - what we might refer to as -"primitive" i.e. prime instincts.

Therefore the very mastery of such primitive impulses (emanating from the unconscious as projections) requires on-going development through the various prime numbered dimensions.

However having said this, the early prime numbers such as 2 and 3 are the most important serving as a template for all further primes.

Thus we can see that the very task of understanding the qualitative nature of prime numbered dimensions is the very means of coming to terms with primitive (involuntary) impulses emanating from the unconscious.

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