It is important to distinguish linear and circular, in holistic mathematical terms, from real and imaginary (which in many ways are closely related).

Initially, linear relates - in a scientific context - to understanding according to either/or logic. Here the crucial polar opposites, which condition all phenomenal experience of reality (internal/external, whole/part and form/emptiness) are clearly separated in interpretation. This then enables rational linkages to be made in an unambiguous sequential fashion. So Conventional Science is characterised by linear (1-dimensional) interpretation.

Such linear understanding is directly posited in a real manner. To posit in this dynamic context (which entails the holistic meaning of +) simply means to make conscious. Real in a holistic mathematical context means understanding that is of a direct conscious nature.

So Conventional Science is linear, corresponding to real rational interpretation in a positive manner.

However in dynamic experiential terms one can negate (as well as posit) phenomena. The very significance of such negation (-) is that it thereby opens the door to unconscious (intuitive) type appreciation.

Now, such intuitive appreciation strictly relates to the generation of spiritual energy (necessary to fuel all conscious dynamics). Just as the positive and negative polarities (in the form of matter and anti-matter) annihilate each other on contact, creating physical energy, likewise the positive and negative polarities of phenomenal understanding likewise "annihilate" each other creating spiritual (intuitive) energy.

Intuition is generated directly therefore in a non-rational manner (through negation of phenomenal constructs).

However when one then later rationally attempts to clarify the nature of such understanding it appears as two-dimensional. This new two-dimensional understanding is based on an alternative circular logical system of interpretation relating to the complementarity - and ultimate identity - of the fundamental polar opposites in experience.

Therefore though we separate polar opposites such as internal and external in (rational) linear interpretation, we recognise these same opposites as complementary, and ultimately identical, from an (intuitive) circular perspective.

So linear understanding is 1-dimensional; circular is 2-dimensional. The structure here of the 2nd dimension of understanding corresponds to the 2nd root in quantitative terms of 1 (i.e. 1 raised to the power of 1/2).

So there is an intimate link as between a qualitative dimension (as D) and its corresponding quantitative root (as 1/D).

Now when the dimension is 1, both D and 1/D are identical. This implies that with linear (1-dimensional) interpretation, no distinction is made as between quantitative and qualitative interpretation!

However for all other integer values of D, a clear distinction is preserved as between quantitative and qualitative (implying the combined use in interpretation of both linear and circular appreciation).

So both/and logic is inherently circular in nature. It is also, as we have seen 2-dimensional (when confined to two opposite poles).

The question then arises as to how such understanding might be converted into linear expression.

Thus to reduce the 2nd to the 1st dimension, we obtain the square root of the 2-dimensional expression (- 1). And this represents the precise holistic mathematical equivalent to the notion of an imaginary number in analytic terms.

So imaginary understanding represents circular type intuitive understanding, indirectly expressed in a linear manner. What this means in effect is that such intuitive understanding therby becomes embodied in conscious phenomena (that are understood in a linear manner).

Properly understood, all phenomena are complex in nature (with real and imaginary aspects).

The real aspect relates to direct conscious appreciation of a local kind.

However the imaginary aspect by contrast relates directly to unconscious appreciation of a holistic nature (indirectly mediated through the local object).

For example if one was to purchase a house, both aspects of understanding would be important. Real conscious appreciation would be used to identify and precisely locate the house. However such a purchase could also fulfil unconscious longings of a holistic kind. So one might well - in this context - refer to one's "dream" house - reflecting such unconscious meaning (which is mediated through the same object).

So real and imaginary, implicitly, always interact in understanding (even in the most rigorous scientific interpretation). When the focus is on analysis, the real aspect is of paramount significance. When the focus by contrast is on qualitative synthesis, the imaginary aspect is now critical. Unfortunately - as we have seen - because of the current solely conscious focus of scientific interpretation, this latter "imaginary" aspect is thereby reduced to the real.

Now if we go back to the definition of the string we can precisely illustrate what is involved.

The conventional (linear) real definition relates to the fact that the patterns of vibrations of the physical 1-dimensional string (representing the fundamental stuff of matter) create all possible matter particles.

However the new (linear) imaginary definition relates to the fact that the patterns of vibrations of the same string (representing the fundamental stuff of psychological interpretation) create all possible dimensions for such interpretation. And as physical and psychological notions are complementary in holistic terms, this equally implies that it is the vibrations of the second aspect of the string that create all possible physical dimensions of reality (i.e. spacetime).

So the string has in fact two intimately related aspects (that are real and imaginary with respect to each other). Indeed we could rightly refer to this as the complex string!

Now if we follow this a little further we will see why differing dimensions of qualitative interpretation are so important.

At the linear 1-dimensional level, only the real positive aspect of the string (as the fundamental "stuff" of all matter) will be recognised.

Then at the 2nd dimension of interpretation the real negative aspect now also becomes apparent as one recognises the role of both conscious (reason) and unconscious (intuition) in the dynamics of understanding. The means - in complementary physical terms - that the string is now given both a specific (local) and a holistic (collective) identity.

Then at the 4th dimension of interpretation, the imaginary aspect of the string unfolds. So at this level of appreciation, one understands the string in complex terms (with both real and imaginary aspects). The imaginary aspect here corresponds to the holisic (circular) identity of the string indirectly expressed in a linear manner.

So as we reach higher dimensions in qualitative terms, actual interpretation with respect to physical reality becomes ever more refined with new aspects of understanding unfolding (which remain hidden at lower dimensions). And it is not just psychological interpretation that changes in this manner but likewise physical reality itself (which directly corresponds to such interpretation).

Thus one could validly say: not alone do we have a uniquely different psychological interpretation of reality corresponding to each new "higher" dimension (the range of which is infinite) but equally we have a uniquely different physical reality!

However, to be even more precise, we should recognise that all these interpretative dimensions (with their corresponding physical realities) are but appearances, or - if one prefers - secondary realities.

True primary reality is non-phenomenal and ineffable, existing continually in the absolute present moment. Phenomenal reality (of matter and spacetime) always serves therefore as a relative expression of what is primary.

So a key insight once more is that the basic relationship as between part (as physical particles) and whole (as the dimensions to which they are relate) are as real to imaginary.

This brings us back to the the crucial point.

To properly investigate physical reality, we need to incorporate a complex rational approach. Such an approach combines real interpretation (suited for analytic interpretation of a quantitative kind) with imaginary interpretation (suited for corresponding holistic interpretation of a qualitative nature).

And because real and imaginary are so closely related to linear and circular, we can also express this complex rational approach in another way (which is highly revealing).

As we know the (analytic) binary system that is so important in IT is based on just two digits 1 and 0 that potentially can be used to encode all information.

However there also exists a corresponding (holistic) binary system that potentially can be used to encode all transformation processes.

So a comprehensive binary system - with potential power to encode with respect to both information and transformation - has both analytic (linear) and holistic (circular) components.

Once more, the fundamental relationship as between whole and part is based on the distinction as between linear and circular understanding (or alternatively real and imaginary).

Put another way the basic relationship as between matter and spacetime requires such a distinction!

The reason why present String Theory is finding it so difficult to properly incorporate spacetime in its approach is because of its inherently reductionist nature. In other ways it is still attempting to explain the whole (dimensions) in terms of the parts (strings) as physical particles. And as long as it persists with this approach it will continually fail to achieve a satisfactory resolution.

So the quest for a coherent TOE along the present reductionist lines is not attainable.

However a much greater prize might yet be won if it leads finally to incorporation of a true holistic aspect in physics based - literally - on recognition of its hidden qualitative dimensions.

With such a realisation, science could then be truly revolutionised in a manner greatly exceeding all previous developments.

## Friday, January 22, 2010

## Tuesday, January 19, 2010

### Another Interesting Connection

I will comment here on one more interesting connection that I can make as between the analytical findings of string theory and my parallel findings in holistic terms.

As the energy of a string increases, its vibration intensifies. However this process does not continue indefinitely. Beyond a certain point additional energy with respect to the string may lead - rather than a further increase in vibration - to the lenghtening of the string. And theoretically its length can then continue without limit!

Now there is a fascinating possible holistic counterpart which had puzzled me for many years.

Once again, this can initially be expressed with respect to psychological development. However - as always - because physical and psychological reality are complementary, it has - I believe - an intimate bearing on the holistic interpretation of strings.

As we have seen normal development in our Western culture largely plateaus with specialisation of 1-dimensional (linear) understanding. However where authentic contemplative development occurs, understanding can potentially reach several higher dimensions.

What happens therefore is than an intensification in spiritual energy takes place with respect to the psychological string (of 1-dimensional understanding) which leads to the generation of new interpretative models of reality (of an increasingly circular nature).

Now if this process continues in a pure contemplative direction, then we thereby have an intensification in spiritual energy greatly increasing vibration (in the dynamic interaction of dynamic polarities).

However there is a limit to such pure contemplative development - which - ultimately becomes unbalanced and unhealthy if one does not learn to return to dealing appropriately with the world of form.

So for development to continue in a sustainable fashion, at a certain point the desire for emptiness must give way to a realisation of the need to equally embrace the world of phenomenal form. And when this occurs there is a considerable restoration of linear type understanding.

Thus with mature radial development a spiritual contemplative does not remain detached from the world of form, but engages with it in an ever more committed manner (demanding specialised linear understanding).

Recently when dealing with the Riemann Hypothesis, I made the holistic connection as between the values of the zeta function (for negative whole integer values of s) and corresponding states of psychological development.

Interestingly the behaviour of the function in this respect supports my position here. In fact the value of the function for negative odd values of steadily diminishes up to s = - 5) and then gradually starts to increase, gradually at first, then more rapidly in a process that continues without limit.

The holistic connection I made here is that this provides evidence for the initial shrinkage with respect to linear understanding (at higher dimensions of understanding) before then changing in the opposite direction.

So I would see the holistic physical counterpart to this psychological finding relating to the behaviour of strings.

Remember strings naturally relate to the prime behaviour of matter. And as the Riemann Hypothesis is intimately connected with prime number behaviour, it therefore seems justifiable that the holistic interpretation of the Riemann Hypothesis would have deep relevance for the dynamic interpretation of strings.

As the energy of a string increases, its vibration intensifies. However this process does not continue indefinitely. Beyond a certain point additional energy with respect to the string may lead - rather than a further increase in vibration - to the lenghtening of the string. And theoretically its length can then continue without limit!

Now there is a fascinating possible holistic counterpart which had puzzled me for many years.

Once again, this can initially be expressed with respect to psychological development. However - as always - because physical and psychological reality are complementary, it has - I believe - an intimate bearing on the holistic interpretation of strings.

As we have seen normal development in our Western culture largely plateaus with specialisation of 1-dimensional (linear) understanding. However where authentic contemplative development occurs, understanding can potentially reach several higher dimensions.

What happens therefore is than an intensification in spiritual energy takes place with respect to the psychological string (of 1-dimensional understanding) which leads to the generation of new interpretative models of reality (of an increasingly circular nature).

Now if this process continues in a pure contemplative direction, then we thereby have an intensification in spiritual energy greatly increasing vibration (in the dynamic interaction of dynamic polarities).

However there is a limit to such pure contemplative development - which - ultimately becomes unbalanced and unhealthy if one does not learn to return to dealing appropriately with the world of form.

So for development to continue in a sustainable fashion, at a certain point the desire for emptiness must give way to a realisation of the need to equally embrace the world of phenomenal form. And when this occurs there is a considerable restoration of linear type understanding.

Thus with mature radial development a spiritual contemplative does not remain detached from the world of form, but engages with it in an ever more committed manner (demanding specialised linear understanding).

Recently when dealing with the Riemann Hypothesis, I made the holistic connection as between the values of the zeta function (for negative whole integer values of s) and corresponding states of psychological development.

Interestingly the behaviour of the function in this respect supports my position here. In fact the value of the function for negative odd values of steadily diminishes up to s = - 5) and then gradually starts to increase, gradually at first, then more rapidly in a process that continues without limit.

The holistic connection I made here is that this provides evidence for the initial shrinkage with respect to linear understanding (at higher dimensions of understanding) before then changing in the opposite direction.

So I would see the holistic physical counterpart to this psychological finding relating to the behaviour of strings.

Remember strings naturally relate to the prime behaviour of matter. And as the Riemann Hypothesis is intimately connected with prime number behaviour, it therefore seems justifiable that the holistic interpretation of the Riemann Hypothesis would have deep relevance for the dynamic interpretation of strings.

### Cornucopia of Riches

I would like to briefly extend further here the holistic mathematical approach to the qualitative interpretation of strings that has the scope to open up new areas of refined understanding (not possible through the conventional approach).

We will start with the very notion of a p-brane. In conventional terms this is defined in a (merely) positive manner. So for example when we speak of a string, it is defined positively in 1-dimensional terms.

Now, in holistic mathematical terms every possible mathematical relationship that we define in conventional terms can be given a holistic (mathematical) interpretation with application to both physical and psychological reality (in complementary fashion).

This implies therefore that a string can be holistically defined with respect to the negative (as well as positive) 1st dimension

Well what does this all mean!

It perhaps is easier to approach the manner initially from a psychological context.

In holistic mathematical terms, to posit is to simply make conscious; to negate - by contrast - is to make unconscious. Now the important thing to remember is that - from a dynamic experiential perspective - both conscious and unconscious are necessarily involved in all understanding. Translated into scientific appreciation this entails that rational interpretation corresponds directly with the positive direction, whereby intuitive appreciation by contrast corresponds - relatively - with the negative.

Though conventional science formally ignores this point, mere rational explanation - of itself - does not constitute meaningful interpretation. Without corresponding ability to - literally - (intuitively) see what is implied by such rational linkages, understanding cannot arise.

Thus in the dynamic holistic interpretation of the string, the positive dimension (+ 1) corresponds directly with the rational aspect and the negative dimension (- 1) directly with the corresponding intuitive aspect of understanding respectively.

Thus for full appreciation of the string - from the interpretive standpoint - both the positive and negative linear understanding i.e. of the 1st dimension is required.

However in dynamic interactive terms both physical and psychological aspects of reality are necessarily complementary. Therefore the clear implication is that a proper definition of the string (in physical terms) likewise requires both the positive and negative signs with respect to the 1st dimension.

What this implies is that string cannot be properly understood, as if it is somehow independent of the rest of reality. In other words while maintaining a certain independence (with respect to the positive sign) this is likewise negated through establishing a necessary interdependence with reality (in overall terms).

Put another way - whereas the string as object is directly defined through the positive aspect - the string as dimension is defined through the negative aspect.

In this way, it can be perhaps appreciated that to give a string a proper dynamic interactive meaning that we must necessarily define it with respect to both positive and negative directions (of the 1st dimension).

So the standard linear interpretation of conventional science (which recognises solely the positive direction) is necessarily therefore of a reduced nature!

Actually this can be highly instructive in thereby arriving at the true meaning implied by a 0-brane (zero brane).

It is now postulated in a new development of string theory (Matrix Theory) that zero branes are in fact the most fundamental entities (from which all strings, membranes and higher branes are ultimately derived).

In dynamic experiential terms, the 0 dimension is best expressed through the equal positing and negating of any higher dimension.

So if we confine ourselves to strings, we can define a zero brane as the equal positing and negating of the 1st dimension.

So 1 - 1 = 0.

Again what does this actually imply?

Well! Once more it is perhaps easier to initially approach the matter from a psychological perspective.

In contemplative terms we cannot associate spirit with either rational (+) or intuitive (-) understanding separately. Rather the possibilities for pure spiritual awareness are maximised where an equal balance as between both is maintained.

We can see this best in geometrical terms as the reconciliation of line and circle (relating to linear and circular understanding). This reconciliation takes place at the midpoint of the circle (which is also the midpoint of the line diameter). So when this state is attained (whereby linear and circular understanding are now perfectly integrated in ineffable manner) one experiences reality in zero dimensional terms (which rightly represents a state of pure spiritual emptiness).

Now if we apply this understanding in complementary fashion to physical reality, it implies that the fundamental starting point of reality occurs when both linear and circular aspects of reality are indistinguishable. What this means in effect is that matter (as potentially existing) has yet no independent (linear) or equally interdependent (circular) capacity. Put another way matter yet has no existence as discernible form; likewise dimensions with respect to physical reality have no meaning.

Thus the zero brane actually implies a state of pure physical emptiness (as potential for existence of phenomenal form).

However this physical understanding of emptiness is indistinguishable in experience from the corresponding experience of spiritual emptiness (both relating to the present moment).

So one can only truly understand the origin of the physical universe as nothing (with potential for all form) through the corresponding realisation of the psychological destiny of this universe (as the realisation of form).

So properly recognised both of these aspects comprise the pure mystical experience of spiritual union.

Once again a merely linear interpretation leads to a reductionist notion of zero-branes (whereby the illusion is maintained that material notions can somehow grasp the essence of nothingness).

We will start with the very notion of a p-brane. In conventional terms this is defined in a (merely) positive manner. So for example when we speak of a string, it is defined positively in 1-dimensional terms.

Now, in holistic mathematical terms every possible mathematical relationship that we define in conventional terms can be given a holistic (mathematical) interpretation with application to both physical and psychological reality (in complementary fashion).

This implies therefore that a string can be holistically defined with respect to the negative (as well as positive) 1st dimension

Well what does this all mean!

It perhaps is easier to approach the manner initially from a psychological context.

In holistic mathematical terms, to posit is to simply make conscious; to negate - by contrast - is to make unconscious. Now the important thing to remember is that - from a dynamic experiential perspective - both conscious and unconscious are necessarily involved in all understanding. Translated into scientific appreciation this entails that rational interpretation corresponds directly with the positive direction, whereby intuitive appreciation by contrast corresponds - relatively - with the negative.

Though conventional science formally ignores this point, mere rational explanation - of itself - does not constitute meaningful interpretation. Without corresponding ability to - literally - (intuitively) see what is implied by such rational linkages, understanding cannot arise.

Thus in the dynamic holistic interpretation of the string, the positive dimension (+ 1) corresponds directly with the rational aspect and the negative dimension (- 1) directly with the corresponding intuitive aspect of understanding respectively.

Thus for full appreciation of the string - from the interpretive standpoint - both the positive and negative linear understanding i.e. of the 1st dimension is required.

However in dynamic interactive terms both physical and psychological aspects of reality are necessarily complementary. Therefore the clear implication is that a proper definition of the string (in physical terms) likewise requires both the positive and negative signs with respect to the 1st dimension.

What this implies is that string cannot be properly understood, as if it is somehow independent of the rest of reality. In other words while maintaining a certain independence (with respect to the positive sign) this is likewise negated through establishing a necessary interdependence with reality (in overall terms).

Put another way - whereas the string as object is directly defined through the positive aspect - the string as dimension is defined through the negative aspect.

In this way, it can be perhaps appreciated that to give a string a proper dynamic interactive meaning that we must necessarily define it with respect to both positive and negative directions (of the 1st dimension).

So the standard linear interpretation of conventional science (which recognises solely the positive direction) is necessarily therefore of a reduced nature!

Actually this can be highly instructive in thereby arriving at the true meaning implied by a 0-brane (zero brane).

It is now postulated in a new development of string theory (Matrix Theory) that zero branes are in fact the most fundamental entities (from which all strings, membranes and higher branes are ultimately derived).

In dynamic experiential terms, the 0 dimension is best expressed through the equal positing and negating of any higher dimension.

So if we confine ourselves to strings, we can define a zero brane as the equal positing and negating of the 1st dimension.

So 1 - 1 = 0.

Again what does this actually imply?

Well! Once more it is perhaps easier to initially approach the matter from a psychological perspective.

In contemplative terms we cannot associate spirit with either rational (+) or intuitive (-) understanding separately. Rather the possibilities for pure spiritual awareness are maximised where an equal balance as between both is maintained.

We can see this best in geometrical terms as the reconciliation of line and circle (relating to linear and circular understanding). This reconciliation takes place at the midpoint of the circle (which is also the midpoint of the line diameter). So when this state is attained (whereby linear and circular understanding are now perfectly integrated in ineffable manner) one experiences reality in zero dimensional terms (which rightly represents a state of pure spiritual emptiness).

Now if we apply this understanding in complementary fashion to physical reality, it implies that the fundamental starting point of reality occurs when both linear and circular aspects of reality are indistinguishable. What this means in effect is that matter (as potentially existing) has yet no independent (linear) or equally interdependent (circular) capacity. Put another way matter yet has no existence as discernible form; likewise dimensions with respect to physical reality have no meaning.

Thus the zero brane actually implies a state of pure physical emptiness (as potential for existence of phenomenal form).

However this physical understanding of emptiness is indistinguishable in experience from the corresponding experience of spiritual emptiness (both relating to the present moment).

So one can only truly understand the origin of the physical universe as nothing (with potential for all form) through the corresponding realisation of the psychological destiny of this universe (as the realisation of form).

So properly recognised both of these aspects comprise the pure mystical experience of spiritual union.

Once again a merely linear interpretation leads to a reductionist notion of zero-branes (whereby the illusion is maintained that material notions can somehow grasp the essence of nothingness).

## Monday, January 18, 2010

### String Theory - a new myth for our age

It is amazing how in life if one waits long enough that things tend to come full circle. And this is true of the development of science itself.

In earlier times, science was much influenced by the intrusion of confused holistic notions of a spiritual nature that significantly impeded proper analysis of physical behaviour.

For example in the middle ages, largely to serve theological requirements, the Earth was believed to be the centre of the solar system. Therefore when Galileo supported an alternative viewpoint (based on objective empirical analysis), he was forced to detract his opinions so as to preserve religious orthodoxy.

So it is only in the last 400 years or so - largely as a result of the monumental contribution by Newton - that science has successfully differentiated itself from subjective beliefs based directly, or indirectly, on religious notions.

Indeed one could argue that the prevalence of the aether (which Einstein finally discarded in the early 20th century), represented an important remnant of such confused understanding i.e. where a holistic spiritual notion influences the nature of analytic investigation.

In this context it is interesting to compare an earlier story of the nature of creation from that emerging from modern science (in the form of string theory).

In the Christian Bible we are told in Genesis (the first book of the Old Testament) that God created the world in 6 days. Now as an acceptable scientific account, amenable to modern tastes, this account is greatly lacking from an analytic perspective. However it is really designed to convey a deeper qualitative (holistic) meaning.

6 was well known in the ancient world as the first perfect number. It is no accident therefore that God creates the world in 6 days as this is designed to convey the deeper significance of His creation as perfect.

So the story of creation in the Bible properly constitutes a myth (though admittedly of a significant nature). And it is the very nature of myths that explanatory symbols that are used are designed to convey holistic - rather than strict analytic - meaning.

Now when we contrast the Bible story with a modern attempt - such as string theory - to explain the nature of creation, we are presented with the opposite extreme.

In other words - precisely because of its analytic exactness - science has now managed to divest itself almost completely of holistic qualitative notions.

However this had led to a significant new problem (which is not properly recognised).

Analysis by its very nature is suited to partial investigation i.e. where part of a system can be investigated (in isolation from the whole).

Thus when we attempt to investigate the whole framework (as distinct from its parts), scientific analysis loses its effectiveness. Indeed - by its very nature - it can only attempt this task in a reductionist fashion i.e. by attempting to reduce the whole to its partial elements.

Because of the ambitious designs of string theory to obtain a whole explanation of reality through formulation of a Theory of Everything (TOE) it is especially open to this reductionist charge.

Thus what we are seeing now with string theory is precisely the opposite problem that affected earlier mythical accounts of creation.

Whereas the design of these accounts was to to principally provide a holistically satisfying explanation (conveying qualitative meaning), the design of a modern scientific account - such as string theory - is to provide an analytically satisfying explanation (of a quantitative nature).

However just as the former accounts were greatly lacking from a satisfactory analytic perspective, string theory is also greatly lacking from a satisfactory holistic perspective.

In other words string theory as it stands cannot provide any coherent intuitive account of the nature of its concepts and this is a truly major issue that has not been properly faced.

Even with respect to standard mathematics, mere rational explanation does not constitute meaningful understanding.

For example if I rationally demonstrate the Pythagorean Theorem to a student, actual understanding does not materialise until the appropriate intuitive connections are likewise made. Only then can then student literally "see" what the Theorem is about.

Fortunately however, at the macro level of appreciation, intuitions are designed to conform to accepted common sense notions of reality (dictated by linear type understanding).

Likewise with respect to string theory, mere rational explanation does not constitute meaningful understanding. However the big difference here is that the confirming intuition to literally "see" what is meant by the theoretical explanations is not actually provided by linear type understanding.

And string theory - as presently constituted - has no means of providing this qualitative intuitive component.

So for example when Edward Witten announces that string theory fundamentally operates in 11 - rather than 10 dimensions - this strictly represents an abstract mathematical finding (based on linear understanding). However it lacks any true qualitative coherence with the holistic nature of physical reality (which at the required level of appreciation requires going substantially beyond 1-dimensional interpretation).

At a deeper level, the implication is that science has now come full circle.

Initially - as we have seen - analytic investigation was greatly impeded through being confused with rigid holistic notions (based on religious beliefs).

Especially since the arrival of Newton, science has made enormous strides with respect to analytic understanding through successfully differentiating itself from confused holistic notions. And of course this aspect of science will continue to flourish for some considerable time to come!

However in the attempt to deal with universal type explanations (pertaining properly to the whole of reality), the limitations of analytic science are exposed.

Therefore I would see that we are at the dawning of a great new stage in scientific understanding where we can now at last begin to deal with universal holistic type issues in a successful manner. However this will require an entirely different qualitative approach that is utterly distinct from present appreciation.

Then eventually when this holistic side of science has been properly appropriated, a truly comprehensive approach to science can then at last unfold (combining specialised analytic and holistic type appreciation).

In earlier times, science was much influenced by the intrusion of confused holistic notions of a spiritual nature that significantly impeded proper analysis of physical behaviour.

For example in the middle ages, largely to serve theological requirements, the Earth was believed to be the centre of the solar system. Therefore when Galileo supported an alternative viewpoint (based on objective empirical analysis), he was forced to detract his opinions so as to preserve religious orthodoxy.

So it is only in the last 400 years or so - largely as a result of the monumental contribution by Newton - that science has successfully differentiated itself from subjective beliefs based directly, or indirectly, on religious notions.

Indeed one could argue that the prevalence of the aether (which Einstein finally discarded in the early 20th century), represented an important remnant of such confused understanding i.e. where a holistic spiritual notion influences the nature of analytic investigation.

In this context it is interesting to compare an earlier story of the nature of creation from that emerging from modern science (in the form of string theory).

In the Christian Bible we are told in Genesis (the first book of the Old Testament) that God created the world in 6 days. Now as an acceptable scientific account, amenable to modern tastes, this account is greatly lacking from an analytic perspective. However it is really designed to convey a deeper qualitative (holistic) meaning.

6 was well known in the ancient world as the first perfect number. It is no accident therefore that God creates the world in 6 days as this is designed to convey the deeper significance of His creation as perfect.

So the story of creation in the Bible properly constitutes a myth (though admittedly of a significant nature). And it is the very nature of myths that explanatory symbols that are used are designed to convey holistic - rather than strict analytic - meaning.

Now when we contrast the Bible story with a modern attempt - such as string theory - to explain the nature of creation, we are presented with the opposite extreme.

In other words - precisely because of its analytic exactness - science has now managed to divest itself almost completely of holistic qualitative notions.

However this had led to a significant new problem (which is not properly recognised).

Analysis by its very nature is suited to partial investigation i.e. where part of a system can be investigated (in isolation from the whole).

Thus when we attempt to investigate the whole framework (as distinct from its parts), scientific analysis loses its effectiveness. Indeed - by its very nature - it can only attempt this task in a reductionist fashion i.e. by attempting to reduce the whole to its partial elements.

Because of the ambitious designs of string theory to obtain a whole explanation of reality through formulation of a Theory of Everything (TOE) it is especially open to this reductionist charge.

Thus what we are seeing now with string theory is precisely the opposite problem that affected earlier mythical accounts of creation.

Whereas the design of these accounts was to to principally provide a holistically satisfying explanation (conveying qualitative meaning), the design of a modern scientific account - such as string theory - is to provide an analytically satisfying explanation (of a quantitative nature).

However just as the former accounts were greatly lacking from a satisfactory analytic perspective, string theory is also greatly lacking from a satisfactory holistic perspective.

In other words string theory as it stands cannot provide any coherent intuitive account of the nature of its concepts and this is a truly major issue that has not been properly faced.

Even with respect to standard mathematics, mere rational explanation does not constitute meaningful understanding.

For example if I rationally demonstrate the Pythagorean Theorem to a student, actual understanding does not materialise until the appropriate intuitive connections are likewise made. Only then can then student literally "see" what the Theorem is about.

Fortunately however, at the macro level of appreciation, intuitions are designed to conform to accepted common sense notions of reality (dictated by linear type understanding).

Likewise with respect to string theory, mere rational explanation does not constitute meaningful understanding. However the big difference here is that the confirming intuition to literally "see" what is meant by the theoretical explanations is not actually provided by linear type understanding.

And string theory - as presently constituted - has no means of providing this qualitative intuitive component.

So for example when Edward Witten announces that string theory fundamentally operates in 11 - rather than 10 dimensions - this strictly represents an abstract mathematical finding (based on linear understanding). However it lacks any true qualitative coherence with the holistic nature of physical reality (which at the required level of appreciation requires going substantially beyond 1-dimensional interpretation).

At a deeper level, the implication is that science has now come full circle.

Initially - as we have seen - analytic investigation was greatly impeded through being confused with rigid holistic notions (based on religious beliefs).

Especially since the arrival of Newton, science has made enormous strides with respect to analytic understanding through successfully differentiating itself from confused holistic notions. And of course this aspect of science will continue to flourish for some considerable time to come!

However in the attempt to deal with universal type explanations (pertaining properly to the whole of reality), the limitations of analytic science are exposed.

Therefore I would see that we are at the dawning of a great new stage in scientific understanding where we can now at last begin to deal with universal holistic type issues in a successful manner. However this will require an entirely different qualitative approach that is utterly distinct from present appreciation.

Then eventually when this holistic side of science has been properly appropriated, a truly comprehensive approach to science can then at last unfold (combining specialised analytic and holistic type appreciation).

## Saturday, January 16, 2010

### Prime Time (and Prime Space)

An important part of my integral approach to science relates to the fundamental role that holistic appreciation of the various number types can play.

In this holistic classification of numbers, I refer firstly to - what I call - the original numbers (1 and 0), then 2 and the other prime numbers, followed by the natural numbers (and integers) then the rationals, followed by the irrationals (algebraic and transcendental), the imaginary and complex and the transfinite.

Of course all of these are well recognised in standard analytic terms. However their true holistic significance has been greatly missed.

In what follows we will be confining ourselves to the holistic interpretation of the original, prime and natural nos.

The original numbers 1 and 0 have their holistic equivalents as oneness and nothingness respectively. Now, we must realise that we are here referring to dynamic - rather than static - notions. Nothingness in this context thereby refers to a physical (and spiritual) void as nothing (in phenomenal terms) which equally implies the potential for all phenomena of form. In the Eastern tradition this notion of nothingness is generally referred to as emptiness.

The critical point is that the ultimate origin (and destiny) of the Universe is often described in terms of the holistic interpretation of the original numbers.

Physical creation emerges from nothingness (holistic 0); likewise its ultimate goal and fulfilment is generally referred to in terms of spiritual oneness (holistic 1).

And as these notions relate to a continual present moment, they both ultimately coincide. So pure contemplative attainment can equally be referred to as spiritual emptiness (of nothingness) or alternatively as spiritual oneness.

What is fascinating is that the very symbols we use to refer to 1 and 0 respectively are the line and the circle. Thus in Western culture - where rational (linear) notions hold greater sway - the ultimate state is generally referred to as oneness; by contrast in Eastern traditions - with a greater recognition of intuitive (circular) notions, the ultimate state - by contrast - is generally referred to as a void (or emptiness).

So the pure ultimate state of the universe - either in terms of its physical origins - or alternatively its psychological destiny (in spirit) relates to a present moment (continually renewed) that is best referred to as the coincidence of oneness and nothingness.

In other words in this ultimate state, form (as independent phenomena) cannot be distinguished from emptiness (as the interdependence of all phenomena).

Thus using geometrical notions, we have here the pure coincidence of both linear and circular notions.

We can then learn a great deal about the possible origins of the physical universe with reference to corresponding development of the psychological universe in a baby infant.

In the beginning the (linear) conscious is not differentiated from (circular) unconscious; therefore neither the experience of phenomena (nor equally of dimensions of space and time) is possible.

Now because of the complementarity of physical and psychological, this likewise means that with the Universe, in the beginning (linear) form through distinctive phenomena, is not distinguishable from (circular) dimensions through interdependent links as between phenomena. So in the original state, one cannot make a distinction as between matter and spacetime (as neither enjoys an independent identity).

In psychological terms, experience of reality commences through the initial separation of conscious and unconscious. This then leads to the birth of duality (i.e. holistic 2).

In corresponding physical terms, actual phenomena come into being through the separation of linear and circular aspects of reality. Here, the most primitive phenomena attain a certain limited independence (while retaining an extremely high level overall of confused interdependence). This likewise creates a starting dimensional context (of space and time) for emerging phenomena.

So the birth of space and time in the Universe (as the holistic context for phenomena) coincides with the birth of distinct phenomena.

However, it is vital to realise that both phenomenal and dimensional characteristics of reality always have a merely relative validity, emerging necessarily from a continual absolute present moment.

Now the earliest infant experience of form (and dimensions) is - literally - of an extremely primitive kind. And in the understanding of "primitive", remarkably we find the true holistic qualitative context for appreciation of prime numbers.

With primitive infant understanding, conscious and unconscious - though not entirely confused - still remain greatly enmeshed with each other.

So, the primitive experience of an object (as conscious) immediately becomes identified with its holistic dimensional background (as unconscious). In this way the infant is unable to maintain a detached view of any object. Rather, because dimensions become immediately confused with objects, a quick collapse takes place in phenomenal events. So initially, experience of phenomena is extremely short-lived with no object constancy possible. This only materialises when the conscious achieves a greater degree of separation from the unconscious!

Again it is remarkably similar in physical terms. The first existence of objects is literally - in holistic mathematical terms - of a prime nature; likewise the dimensional context in which these objects exist is also prime. So the first phenomena exist in prime spacetime (with both aspects inextricably intertwined).

So the very essence of prime behaviour in qualitative terms is that both object phenomena and related dimensions (of space and time) remain tightly interwoven with each other. Therefore phenomena cannot maintain any constancy (which would require a stable background of space and time).

Now all this is deeply relevant to the reality we associate with string theory, for in a precise holistic mathematical sense, strings comprise the prime constituents (of both matter and dimensions).

If we look briefly now at the conventional understanding of prime numbers in mathematics it is quite revealing, for once again only the linear component is evident.

In other words prime numbers are looked on as the basic building blocks of the natural numbers. In like manner in physical terms, strings (as prime components) are looked on as the basic building blocks of all matter.

However there is an equal circular aspect to prime numbers. This relates to the fact that in their general distributional behaviour, they display a remarkable interdependence with the natural nos.

So from one valid analytic (linear) perspective, the prime nos. are the most independent structures, serving as the building blocks of all natural numbers.

However from the equally valid holistic (circular) perspective, the prime nos. are the most interdependent, being totally dependent on the natural nos. for their precise distribution. So as well as each prime number enjoying individual structure (as independent), overall prime numbers share a general state (as interdependent)

This then implies that there is a key ingredient missing from the conventional physical perspective on strings. Whereas the linear perspective is very prominent (i.e. with strings as structure forming the basic building blocks of matter) there is no equal appreciation of their important circular aspect as state. Here the overall behaviour of strings (relating directly to their dimensional characteristics) intimately depends on natural phenomena (to which they are related).

Thus a two-way relationship therefore necessarily exists as between strings (as prime constituents of matter) and dimensions (in the general relationship of strings to matter). Whereas it may be valid to say that (manifest) physical particles result from unique dynamic vibrations of a string, the actual dimensional properties of strings (in general) result in turn from their overall relationship to such physical particles.

All along I have maintained that one cannot divorce the (physical) properties of nature from the (psychological) dimensions employed for its interpretation.

As I have repeatedly stated, conventional science is based on 1-dimensional interpretation and is thereby - literally - linear in nature.

And in this view the basic ingredient or "stuff" of everything in nature is a string which again is - literally - envisaged as a 1-dimensional line.

So we can see here a remarkable correspondence as between physical matter and its corresponding psychological interpretation both of which are 1-dimensional!

Thus the starting point for a more balanced dynamic treatment (with respect to both physical understanding and its psychological mode of interpretation) is to explicitly combine linear and circular aspects.

And this is done through combining the present conventional understanding of strings (linear) with several higher qualitative dimensions of understanding (circular) thereby providing many unique interpretations of string reality.

In this holistic classification of numbers, I refer firstly to - what I call - the original numbers (1 and 0), then 2 and the other prime numbers, followed by the natural numbers (and integers) then the rationals, followed by the irrationals (algebraic and transcendental), the imaginary and complex and the transfinite.

Of course all of these are well recognised in standard analytic terms. However their true holistic significance has been greatly missed.

In what follows we will be confining ourselves to the holistic interpretation of the original, prime and natural nos.

The original numbers 1 and 0 have their holistic equivalents as oneness and nothingness respectively. Now, we must realise that we are here referring to dynamic - rather than static - notions. Nothingness in this context thereby refers to a physical (and spiritual) void as nothing (in phenomenal terms) which equally implies the potential for all phenomena of form. In the Eastern tradition this notion of nothingness is generally referred to as emptiness.

The critical point is that the ultimate origin (and destiny) of the Universe is often described in terms of the holistic interpretation of the original numbers.

Physical creation emerges from nothingness (holistic 0); likewise its ultimate goal and fulfilment is generally referred to in terms of spiritual oneness (holistic 1).

And as these notions relate to a continual present moment, they both ultimately coincide. So pure contemplative attainment can equally be referred to as spiritual emptiness (of nothingness) or alternatively as spiritual oneness.

What is fascinating is that the very symbols we use to refer to 1 and 0 respectively are the line and the circle. Thus in Western culture - where rational (linear) notions hold greater sway - the ultimate state is generally referred to as oneness; by contrast in Eastern traditions - with a greater recognition of intuitive (circular) notions, the ultimate state - by contrast - is generally referred to as a void (or emptiness).

So the pure ultimate state of the universe - either in terms of its physical origins - or alternatively its psychological destiny (in spirit) relates to a present moment (continually renewed) that is best referred to as the coincidence of oneness and nothingness.

In other words in this ultimate state, form (as independent phenomena) cannot be distinguished from emptiness (as the interdependence of all phenomena).

Thus using geometrical notions, we have here the pure coincidence of both linear and circular notions.

We can then learn a great deal about the possible origins of the physical universe with reference to corresponding development of the psychological universe in a baby infant.

In the beginning the (linear) conscious is not differentiated from (circular) unconscious; therefore neither the experience of phenomena (nor equally of dimensions of space and time) is possible.

Now because of the complementarity of physical and psychological, this likewise means that with the Universe, in the beginning (linear) form through distinctive phenomena, is not distinguishable from (circular) dimensions through interdependent links as between phenomena. So in the original state, one cannot make a distinction as between matter and spacetime (as neither enjoys an independent identity).

In psychological terms, experience of reality commences through the initial separation of conscious and unconscious. This then leads to the birth of duality (i.e. holistic 2).

In corresponding physical terms, actual phenomena come into being through the separation of linear and circular aspects of reality. Here, the most primitive phenomena attain a certain limited independence (while retaining an extremely high level overall of confused interdependence). This likewise creates a starting dimensional context (of space and time) for emerging phenomena.

So the birth of space and time in the Universe (as the holistic context for phenomena) coincides with the birth of distinct phenomena.

However, it is vital to realise that both phenomenal and dimensional characteristics of reality always have a merely relative validity, emerging necessarily from a continual absolute present moment.

Now the earliest infant experience of form (and dimensions) is - literally - of an extremely primitive kind. And in the understanding of "primitive", remarkably we find the true holistic qualitative context for appreciation of prime numbers.

With primitive infant understanding, conscious and unconscious - though not entirely confused - still remain greatly enmeshed with each other.

So, the primitive experience of an object (as conscious) immediately becomes identified with its holistic dimensional background (as unconscious). In this way the infant is unable to maintain a detached view of any object. Rather, because dimensions become immediately confused with objects, a quick collapse takes place in phenomenal events. So initially, experience of phenomena is extremely short-lived with no object constancy possible. This only materialises when the conscious achieves a greater degree of separation from the unconscious!

Again it is remarkably similar in physical terms. The first existence of objects is literally - in holistic mathematical terms - of a prime nature; likewise the dimensional context in which these objects exist is also prime. So the first phenomena exist in prime spacetime (with both aspects inextricably intertwined).

So the very essence of prime behaviour in qualitative terms is that both object phenomena and related dimensions (of space and time) remain tightly interwoven with each other. Therefore phenomena cannot maintain any constancy (which would require a stable background of space and time).

Now all this is deeply relevant to the reality we associate with string theory, for in a precise holistic mathematical sense, strings comprise the prime constituents (of both matter and dimensions).

If we look briefly now at the conventional understanding of prime numbers in mathematics it is quite revealing, for once again only the linear component is evident.

In other words prime numbers are looked on as the basic building blocks of the natural numbers. In like manner in physical terms, strings (as prime components) are looked on as the basic building blocks of all matter.

However there is an equal circular aspect to prime numbers. This relates to the fact that in their general distributional behaviour, they display a remarkable interdependence with the natural nos.

So from one valid analytic (linear) perspective, the prime nos. are the most independent structures, serving as the building blocks of all natural numbers.

However from the equally valid holistic (circular) perspective, the prime nos. are the most interdependent, being totally dependent on the natural nos. for their precise distribution. So as well as each prime number enjoying individual structure (as independent), overall prime numbers share a general state (as interdependent)

This then implies that there is a key ingredient missing from the conventional physical perspective on strings. Whereas the linear perspective is very prominent (i.e. with strings as structure forming the basic building blocks of matter) there is no equal appreciation of their important circular aspect as state. Here the overall behaviour of strings (relating directly to their dimensional characteristics) intimately depends on natural phenomena (to which they are related).

Thus a two-way relationship therefore necessarily exists as between strings (as prime constituents of matter) and dimensions (in the general relationship of strings to matter). Whereas it may be valid to say that (manifest) physical particles result from unique dynamic vibrations of a string, the actual dimensional properties of strings (in general) result in turn from their overall relationship to such physical particles.

All along I have maintained that one cannot divorce the (physical) properties of nature from the (psychological) dimensions employed for its interpretation.

As I have repeatedly stated, conventional science is based on 1-dimensional interpretation and is thereby - literally - linear in nature.

And in this view the basic ingredient or "stuff" of everything in nature is a string which again is - literally - envisaged as a 1-dimensional line.

So we can see here a remarkable correspondence as between physical matter and its corresponding psychological interpretation both of which are 1-dimensional!

Thus the starting point for a more balanced dynamic treatment (with respect to both physical understanding and its psychological mode of interpretation) is to explicitly combine linear and circular aspects.

And this is done through combining the present conventional understanding of strings (linear) with several higher qualitative dimensions of understanding (circular) thereby providing many unique interpretations of string reality.

## Friday, January 15, 2010

### Brane Power

Another of the findings of M-theory is the realisation that 1-dimensional strings are not the only fundamental "objects". Rather a whole host of extended objects in higher dimensions also exist called p-branes, where p = no. of dimensions involved.

Also in 11 dimensional M-theory, where we have 10 spatial dimensions, the number of possible branes ranges from 0 - 9 dimensions.

In parallel fashion, I have long been aware of a similar situation with respect to its holistic counterpart, where we allow for differing dimensions of interpretation with respect to string concepts.

Because this understanding initially arose with respect to clarification of the stages of psychological development, I will discuss my findings in this context.

When understanding of a particular dimensional level unfolds, strictly one should refer to it as the default level of understanding.

So for example, when the rational linear stages properly unfold in experience, one thereby obtains default 1-dimensional understanding.

Then when - as with authentic contemplative progress - development evolves to the 2nd dimension, one now acquires the default understanding of that dimension.

Then as futher development unfolds, a new perspective unfolds by which its links with earlier stages can take place. Therefore as development passes beyond 2-dimensions, one now can establish an enhanced appreciation of earlier 1-dimensional understanding (from the perspective of the now attained higher 2nd dimension).

So strictly speaking, not alone can we have (default) 1-dimensional interpretation, but also a whole range of enhanced interpretations from the perspective of higher dimensions attained.

This was a revelation to me at the time, as I now realised that linear understanding was rooted - not only in its own dimension - but also in each of the higher dimensions (excluding the highest yet attained).

Now it would not be strictly possible for someone who has reached the 8th dimension - which coincides with pure contemplative awareness - to obtain an enhanced appreciation of earlier 1-dimensional interpretation (from the 8th dimension). While this (default) dimension is being consolidated in experience, one is unable to obtain an enhanced perspective of earlier dimensions! Put another way, while the default dimensional experience is unfolding, it remains somewhat closed (to other dimensions). However with further development it becomes more open. Thus the enhanced appreciation of the 1st dimension (from a higher dimension) reflects the fact that it thereby becomes temporarily constrained to this 1st dimension (providing that dimension with its enriched perspective).

Just to clarify what is involved here, I will briefly illustrate - with respect to the stages of development - the distinction as between (default) 1-dimensional interpretation (from the perspective of the 1st dimension) and enhanced 1-dimensional interpretation (from the perspective of the 2nd dimension).

In the former default case, one views the stages of development as unfolding essentially in a linear fashion (so that for example the lower necessarily unfolds before the higher stage).

However, in the enhanced view (from the perspective of the 2nd dimension) one realises that there are in fact two aspects (internal and external) involved. So one now envisages development taking place in linear terms with respect to (internal) stages relating to psychological development of the self and (external) physical stages relating to understanding of the world.

The value of this enhanced perspective is that in dynamic interaction both aspects will then operate - relatively - opposite to each other, introducing a circular paradoxical element to development. By contrast, in the default linear interpretation of stages, no such subtlety is involved.

Now this important finding - regarding a whole range of enhanced 1-dimensional interpretations (from the perspective of higher dimensions) - seems to me to equate pretty well with the corresponding discovery of extended objects within string theory.

Thus the 2-brane in string theory is the analytic correspondent of enhanced linear interpretation (from the 2nd dimension) in holistic terms.

Likewise, for example, a 4-brane would be the analytic correspondent of enhanced linear interpretation (from the perspective of the 4th dimension)!

However the holistic approach I have outlined would suggest that there are several more elements (that perhaps have not been generally recognised in M-theory).

For example, just as one can obtain enhanced appreciation in psychological terms of a lower dimension of understanding (from the perspective of a higher) likewise one can obtain a diminished appreciation of a higher dimension (from the perspective of a lower).

Now, if we were to try and suggest what this might imply for the analytic theory of strings, perhaps it would mean that what is - in truth - a p-brane (where p >1) would appear as a string!

Also in holistic terms, we can get an enhanced perspective of any lower dimension from a higher e.g. enhanced appreciation of 2-dimensional interpretation from the perspective - say - of the 4th. Likewise we can get a diminished appreciation of any higher dimension from a lower e.g. diminished interpretation of the 4th - say - from the perspective of the 2nd.

What the correspondent of this for analytic strings would be is hard to say! Perhaps it would imply in some way lower brane objects being transformed into higher (in the first case) and in the 2nd higher brane objects being transformed into lower.

So for example a 2 brane object could possibly transform into a 4-brane and in turn in other circumstances a 4-brane into a 2-brane!

Recently, there has been speculation regarding another class of "object" referred to as a 0-brane (wittingly referred to as a no-braner) which it is hoped will throw light on the fundamental origins of the Universe. However this for me is where M-theory - or more properly in this case Matrix theory - finally strays completely outside of its interpretative limits. Defining an object ultimately in terms of a point represents but another idealised conception that has no direct relationship to physical reality.

The corresponding psychological counterpart to a 0-brane would relate to understanding that is 0-dimensional i.e. non-dimensional.

However such understanding represents purely contemplative (empty) understanding of reality that is totally ineffable (and thereby incomprehensible in rational terms).

Though such experience indeed represents the zenith of qualitative type appreciation of reality it has no direct correspondent in linear understanding.

Once again whereas 1 represents linear understanding (amenable to reason), 0 by contrast represents circular understanding (amenable to intuition).

So the paradox for present physics is that true appreciation of 0-brane reality in physics, can only come through the extreme expression of qualitative - rather than quantitative - type interpretation.

However - whatever the specific merit of such ideas - string theorists need to accept that the current language of interpretation is largely meaningless from any coherent philosophical perspective.

I accept that - when interpreted in a 1-dimensional manner - the findings of string and now M-theory, portray reality accurately as it appears (through the interpretative lens of conventional science).

However the key point again is that this interpretation model is quite inadequate to properly describe the dynamic nature of reality involved.

Therefore, in my opinion, an enormous amount of interpretative decoding (of a holistic kind) is required to convert string theory into an acceptable physical model of reality.

Also in 11 dimensional M-theory, where we have 10 spatial dimensions, the number of possible branes ranges from 0 - 9 dimensions.

In parallel fashion, I have long been aware of a similar situation with respect to its holistic counterpart, where we allow for differing dimensions of interpretation with respect to string concepts.

Because this understanding initially arose with respect to clarification of the stages of psychological development, I will discuss my findings in this context.

When understanding of a particular dimensional level unfolds, strictly one should refer to it as the default level of understanding.

So for example, when the rational linear stages properly unfold in experience, one thereby obtains default 1-dimensional understanding.

Then when - as with authentic contemplative progress - development evolves to the 2nd dimension, one now acquires the default understanding of that dimension.

Then as futher development unfolds, a new perspective unfolds by which its links with earlier stages can take place. Therefore as development passes beyond 2-dimensions, one now can establish an enhanced appreciation of earlier 1-dimensional understanding (from the perspective of the now attained higher 2nd dimension).

So strictly speaking, not alone can we have (default) 1-dimensional interpretation, but also a whole range of enhanced interpretations from the perspective of higher dimensions attained.

This was a revelation to me at the time, as I now realised that linear understanding was rooted - not only in its own dimension - but also in each of the higher dimensions (excluding the highest yet attained).

Now it would not be strictly possible for someone who has reached the 8th dimension - which coincides with pure contemplative awareness - to obtain an enhanced appreciation of earlier 1-dimensional interpretation (from the 8th dimension). While this (default) dimension is being consolidated in experience, one is unable to obtain an enhanced perspective of earlier dimensions! Put another way, while the default dimensional experience is unfolding, it remains somewhat closed (to other dimensions). However with further development it becomes more open. Thus the enhanced appreciation of the 1st dimension (from a higher dimension) reflects the fact that it thereby becomes temporarily constrained to this 1st dimension (providing that dimension with its enriched perspective).

Just to clarify what is involved here, I will briefly illustrate - with respect to the stages of development - the distinction as between (default) 1-dimensional interpretation (from the perspective of the 1st dimension) and enhanced 1-dimensional interpretation (from the perspective of the 2nd dimension).

In the former default case, one views the stages of development as unfolding essentially in a linear fashion (so that for example the lower necessarily unfolds before the higher stage).

However, in the enhanced view (from the perspective of the 2nd dimension) one realises that there are in fact two aspects (internal and external) involved. So one now envisages development taking place in linear terms with respect to (internal) stages relating to psychological development of the self and (external) physical stages relating to understanding of the world.

The value of this enhanced perspective is that in dynamic interaction both aspects will then operate - relatively - opposite to each other, introducing a circular paradoxical element to development. By contrast, in the default linear interpretation of stages, no such subtlety is involved.

Now this important finding - regarding a whole range of enhanced 1-dimensional interpretations (from the perspective of higher dimensions) - seems to me to equate pretty well with the corresponding discovery of extended objects within string theory.

Thus the 2-brane in string theory is the analytic correspondent of enhanced linear interpretation (from the 2nd dimension) in holistic terms.

Likewise, for example, a 4-brane would be the analytic correspondent of enhanced linear interpretation (from the perspective of the 4th dimension)!

However the holistic approach I have outlined would suggest that there are several more elements (that perhaps have not been generally recognised in M-theory).

For example, just as one can obtain enhanced appreciation in psychological terms of a lower dimension of understanding (from the perspective of a higher) likewise one can obtain a diminished appreciation of a higher dimension (from the perspective of a lower).

Now, if we were to try and suggest what this might imply for the analytic theory of strings, perhaps it would mean that what is - in truth - a p-brane (where p >1) would appear as a string!

Also in holistic terms, we can get an enhanced perspective of any lower dimension from a higher e.g. enhanced appreciation of 2-dimensional interpretation from the perspective - say - of the 4th. Likewise we can get a diminished appreciation of any higher dimension from a lower e.g. diminished interpretation of the 4th - say - from the perspective of the 2nd.

What the correspondent of this for analytic strings would be is hard to say! Perhaps it would imply in some way lower brane objects being transformed into higher (in the first case) and in the 2nd higher brane objects being transformed into lower.

So for example a 2 brane object could possibly transform into a 4-brane and in turn in other circumstances a 4-brane into a 2-brane!

Recently, there has been speculation regarding another class of "object" referred to as a 0-brane (wittingly referred to as a no-braner) which it is hoped will throw light on the fundamental origins of the Universe. However this for me is where M-theory - or more properly in this case Matrix theory - finally strays completely outside of its interpretative limits. Defining an object ultimately in terms of a point represents but another idealised conception that has no direct relationship to physical reality.

The corresponding psychological counterpart to a 0-brane would relate to understanding that is 0-dimensional i.e. non-dimensional.

However such understanding represents purely contemplative (empty) understanding of reality that is totally ineffable (and thereby incomprehensible in rational terms).

Though such experience indeed represents the zenith of qualitative type appreciation of reality it has no direct correspondent in linear understanding.

Once again whereas 1 represents linear understanding (amenable to reason), 0 by contrast represents circular understanding (amenable to intuition).

So the paradox for present physics is that true appreciation of 0-brane reality in physics, can only come through the extreme expression of qualitative - rather than quantitative - type interpretation.

However - whatever the specific merit of such ideas - string theorists need to accept that the current language of interpretation is largely meaningless from any coherent philosophical perspective.

I accept that - when interpreted in a 1-dimensional manner - the findings of string and now M-theory, portray reality accurately as it appears (through the interpretative lens of conventional science).

However the key point again is that this interpretation model is quite inadequate to properly describe the dynamic nature of reality involved.

Therefore, in my opinion, an enormous amount of interpretative decoding (of a holistic kind) is required to convert string theory into an acceptable physical model of reality.

### Dualities

One the key ideas that Witten proposed in 1995 was the idea of dualities.

Thus the five recognised string theories - which initially were believed to be separate - were in fact connected by duality transformations, so that by using the appropriate key one theory could be mapped on to another (revealing precious new insights in the process).

Now interestingly my own holistic approach is based directly on polar dualities i.e. internal/external, whole/part and form/emptiness and immanence/transcendence.

In the Type 0 approach - which concurs with conventional scientific interpretation - these dualities are considered as separate; however the four other Types revealing increasing levels of complementarity (and ultimate identity) as between these opposites.

So in the (conventional) analytic approach the five recognised string theories provide unique perspectives on the ultimate nature of reality. Then through appropriate transformations they can be seen as in fact equivalent expressions.

Likewise from the holistic qualitative aspect each of the five dimensional Types (singled out as especially relevant) provide unique perspectives for attempted interpretation of this reality. Also through appropriate transformations we can show that they are equivalent (though using a different language of expression).

However the really interesting area is making closer links as between the analytic and holistic perspectives in the hope of ultimately applying intuitively satisfying explanations for all key string notions.

Now the first of the holistic models (Type 0) in fact represents the conventional scientific interpretation.

However though this Type is best in terms of detailed rational interpretation (of an analytic kind) it is least satisfactory in terms of providing the appropriate qualitative understanding to enable its concepts to resonate intuitively with (appropriate) psychological experience of reality.

So there is a huge role - of which my own limited attempts represent but a beginning - in terms of transforming present Type 0 understanding through the interpretative lenses of the other four Types.

Thus in a more complete understanding we should be able to immediately provide the equivalent qualitative interpretations for the Type 0 findings of conventional science through each of the four other models.

And of course the process would work both ways as one could move from qualitative appreciation at higher dimensions to its implications for the Type 0 level. In this way, highly creative new thinking could be better incorporated in standard string theory development.

However the key point must be repeated continually until its significance is eventually absorbed.

The time has clearly come for science to greatly enlarge its possible scope by at last admitting its - hidden - holistic dimension.

Whereas the standard conventional approach is directly suited for quantitative analysis of reality, the complementary holistic approach is best suited for qualitative synthesis of that same realty.

Like two blades of a scissors both aspects need to be incorporated in a more comprehensive vision of science (which I term radial).

However before such a comprehensive approach can prosper, considerable attention must be first given to development of the (neglected) holistic aspect.

Thus the five recognised string theories - which initially were believed to be separate - were in fact connected by duality transformations, so that by using the appropriate key one theory could be mapped on to another (revealing precious new insights in the process).

Now interestingly my own holistic approach is based directly on polar dualities i.e. internal/external, whole/part and form/emptiness and immanence/transcendence.

In the Type 0 approach - which concurs with conventional scientific interpretation - these dualities are considered as separate; however the four other Types revealing increasing levels of complementarity (and ultimate identity) as between these opposites.

So in the (conventional) analytic approach the five recognised string theories provide unique perspectives on the ultimate nature of reality. Then through appropriate transformations they can be seen as in fact equivalent expressions.

Likewise from the holistic qualitative aspect each of the five dimensional Types (singled out as especially relevant) provide unique perspectives for attempted interpretation of this reality. Also through appropriate transformations we can show that they are equivalent (though using a different language of expression).

However the really interesting area is making closer links as between the analytic and holistic perspectives in the hope of ultimately applying intuitively satisfying explanations for all key string notions.

Now the first of the holistic models (Type 0) in fact represents the conventional scientific interpretation.

However though this Type is best in terms of detailed rational interpretation (of an analytic kind) it is least satisfactory in terms of providing the appropriate qualitative understanding to enable its concepts to resonate intuitively with (appropriate) psychological experience of reality.

So there is a huge role - of which my own limited attempts represent but a beginning - in terms of transforming present Type 0 understanding through the interpretative lenses of the other four Types.

Thus in a more complete understanding we should be able to immediately provide the equivalent qualitative interpretations for the Type 0 findings of conventional science through each of the four other models.

And of course the process would work both ways as one could move from qualitative appreciation at higher dimensions to its implications for the Type 0 level. In this way, highly creative new thinking could be better incorporated in standard string theory development.

However the key point must be repeated continually until its significance is eventually absorbed.

The time has clearly come for science to greatly enlarge its possible scope by at last admitting its - hidden - holistic dimension.

Whereas the standard conventional approach is directly suited for quantitative analysis of reality, the complementary holistic approach is best suited for qualitative synthesis of that same realty.

Like two blades of a scissors both aspects need to be incorporated in a more comprehensive vision of science (which I term radial).

However before such a comprehensive approach can prosper, considerable attention must be first given to development of the (neglected) holistic aspect.

### What is M-Theory?

What is now known as "the second superstring revolution" took place in 1995 following publication of a paper by its acknowledged leading proponent, Edward Witten.

Up to this, a well recognised problem with string theory was the lack of one unique theory. In fact five - seemingly - separate theories existed referred to as type I, types IIA and IIB and two heterotic (hybrid) string theories.

The hope at the time was that just one of these would eventually win out to qualify as the long sought for TOE.

However Witten was to surprise the string community by demonstrating very close links as between all the existing theories and postulated that they were in fact part of on an even grander synthesis (M-theory).

He also argued that this overarching theory would find expression in an 11 - rather than 10 - dimensional framework.

Now of course, I am by no means qualified to deal with the analytic issues involved.

My purpose is rather to point to the integral (holistic) scientific significance of such developments.

From the holistic perspective, no single unique interpretation of reality can be given. Rather - as we have seen - a distinct interpretation can be associated with each number (as dimension) so that potentially an infinite no. of possible interpretations exist.

However, we have argued that in practice only a small finite number of such explanations are especially relevant.

Indeed remarkably - though perhaps coincidental - we can distinguish 5 such interpretative models (for which I have already given a simple mathematical justification in "The Number 24").

These five models coincide with 1, 2, 4, 8, and 24-dimensional holistic interpretation respectively.

Even before I heard anything regarding M-theory, I had referred to the first 4, as Type 0 (this 1st type - which represents linear understanding - is inherently unsuited to true integral appreciation; hence the use of 0), Type 1, Type 2 and Type 3 Integration respectively. Only recently - largely through making connections with string theory - have I given proper consideration to the 5th which could be designated as Type 4. So even my very designation of the various holistic interpretations bears similarity with the corresponding analytic treatment in string theory!

Each of the integral interpretations therefore offers a certain unique qualitative perspective with respect to the "same" reality. Though the higher dimensional perspectives are by their very nature more refined in holistic terms, they also suffer in that they are likewise further removed from analytic type consideration.

So there is an inevitable "Uncertainty Principle" at work. In other words the more accurately defined one's qualitative holistic interpretation of reality, the less amenable it becomes to any specific kind of phenomenal analysis.

Of course the reverse is true with respect to conventional string theories. Therefore the more exact such analytic theories become in terms of successfully explaining the nature of physical reality, the less amenable they become to any kind of holistic intuitive understanding.

Indeed this is already readily apparent with string theorists quite unable to provide in qualitative terms an adequate philosophical perspective of what their world view entails.

This therefore would lead one to be very sceptical regarding the true nature of this so-called M-theory. In many ways the M most accurately stands for mirage for it is pointing to a reality (which greatly exceeds the explanatory limits of the standard 1-dimensional model of interpretation).

Even the finding that we now need 11 rather than 10 dimensions points to this fact. As I have stated in corresponding holistic terms, the need for an extra dimension implies an admission that the current level of psychological intuition is inadequate to appropriate the nature of the reality investigated.

So likewise in analytic terms the need for 11 dimensions implies that some key element is missing in terms of conventional scientific understanding.

Reality at its most fundamental physical level requires going below the Planck length.

However though enormously important in terms of any ultimate understanding, eventually it becomes impossible to meaningfully deal with such reality in a detached objective manner.

Likewise from the holistic perspective at very high levels of spiritual integration, dynamic interaction with respect to phenomena becomes so rapid that they no longer even appear to arise in experience.

And this is the essential point! Science - which always requires a degree of detachment from the environment - can only deal with phenomenal appearances (from both analytic and holistic perspectives).

So in the end science (with respect to either aspect) can only deal with secondary phenomenal appearances and thereby cannot directly probe essential reality.

We can only approximate experience of such reality (that ultimately is experientially attained in complete unity and emptiness). However appearances will always remain necessary in dynamically approximating reality and thereby realising the true secret of this all important game (which we know as life itself).

Up to this, a well recognised problem with string theory was the lack of one unique theory. In fact five - seemingly - separate theories existed referred to as type I, types IIA and IIB and two heterotic (hybrid) string theories.

The hope at the time was that just one of these would eventually win out to qualify as the long sought for TOE.

However Witten was to surprise the string community by demonstrating very close links as between all the existing theories and postulated that they were in fact part of on an even grander synthesis (M-theory).

He also argued that this overarching theory would find expression in an 11 - rather than 10 - dimensional framework.

Now of course, I am by no means qualified to deal with the analytic issues involved.

My purpose is rather to point to the integral (holistic) scientific significance of such developments.

From the holistic perspective, no single unique interpretation of reality can be given. Rather - as we have seen - a distinct interpretation can be associated with each number (as dimension) so that potentially an infinite no. of possible interpretations exist.

However, we have argued that in practice only a small finite number of such explanations are especially relevant.

Indeed remarkably - though perhaps coincidental - we can distinguish 5 such interpretative models (for which I have already given a simple mathematical justification in "The Number 24").

These five models coincide with 1, 2, 4, 8, and 24-dimensional holistic interpretation respectively.

Even before I heard anything regarding M-theory, I had referred to the first 4, as Type 0 (this 1st type - which represents linear understanding - is inherently unsuited to true integral appreciation; hence the use of 0), Type 1, Type 2 and Type 3 Integration respectively. Only recently - largely through making connections with string theory - have I given proper consideration to the 5th which could be designated as Type 4. So even my very designation of the various holistic interpretations bears similarity with the corresponding analytic treatment in string theory!

Each of the integral interpretations therefore offers a certain unique qualitative perspective with respect to the "same" reality. Though the higher dimensional perspectives are by their very nature more refined in holistic terms, they also suffer in that they are likewise further removed from analytic type consideration.

So there is an inevitable "Uncertainty Principle" at work. In other words the more accurately defined one's qualitative holistic interpretation of reality, the less amenable it becomes to any specific kind of phenomenal analysis.

Of course the reverse is true with respect to conventional string theories. Therefore the more exact such analytic theories become in terms of successfully explaining the nature of physical reality, the less amenable they become to any kind of holistic intuitive understanding.

Indeed this is already readily apparent with string theorists quite unable to provide in qualitative terms an adequate philosophical perspective of what their world view entails.

This therefore would lead one to be very sceptical regarding the true nature of this so-called M-theory. In many ways the M most accurately stands for mirage for it is pointing to a reality (which greatly exceeds the explanatory limits of the standard 1-dimensional model of interpretation).

Even the finding that we now need 11 rather than 10 dimensions points to this fact. As I have stated in corresponding holistic terms, the need for an extra dimension implies an admission that the current level of psychological intuition is inadequate to appropriate the nature of the reality investigated.

So likewise in analytic terms the need for 11 dimensions implies that some key element is missing in terms of conventional scientific understanding.

Reality at its most fundamental physical level requires going below the Planck length.

However though enormously important in terms of any ultimate understanding, eventually it becomes impossible to meaningfully deal with such reality in a detached objective manner.

Likewise from the holistic perspective at very high levels of spiritual integration, dynamic interaction with respect to phenomena becomes so rapid that they no longer even appear to arise in experience.

And this is the essential point! Science - which always requires a degree of detachment from the environment - can only deal with phenomenal appearances (from both analytic and holistic perspectives).

So in the end science (with respect to either aspect) can only deal with secondary phenomenal appearances and thereby cannot directly probe essential reality.

We can only approximate experience of such reality (that ultimately is experientially attained in complete unity and emptiness). However appearances will always remain necessary in dynamically approximating reality and thereby realising the true secret of this all important game (which we know as life itself).

## Thursday, January 14, 2010

### New Explanation of Dimensions

The basic rationale for this new understanding of dimensions - which applies equally to both physical and psychological reality - is that is based initially on the two key polarities sets which necessarily underlie all phenomenal experience.

Now these two polarity sets can be referred to as horizontal and vertical with respect to each other.

The horizontal relates to the basic distinction as between internal (subjective) and external (objective); the vertical then relates to the further critical distinction - in any context - as between whole (general) and part (specific).

Now we can represent these polarities as four equidistant coordinate points on the circle of unit radius with internal and external the end points along the horizontal line and whole and part end points along the vertical line respectively (dividing the circle).

In physical terms, the dimensions of space and time arise through the interaction of these polarities; likewise in psychological terms, experience of space and time arises through a similar interaction.

Conventional notions of the 4 dimensions (3-space, 1-time) stem directly from the linear manner of interpretation adopted. What essentially happens is that whole and part are combined (in a static reduced manner) and then considered as external to the observer. This then results in the typical 3-dimensional spatial rigidity which objects thereby possess. The final 4th dimension is thereby separated from the spatial and interpreted as time.

So standard linear interpretation is associated with an asymmetrical understanding of space and time.

Now when we adopt a 2-dimensional interpretation, space and time now appear as paradoxical and symmetrical having complementary positive and negative aspects with respect to both space and time.

This represents (integral) holistic as opposed to (differentiated) analytic understanding.

So space and time have now both two dimensions (that are positive and negative with respect to each other)

When we adopt a 4-dimensional interpretation, space and time again appear as paradoxical and symmetrical having complementary real and imaginary as well as positive and negative aspects with respect to both space and time.

This qualitative interpretation corresponds directly with the 4 roots of unity.

So both space and time now have both real and imaginary aspects (in positive and negative terms); now this might suggest 8 - rather than 4 - dimensions. However it has to be remembered that real and imaginary keep switching in dynamic interactive terms (and positive and negative). So when time is real, space is imaginary; likewise when space is now real, time is imaginary; also the positing of one aspect with respect to either space or time requires the negation of the other and vice versa.

From an equivalent perspective, in dynamic interactive terms, the whole (in any context) is imaginary with respect to the part and vice versa; and internal and external are positive and negative with respect to each other.

When we adopt an 8-dimensional interpretation we generate four additional dimensions that have a complex structure (with equal real and imaginary aspects).

As explained in previous blogs these provide the holistic mathematical structure of the four forces (in both physical and psychological terms).

All other (qualitative) dimensions are obtained with reference to the corresponding root structure of 1 (in quantitative terms).

So to obtain for example the qualitative structure of the 100th dimension, we obtain the corresponding 100th root of 1 (in a quantitative manner).

Now these additional roots will all have a complex structure (with real and imaginary aspects).

This entails a corresponding complex structure to the nature of space and time expressing in turn a highly dynamic configuration of the four fundamental polarities (internal, external, whole and part).

In corresponding psychological terms this entails a highly refined interaction as between conscious (rational) and unconscious (intuitive) aspects of experience.

One final point! it is only in the 1-dimensional linear interpretation that an attempt is made to separate both the linear and circular notion of dimension (which is very evident in terms of the standard explanation of dimensions in string theory).

This in turn reflects the fact that conventional interpretation is based formally on merely (conscious) rational notions of understanding.

In all other dimensional interpretations, it is assumed that both linear and circular notions necessarily interact with each other (as in turn does conscious and unconscious).

Now these two polarity sets can be referred to as horizontal and vertical with respect to each other.

The horizontal relates to the basic distinction as between internal (subjective) and external (objective); the vertical then relates to the further critical distinction - in any context - as between whole (general) and part (specific).

Now we can represent these polarities as four equidistant coordinate points on the circle of unit radius with internal and external the end points along the horizontal line and whole and part end points along the vertical line respectively (dividing the circle).

In physical terms, the dimensions of space and time arise through the interaction of these polarities; likewise in psychological terms, experience of space and time arises through a similar interaction.

Conventional notions of the 4 dimensions (3-space, 1-time) stem directly from the linear manner of interpretation adopted. What essentially happens is that whole and part are combined (in a static reduced manner) and then considered as external to the observer. This then results in the typical 3-dimensional spatial rigidity which objects thereby possess. The final 4th dimension is thereby separated from the spatial and interpreted as time.

So standard linear interpretation is associated with an asymmetrical understanding of space and time.

Now when we adopt a 2-dimensional interpretation, space and time now appear as paradoxical and symmetrical having complementary positive and negative aspects with respect to both space and time.

This represents (integral) holistic as opposed to (differentiated) analytic understanding.

So space and time have now both two dimensions (that are positive and negative with respect to each other)

When we adopt a 4-dimensional interpretation, space and time again appear as paradoxical and symmetrical having complementary real and imaginary as well as positive and negative aspects with respect to both space and time.

This qualitative interpretation corresponds directly with the 4 roots of unity.

So both space and time now have both real and imaginary aspects (in positive and negative terms); now this might suggest 8 - rather than 4 - dimensions. However it has to be remembered that real and imaginary keep switching in dynamic interactive terms (and positive and negative). So when time is real, space is imaginary; likewise when space is now real, time is imaginary; also the positing of one aspect with respect to either space or time requires the negation of the other and vice versa.

From an equivalent perspective, in dynamic interactive terms, the whole (in any context) is imaginary with respect to the part and vice versa; and internal and external are positive and negative with respect to each other.

When we adopt an 8-dimensional interpretation we generate four additional dimensions that have a complex structure (with equal real and imaginary aspects).

As explained in previous blogs these provide the holistic mathematical structure of the four forces (in both physical and psychological terms).

All other (qualitative) dimensions are obtained with reference to the corresponding root structure of 1 (in quantitative terms).

So to obtain for example the qualitative structure of the 100th dimension, we obtain the corresponding 100th root of 1 (in a quantitative manner).

Now these additional roots will all have a complex structure (with real and imaginary aspects).

This entails a corresponding complex structure to the nature of space and time expressing in turn a highly dynamic configuration of the four fundamental polarities (internal, external, whole and part).

In corresponding psychological terms this entails a highly refined interaction as between conscious (rational) and unconscious (intuitive) aspects of experience.

One final point! it is only in the 1-dimensional linear interpretation that an attempt is made to separate both the linear and circular notion of dimension (which is very evident in terms of the standard explanation of dimensions in string theory).

This in turn reflects the fact that conventional interpretation is based formally on merely (conscious) rational notions of understanding.

In all other dimensional interpretations, it is assumed that both linear and circular notions necessarily interact with each other (as in turn does conscious and unconscious).

### Linear and Circular Dimensions

I fully accept that enormous mathematical strides have been made with respect to the development of string theory. In many cases these resonate strongly with physical understanding of the Universe apparently offering the hope that many key difficulties (such as the integration of Quantum Mechanics with the Theory Of Relativity) can at last be successfully achieved.

However from a philosophical perspective I would find that the attempted explanation of many of the fundamental concepts of string theory (such as the nature of a "string" and the meaning of "dimensions) remains very confused.

Once again I would see the reason for this problem as representing the limits of what can be achieved through conventional scientific method (based on linear understanding). Strictly speaking the philosophical limitations of this approach had already been exposed through the paradoxical findings of Quantum Mechanics (though in practice largely ignored). Though clearly these philosophical reservations would also naturally apply to string theory, we witness instead a renewed hope in the reductionist approach (in its ability to finally arrive at a TOE). It is almost as if string theorists believe that by going beyond quantum mechanics they can somehow bypass all its mysteries by rooting it in even more fundamental reductionist interpretation of nature.

My basic contention with respect to science (which of course includes physics) generally is that it needs to be widened to include three (rather the present one) areas.

So as stated on several occasions previously we need:

1) Conventional (analytic) science - representing the present understanding of science - geared directly to quantitative type interpretation of reality;

2) Integral (holistic) science - representing the approach pursued on this blog - geared directly to qualitative type appreciation. From this perspective the integral scientific approach is especially geared to deal with philosophical issues with respect to string theory concepts;

3) Radial (comprehensive) science - representing the mature interaction of specialised analytic and holistic understanding. Needless to say there is little possibility of this 3rd aspect being developed at present due to the - almost - complete lack of recognition of the integral (holistic) approach!

Using the integral scientific approach, I have already suggested that the very notion of a "string" needs to be considerably widened to include both an analytic and holistic aspect.

Whereas the analytic aspect concurs with present definition, the holistic aspect relates directly to the psychological manner of interpretation (of physical data and concepts). So rather than just one default interpretation for physical reality i.e. 1-dimensional rational, potentially an infinite number are available (though in practice I would expect that a relatively small number would suffice).

The fascinating thing is that the holistic aspect literally relates to the qualitative mathematical notion of dimension and it is only in this context that "dimensions" in string theory can be properly interpreted.

Put another way, present developments with respect to the analytic understanding of string theory are being severely impaired due to lack of corresponding lack of development with respect to the qualitative notion of dimensions.

Indeed I believe that the key insight with respect to string theory (akin to the equivalence principle of General Relativity) is much more revolutionary than at present realised! In other words it really is pointing to the need for two distinctive aspects of scientific understanding i.e. analytic and holistic respectively, as the fundamental relationship as between object phenomena and dimensions (of space and time) requires this distinction.

In this context it is fascinating to examine how the notion of "dimensions" is dealt with in present string theory.

Conventional macro understanding of 4-dimensions (3 of space and 1 of time) simply reflects (in qualitative philosophical terms) the linear approach.

Thus though 4-dimensions are recognised (in quantitative terms) this qualitatively reflects 1-dimensional understanding. In fact this directly concurs with treating time as 1-dimensional.

Now when speaking of 10 - or now perhaps 11 - string theorists have an obvious problem in dealing with "higher" dimensions (which do not conform to linear interpretation).

So in the linear (qualitative) approach time is still treated as 1-dimensional with the remaining dimensions spatial.

However - say in a 10-dimensional framework - we thereby have 9 spatial dimensions (only 3 of which are recognised according to linear understanding).

So the standard representation of the remaining 6 is to treat them as rolled up circular dimensions that are so small (as to be invisible to normal linear detection).

Now there is fascinating counterpart issue with respect to the holistic dimensions of psychological understanding.

Moving qualitatively into higher dimensions in this context entails developing an increasingly refined intuitive type appreciation of reality (based on circular notions).

In other words as contemplative development proceeds - rather than viewing the physical world in a detached objective manner - one increasingly realises the complementary nature of all physical and psychological constructs (which qualitatively represents circular understanding).

Now one who remains firmly rooted in linear understanding - quite literally - will not be able to intuitively "see" (from the perspective of the "higher" contemplative perspective). Rather interpretation will be reduced to the understanding of the lower 1st dimension. So again, the development in these new circular dimensions of spiritual "seeing" will thereby remain so limited as to be invisible.

What this therefore entails is that the very explanation that is offered for the extra "dimensions" in string theory in itself reflects a merely linear manner of interpretation (which is quite inadequate for the kind of reality involved).

Thus when one qualitatively attempts to interpret these extra "dimensions" - not from the conventional linear standpoint but rather - from the intuitively refined higher dimensions of understanding, an entirely distinctive perspective unfolds.

So from the perspective of 2-dimensional understanding, one already understands the notion of a dimension in an inherently dynamic interactive manner (where both linear and circular aspects interact).

It cannot be stated too strongly that the (conventional) scientific manner of interpreting relationships, reflects merely - in qualitative terms - the linear (1-dimensional) approach.

Thus when we adopt the alternative understanding of a different dimension, an uniquely distinct interpretation unfolds.

The linear approach is inadequate to properly convey the nature of "higher" dimensions. Therefore we need to incorporate the holistic integral aspect (based on higher dimensional appreciation) into overall appreciation.

Once again the notion of dimension that is appropriate to string theory has very little to do with conventional notions of space and time.

Remarkably however it is directly related to the mathematical notion of dimension (when given a coherent qualitative interpretation).

And structurally this qualitative notion of dimension is directly related to the corresponding quantitative notion of its corresponding root.

However from a philosophical perspective I would find that the attempted explanation of many of the fundamental concepts of string theory (such as the nature of a "string" and the meaning of "dimensions) remains very confused.

Once again I would see the reason for this problem as representing the limits of what can be achieved through conventional scientific method (based on linear understanding). Strictly speaking the philosophical limitations of this approach had already been exposed through the paradoxical findings of Quantum Mechanics (though in practice largely ignored). Though clearly these philosophical reservations would also naturally apply to string theory, we witness instead a renewed hope in the reductionist approach (in its ability to finally arrive at a TOE). It is almost as if string theorists believe that by going beyond quantum mechanics they can somehow bypass all its mysteries by rooting it in even more fundamental reductionist interpretation of nature.

My basic contention with respect to science (which of course includes physics) generally is that it needs to be widened to include three (rather the present one) areas.

So as stated on several occasions previously we need:

1) Conventional (analytic) science - representing the present understanding of science - geared directly to quantitative type interpretation of reality;

2) Integral (holistic) science - representing the approach pursued on this blog - geared directly to qualitative type appreciation. From this perspective the integral scientific approach is especially geared to deal with philosophical issues with respect to string theory concepts;

3) Radial (comprehensive) science - representing the mature interaction of specialised analytic and holistic understanding. Needless to say there is little possibility of this 3rd aspect being developed at present due to the - almost - complete lack of recognition of the integral (holistic) approach!

Using the integral scientific approach, I have already suggested that the very notion of a "string" needs to be considerably widened to include both an analytic and holistic aspect.

Whereas the analytic aspect concurs with present definition, the holistic aspect relates directly to the psychological manner of interpretation (of physical data and concepts). So rather than just one default interpretation for physical reality i.e. 1-dimensional rational, potentially an infinite number are available (though in practice I would expect that a relatively small number would suffice).

The fascinating thing is that the holistic aspect literally relates to the qualitative mathematical notion of dimension and it is only in this context that "dimensions" in string theory can be properly interpreted.

Put another way, present developments with respect to the analytic understanding of string theory are being severely impaired due to lack of corresponding lack of development with respect to the qualitative notion of dimensions.

Indeed I believe that the key insight with respect to string theory (akin to the equivalence principle of General Relativity) is much more revolutionary than at present realised! In other words it really is pointing to the need for two distinctive aspects of scientific understanding i.e. analytic and holistic respectively, as the fundamental relationship as between object phenomena and dimensions (of space and time) requires this distinction.

In this context it is fascinating to examine how the notion of "dimensions" is dealt with in present string theory.

Conventional macro understanding of 4-dimensions (3 of space and 1 of time) simply reflects (in qualitative philosophical terms) the linear approach.

Thus though 4-dimensions are recognised (in quantitative terms) this qualitatively reflects 1-dimensional understanding. In fact this directly concurs with treating time as 1-dimensional.

Now when speaking of 10 - or now perhaps 11 - string theorists have an obvious problem in dealing with "higher" dimensions (which do not conform to linear interpretation).

So in the linear (qualitative) approach time is still treated as 1-dimensional with the remaining dimensions spatial.

However - say in a 10-dimensional framework - we thereby have 9 spatial dimensions (only 3 of which are recognised according to linear understanding).

So the standard representation of the remaining 6 is to treat them as rolled up circular dimensions that are so small (as to be invisible to normal linear detection).

Now there is fascinating counterpart issue with respect to the holistic dimensions of psychological understanding.

Moving qualitatively into higher dimensions in this context entails developing an increasingly refined intuitive type appreciation of reality (based on circular notions).

In other words as contemplative development proceeds - rather than viewing the physical world in a detached objective manner - one increasingly realises the complementary nature of all physical and psychological constructs (which qualitatively represents circular understanding).

Now one who remains firmly rooted in linear understanding - quite literally - will not be able to intuitively "see" (from the perspective of the "higher" contemplative perspective). Rather interpretation will be reduced to the understanding of the lower 1st dimension. So again, the development in these new circular dimensions of spiritual "seeing" will thereby remain so limited as to be invisible.

What this therefore entails is that the very explanation that is offered for the extra "dimensions" in string theory in itself reflects a merely linear manner of interpretation (which is quite inadequate for the kind of reality involved).

Thus when one qualitatively attempts to interpret these extra "dimensions" - not from the conventional linear standpoint but rather - from the intuitively refined higher dimensions of understanding, an entirely distinctive perspective unfolds.

So from the perspective of 2-dimensional understanding, one already understands the notion of a dimension in an inherently dynamic interactive manner (where both linear and circular aspects interact).

It cannot be stated too strongly that the (conventional) scientific manner of interpreting relationships, reflects merely - in qualitative terms - the linear (1-dimensional) approach.

Thus when we adopt the alternative understanding of a different dimension, an uniquely distinct interpretation unfolds.

The linear approach is inadequate to properly convey the nature of "higher" dimensions. Therefore we need to incorporate the holistic integral aspect (based on higher dimensional appreciation) into overall appreciation.

Once again the notion of dimension that is appropriate to string theory has very little to do with conventional notions of space and time.

Remarkably however it is directly related to the mathematical notion of dimension (when given a coherent qualitative interpretation).

And structurally this qualitative notion of dimension is directly related to the corresponding quantitative notion of its corresponding root.

## Wednesday, January 13, 2010

### Other Interesting Connections

It might be helpful to further extend the complementary connections as between the two notions of strings i.e. analytic and holistic, respectively.

From the analytic perspective it is readily admitted that, as the string can vibrate in an infinite number of ways (with each unique vibration corresponding to a distinct matter particle) that potentially therefore we can generate an infinite no. of particles.

Now so far, only a relatively small finite number of distinct particles have been found. The actual explanation for this fact is due to the fact that actual particles discovered correspond to extremely low eneregy levels of vibration of the string. These likewise entails less energy (corresponding to relatively low masses).

New particles entailing greater vibration of the string would require extremely high amounts of energy (well beyond present technological capacity).

The reassuring fact therefore is that in terms of "normal" energy states we need only concern ourselves with a relatively small group of particles (corresponding to low vibrations of the string).

There is a fascinating counterpart in terms of the holistic notion of the string (corresponding to qualitative interpretation of reality).

Potentially as there are an infinite no. of possible (whole) dimensions, therefore we can likewise provide an infinite no. of possible interpretations for any physical event (with each interpretation relating to a unique dimensional number).

So the situation here might therefore seem hopeless for science (due an infinite range of possible interpretations).

However, given the present level of human evolution, we are capable of exploring only a very limited range of these dimensional interpretations.

As we have seen Conventional Science is still firmly rooted in the lowest psychological energy state (associated with 1-dimensional interpretation).

Though higher energy states are associated with authentic contemplative development, it would be quite rare - in terms of corresponding cognitive development - for it to grow significantly beyond the lower dimensions.

And I have persistently argued that these lower dimensions - certainly up to 8 - are of special significance in terms of integral appreciation.

It is possible however to describe in general terms what happens to interpretation at much higher (spiritual) energy states. Here phenomenal understanding becomes so transparent that it no longer even appears to arise in experience (with a person continually absorbed in a deep contemplative state of union).

And just as mass becomes significantly greater in physical terms (at extremely high energy levels) in reverse complementary fashion, the psychological experience of mass becomes significantly lower (as phenomena acquire a purely transparent existence).

So just as the Planck length sets a certain limit to the possibilities of phenomenal investigation (in physical terms), we have in a sense a corresponding Planck length (in psychological terms) which sets a certain limit to the possibilities of rational type interpretation. What this means in effect is that the dynamic interaction of polarities becomes so fluid that it is no longer possible to explicitly preserve any rigid linear element!

So even though the range of possible dimensional interpretations of reality is potentially infinite, explicitly in rational terms, meaningful interpretation could only take place within a - relatively small - finite number of these dimensions.

Thus in both physical and psychological terms, though phenomenal interactions still take place, they remain at a merely implicit level.

So from the physical perspective we can no longer experimentally investigate such interactions; equally from the psychological perspective we can no longer formally give them rational interpretation (even in an extremely refined intuitive manner).

However the actual unification of both aspects of strings (analytic and holistic) paradoxically can only take place through penetrating those very regions (below the Planck length).

In other words, ultimate unification with respect to strings comes neither at the level of detached (physical) verification nor (psychological) rational understanding. Rather it takes place in pure ineffable mystery (as the ever present source and goal of all life, both physical and psychological).

From the analytic perspective it is readily admitted that, as the string can vibrate in an infinite number of ways (with each unique vibration corresponding to a distinct matter particle) that potentially therefore we can generate an infinite no. of particles.

Now so far, only a relatively small finite number of distinct particles have been found. The actual explanation for this fact is due to the fact that actual particles discovered correspond to extremely low eneregy levels of vibration of the string. These likewise entails less energy (corresponding to relatively low masses).

New particles entailing greater vibration of the string would require extremely high amounts of energy (well beyond present technological capacity).

The reassuring fact therefore is that in terms of "normal" energy states we need only concern ourselves with a relatively small group of particles (corresponding to low vibrations of the string).

There is a fascinating counterpart in terms of the holistic notion of the string (corresponding to qualitative interpretation of reality).

Potentially as there are an infinite no. of possible (whole) dimensions, therefore we can likewise provide an infinite no. of possible interpretations for any physical event (with each interpretation relating to a unique dimensional number).

So the situation here might therefore seem hopeless for science (due an infinite range of possible interpretations).

However, given the present level of human evolution, we are capable of exploring only a very limited range of these dimensional interpretations.

As we have seen Conventional Science is still firmly rooted in the lowest psychological energy state (associated with 1-dimensional interpretation).

Though higher energy states are associated with authentic contemplative development, it would be quite rare - in terms of corresponding cognitive development - for it to grow significantly beyond the lower dimensions.

And I have persistently argued that these lower dimensions - certainly up to 8 - are of special significance in terms of integral appreciation.

It is possible however to describe in general terms what happens to interpretation at much higher (spiritual) energy states. Here phenomenal understanding becomes so transparent that it no longer even appears to arise in experience (with a person continually absorbed in a deep contemplative state of union).

And just as mass becomes significantly greater in physical terms (at extremely high energy levels) in reverse complementary fashion, the psychological experience of mass becomes significantly lower (as phenomena acquire a purely transparent existence).

So just as the Planck length sets a certain limit to the possibilities of phenomenal investigation (in physical terms), we have in a sense a corresponding Planck length (in psychological terms) which sets a certain limit to the possibilities of rational type interpretation. What this means in effect is that the dynamic interaction of polarities becomes so fluid that it is no longer possible to explicitly preserve any rigid linear element!

So even though the range of possible dimensional interpretations of reality is potentially infinite, explicitly in rational terms, meaningful interpretation could only take place within a - relatively small - finite number of these dimensions.

Thus in both physical and psychological terms, though phenomenal interactions still take place, they remain at a merely implicit level.

So from the physical perspective we can no longer experimentally investigate such interactions; equally from the psychological perspective we can no longer formally give them rational interpretation (even in an extremely refined intuitive manner).

However the actual unification of both aspects of strings (analytic and holistic) paradoxically can only take place through penetrating those very regions (below the Planck length).

In other words, ultimate unification with respect to strings comes neither at the level of detached (physical) verification nor (psychological) rational understanding. Rather it takes place in pure ineffable mystery (as the ever present source and goal of all life, both physical and psychological).

### More on Dimensions in String Theory

As stated so frequently in these blogs, the standard linear (1-dimensional) approach employed in Conventional Science is unable to maintain the key qualitative distinction (in any appropriate context) as between whole and part. It can only operate therefore by essentially reducing whole to part notions (in real conscious terms) or alternatively part to whole notions (in a likewise real conscious manner).

Fundamental therefore to maintaining the proper qualitative distinction as between both aspects is the recognition that unconscious (circular) and conscious (linear) notions must be formally incorporated with each other in interpretation.

As we have seen, whereas in a direct sense the conscious aspect of understanding relates to (real) rational interpretation (corresponding to either/or logic)), the unconscious relates directly to corresponding intuitive recognition (relating to complementary both/and logic).

However this latter intuitive aspect can be given an indirect rational interpretation in - what in precise holistic mathematical fashion is - an imaginary fashion.

So Conventional Science deals essentially with "reality" that is amenable to real rational interpretation. Though it must be readily admitted that complex mathematical notions are also widely used, these are restricted to merely quantitative type analysis. Thus the qualitative method of interpretation remains decidedly real.

However to deal adequately with "reality" requires that we incorporate likewise in qualitative terms an approach that is both real and imaginary.

Here essentially in terms of rational understanding we give expression to two distinct types of logical understanding. The real aspect requires standard either/or logic (based on the clear separation of polar opposites in experience); the imaginary aspect uses an alternative both/and logic (based on the dynamic complementarity of these same polar opposites in experience).

Thus, whereas the analytic aspect of scientific understanding (suited to differentiated interpretation) is directly associated with the real aspect, the corresponding holistic aspect (suited to integral interpretaton) is associated with the imaginary aspect.

So in qualitative terms, science needs to incorporate a complex rational approach (combining both real and imaginary aspects of understanding).

Now this is all deeply relevant to the very understanding of dimension in science.

Current accepted understanding - which is heavily based on solely real interpretation - is but a reduced notion that does not represent its true meaning.

Quite remarkably the true notion of dimension (with respect to both physical and psychological reality) corresponds exactly with the holistic mathematical notion (when interpreted in its qualitative fashion).

The very relationship as between object phenomena and dimensions relates in turn to the fundamental relationship of whole and part.

Now to properly preserve the true qualitative distinction as between whole and part (thereby avoiding reductionism) we must understand both aspects as real and imaginary with respect to each other.

In the very dynamics of experience, our actual appreciation of object phenomena and related dimensions (of space and time) requires the interaction of conscious and unconscious. Whereas the appreciation of objects relates directly to conscious recognition, dimensional appreciation (in providing a whole background context) is by contrast provided directly by the unconscious. Unfortunately, subsequently in rational interpretation, dimensions are simply reduced in terms of the parts (so that the whole - in any context - tends to be viewed as the sum of its quantitative parts).

To appreciate the true relationship of objects and dimensions, we need to consider the simple mathematical relationship whereby 1 is raised to a rational fractional power (say 1/4).

So if start with the base (object) number quantity as 1 and the dimension (i.e. power or exponent) as 1/4.

Now both of these numbers are linear (i.e. lie on the straight line).

However when we allow for interaction as between object quantity and dimensional quantity (through raising the former to the latter) a remarkable transformation takes place.

So when we raise 1 to 1/4 we obtain the result i (the square root of -1).

Now this new number is not linear (i.e. does not lie on the straight line). However it is circular (i.e. lies on the circle of unit radius drawn in the complex plane).

Thus whenever we raise a rational number to a rational fractional dimension (provided that the expression cannot be reduced further) a transformation takes place from linear to circular (in quantitative terms).

(In reverse manner when we now raise 1 to the circular dimension i, once again a transformation takes place this time from circular to linear.

So the result .207879... is linear lying on the straight line number scale).

Now what is completely missed in conventional mathematical understanding is that when we now raise the same number to a whole number dimension that a transformation likewise takes place from linear to circular (but now in qualitative terms).

So in holistic mathematical terms when we raise 1 to 4 i.e. express the number 1 with respect to 4-dimensional interpretation, the result is imaginary (corresponding to circular understanding).

Likewise when we interpret any relationship in an integer dimension (other than 1) a transformation takes place in the nature of understanding from linear to circular.

Now the very reason why this important finding is missed in conventional interpretation it solely operates in a linear manner (and thereby unable to preserve the uniqueness of qualitative distinctions).

So when we raise 1 to 4, though the qualitative nature of the relationship has now changed, in quantitative terms the result remains the same. In other words 1 (raised to the power of 4) is indistinguishable from 1 (raised to the power of 1) in standard linear interpretation. This is why - in a very precise manner - standard mathematical - and by extension standard scientific - interpretation is literally 1-dimensional!

So the true nature of object phenomena to dimensions (both with respect to physical reality and corresponding psychological interpretation) is as linear to circular which in rational translation is as real to imaginary.

Thus when "reality" is properly understood in dynamic interactive terms it is necessarily of a complex nature (with interacting real and imaginary components).

Now you may wonder where this all gets us with respect to string theory!

In the last blog, I made the important observation - that properly speaking - the very notion of a string can be given two distinct interpretations (which ultimately are complementary).

Once again in standard physical terms the 1-dimensional string is looked on as the fundamental building block of matter. The dynamic vibrations of the string then lead to the physical particles that comprise reality.

However there is equally another (unrecognised) qualitative psychological notion of a string. Here the 1-dimensional string (i.e. linear type understanding) is looked on as the basic building block for understanding of reality. However when such understanding dynamically vibrates it can then generate all the "higher" dimensions of understanding that comprise our potential interpretation of reality.

In this context in terms of our second notion of a string, conventional scientific appreciation (which is decidedly 1-dimensional in nature) simply represents the lowest possible energy state of the string (where very little dynamic vibration or interaction) is allowed.

One of the big "eureka" moments for me with respect to my complementary approach to stings came when reading Brian Greene's excellent book "The Elegant Universe".

On P. 144, in Figure 6.2 he gives some examples of vibrating strings, where just as the different vibrational patterns of a violin string give rise to different musical notes, the different patterns of a fundamental string give rise to different mass and force charges.

Now the three diagrams presented in this figure resemble pretty exactly the geometrical interpretation of the 2, 4 and 8 roots of unity respectively (which in holistic mathematical terms corresponds with the 2, 4 and 8 dimensions of scientific interpretation). And these are the very dimensions of interpretation that I have long advocated as essential in the integral scientific approach!

In "The Fabric of the Cosmos" Greene then repeats this diagram on p.357, now including an extra diagram (geometrically resembing the 16 roots of unity). And recently I have started to qualitatively incorporate 16-dimensional understanding in my interpretative model!

So the point once again is that in a more comprehensive understanding, the notion of a string needs to be defined in two complementary ways (corresponding to two distinct logical systems).

Once again the existing definition corresponds to attempted analytic understanding of physical reality (i.e. the real aspect of interpretation).

However the alternative definition, that I am providing, corresponds - by contrast - to attempted holistic understanding of both physical and psychological reality as complementary (i.e. the imaginary aspect of interpretation).

Adn then this is the crucial point!

Just as the relationship as between object phenomena to dimensions is correctly complex (as real to imaginary) then this clearly implies that we cannot hope to properly incorporate dimensions in string theory without likewise incorporating this alternative holistic understanding.

So to sum up, in qualitative holistic mathematical terms:

Conventional (Analytic) Science comprises the real part of (scientific) interpretation;

Integral (Holistic) Science comprises the imaginary part;

Radial (Comprehensive) Science combines both parts in a complex rational approach.

Fundamental therefore to maintaining the proper qualitative distinction as between both aspects is the recognition that unconscious (circular) and conscious (linear) notions must be formally incorporated with each other in interpretation.

As we have seen, whereas in a direct sense the conscious aspect of understanding relates to (real) rational interpretation (corresponding to either/or logic)), the unconscious relates directly to corresponding intuitive recognition (relating to complementary both/and logic).

However this latter intuitive aspect can be given an indirect rational interpretation in - what in precise holistic mathematical fashion is - an imaginary fashion.

So Conventional Science deals essentially with "reality" that is amenable to real rational interpretation. Though it must be readily admitted that complex mathematical notions are also widely used, these are restricted to merely quantitative type analysis. Thus the qualitative method of interpretation remains decidedly real.

However to deal adequately with "reality" requires that we incorporate likewise in qualitative terms an approach that is both real and imaginary.

Here essentially in terms of rational understanding we give expression to two distinct types of logical understanding. The real aspect requires standard either/or logic (based on the clear separation of polar opposites in experience); the imaginary aspect uses an alternative both/and logic (based on the dynamic complementarity of these same polar opposites in experience).

Thus, whereas the analytic aspect of scientific understanding (suited to differentiated interpretation) is directly associated with the real aspect, the corresponding holistic aspect (suited to integral interpretaton) is associated with the imaginary aspect.

So in qualitative terms, science needs to incorporate a complex rational approach (combining both real and imaginary aspects of understanding).

Now this is all deeply relevant to the very understanding of dimension in science.

Current accepted understanding - which is heavily based on solely real interpretation - is but a reduced notion that does not represent its true meaning.

Quite remarkably the true notion of dimension (with respect to both physical and psychological reality) corresponds exactly with the holistic mathematical notion (when interpreted in its qualitative fashion).

The very relationship as between object phenomena and dimensions relates in turn to the fundamental relationship of whole and part.

Now to properly preserve the true qualitative distinction as between whole and part (thereby avoiding reductionism) we must understand both aspects as real and imaginary with respect to each other.

In the very dynamics of experience, our actual appreciation of object phenomena and related dimensions (of space and time) requires the interaction of conscious and unconscious. Whereas the appreciation of objects relates directly to conscious recognition, dimensional appreciation (in providing a whole background context) is by contrast provided directly by the unconscious. Unfortunately, subsequently in rational interpretation, dimensions are simply reduced in terms of the parts (so that the whole - in any context - tends to be viewed as the sum of its quantitative parts).

To appreciate the true relationship of objects and dimensions, we need to consider the simple mathematical relationship whereby 1 is raised to a rational fractional power (say 1/4).

So if start with the base (object) number quantity as 1 and the dimension (i.e. power or exponent) as 1/4.

Now both of these numbers are linear (i.e. lie on the straight line).

However when we allow for interaction as between object quantity and dimensional quantity (through raising the former to the latter) a remarkable transformation takes place.

So when we raise 1 to 1/4 we obtain the result i (the square root of -1).

Now this new number is not linear (i.e. does not lie on the straight line). However it is circular (i.e. lies on the circle of unit radius drawn in the complex plane).

Thus whenever we raise a rational number to a rational fractional dimension (provided that the expression cannot be reduced further) a transformation takes place from linear to circular (in quantitative terms).

(In reverse manner when we now raise 1 to the circular dimension i, once again a transformation takes place this time from circular to linear.

So the result .207879... is linear lying on the straight line number scale).

Now what is completely missed in conventional mathematical understanding is that when we now raise the same number to a whole number dimension that a transformation likewise takes place from linear to circular (but now in qualitative terms).

So in holistic mathematical terms when we raise 1 to 4 i.e. express the number 1 with respect to 4-dimensional interpretation, the result is imaginary (corresponding to circular understanding).

Likewise when we interpret any relationship in an integer dimension (other than 1) a transformation takes place in the nature of understanding from linear to circular.

Now the very reason why this important finding is missed in conventional interpretation it solely operates in a linear manner (and thereby unable to preserve the uniqueness of qualitative distinctions).

So when we raise 1 to 4, though the qualitative nature of the relationship has now changed, in quantitative terms the result remains the same. In other words 1 (raised to the power of 4) is indistinguishable from 1 (raised to the power of 1) in standard linear interpretation. This is why - in a very precise manner - standard mathematical - and by extension standard scientific - interpretation is literally 1-dimensional!

So the true nature of object phenomena to dimensions (both with respect to physical reality and corresponding psychological interpretation) is as linear to circular which in rational translation is as real to imaginary.

Thus when "reality" is properly understood in dynamic interactive terms it is necessarily of a complex nature (with interacting real and imaginary components).

Now you may wonder where this all gets us with respect to string theory!

In the last blog, I made the important observation - that properly speaking - the very notion of a string can be given two distinct interpretations (which ultimately are complementary).

Once again in standard physical terms the 1-dimensional string is looked on as the fundamental building block of matter. The dynamic vibrations of the string then lead to the physical particles that comprise reality.

However there is equally another (unrecognised) qualitative psychological notion of a string. Here the 1-dimensional string (i.e. linear type understanding) is looked on as the basic building block for understanding of reality. However when such understanding dynamically vibrates it can then generate all the "higher" dimensions of understanding that comprise our potential interpretation of reality.

In this context in terms of our second notion of a string, conventional scientific appreciation (which is decidedly 1-dimensional in nature) simply represents the lowest possible energy state of the string (where very little dynamic vibration or interaction) is allowed.

One of the big "eureka" moments for me with respect to my complementary approach to stings came when reading Brian Greene's excellent book "The Elegant Universe".

On P. 144, in Figure 6.2 he gives some examples of vibrating strings, where just as the different vibrational patterns of a violin string give rise to different musical notes, the different patterns of a fundamental string give rise to different mass and force charges.

Now the three diagrams presented in this figure resemble pretty exactly the geometrical interpretation of the 2, 4 and 8 roots of unity respectively (which in holistic mathematical terms corresponds with the 2, 4 and 8 dimensions of scientific interpretation). And these are the very dimensions of interpretation that I have long advocated as essential in the integral scientific approach!

In "The Fabric of the Cosmos" Greene then repeats this diagram on p.357, now including an extra diagram (geometrically resembing the 16 roots of unity). And recently I have started to qualitatively incorporate 16-dimensional understanding in my interpretative model!

So the point once again is that in a more comprehensive understanding, the notion of a string needs to be defined in two complementary ways (corresponding to two distinct logical systems).

Once again the existing definition corresponds to attempted analytic understanding of physical reality (i.e. the real aspect of interpretation).

However the alternative definition, that I am providing, corresponds - by contrast - to attempted holistic understanding of both physical and psychological reality as complementary (i.e. the imaginary aspect of interpretation).

Adn then this is the crucial point!

Just as the relationship as between object phenomena to dimensions is correctly complex (as real to imaginary) then this clearly implies that we cannot hope to properly incorporate dimensions in string theory without likewise incorporating this alternative holistic understanding.

So to sum up, in qualitative holistic mathematical terms:

Conventional (Analytic) Science comprises the real part of (scientific) interpretation;

Integral (Holistic) Science comprises the imaginary part;

Radial (Comprehensive) Science combines both parts in a complex rational approach.

## Tuesday, January 12, 2010

### The Problem With A String

I have always had philosophical problems with the definition of a string. Indeed my interest in the area originally arose out of an attempt to redefine some of its key concepts in a way that I - at least - could find intuitively satisfying.

This relates to a deeper problem with the whole area in that theorists and practitioners seem unable to bridge the gap as between mathematically satisfying results and a coherent explanation of the physical concepts involved (that can evoke any acceptable resonance with the manner in which people understand reality).

So at the moment string theory resembles a kind of secret code that undoubtedly can generate many exciting mathematical results (suggestive of deep physical connections). However without a much more coherent philosophical decoding of the nature of its concepts it cannot really qualify as a true physical explanation of reality.

So the problem with strings not alone relates to the present difficulties in finding ways of experimentally testing its mathematical findings; perhaps more significantly, it also relates to even greater difficulties in providing an intuitively satisfying means of the nature of its concepts.

From my own perspective the root of this problem is easy enough to state. Once again conventional scientific method is based formally on mere 1-dimensional interpretation of reality (which conforms best with everyday intuitive notions of the nature of macro reality).

However when we probe at the extreme margins of reality, 1-dimensional interpretation breaks down as a means of adequately conveying the nature of reality investigated.

What is needed in effect are progressively higher dimensional interpretations that incorporate both (analytic) linear and (holistic) circular notions in ever more refined fashion.

So my own investigations with respect to Integral Science are designed with a view to providing - in basic fashion - this much needed holistic dimension. It is not properly geared to developing quantitative theories (that can in principle be tested experimentally). Rather it is designed to provide the holistic framework within which concepts - such as in string theory - can be given an appropriate philosophical explanation (that intuitively concurs with the new understanding adopted).

It must be apparent to conventional physicists that the attempted definition of a string is unsatisfactory.

We are led to believe that a string is an object with one spatial dimension of length (but lacking any other dimensions).

Though it might indeed be useful in mathematical terms to characterise a string in such a fashion, clearly it does not stand up in philosophical terms.

In conventional terms we cannot conceive of an object that is 1-dimensional. Once again though in geometrical terms we can represent a line that is 1-dimensional, this is simply an idealisation that does not strictly hold in physical terms. So any line that we actually try to represent must inevitably possess a degree of width (for its phenomenal identity to be established).

So if a string has length (without any thickness) how can its phenomenal identity be established? Also what about time in such a characterisation? Surely, again a string to have phenomenal meaning must have some sort of existence in time!

Also to even talk about a string is to attempt to give it a distinct identity (which is a merely linear notion of interpretation). And this presupposes that we can somehow place the string in a pre-established dimensional framework (of space and time). But even physicists will accept that realistically speaking, that the string must in some way embody these very dimensions (as contained in the same entity).

The best way of moving towards a more satisfactory explanation is initially with reference to the conventional piece of string. As we know we can stretch a string out in a linear manner. We can also if we wish fold it around in circular fashion. Or we can equally bend and twist the string in variety of configurations (in both linear and circular fashion).

So in philosophical terms the basic starting point for a coherent definition of strings is the realisation that we must combine both linear (analytic) and circular (holistic) notions. From a psychological perspective this entails that interpretation must necessarily entail meaning pertaining to both conscious and unconscious. Whereas in direct sense the conscious (analytic) aspect corresponds to rational understanding, the unconscious (holistic) properly relates to intuitive appreciation.

Therefore in corresponding physical fashion we must conceive of reality itself entailing the interaction of two distinct modes that are real and imaginary with respect to each other.

Therefore a string (and indeed combined group of strings) must be rooted in a dynamically conceived complex notion of reality (with - relatively - switching, real and imaginary aspects)

In this way both the (whole) dimensional and (part) object aspects of the strings can be viewed in dynamic interacting real and imaginary fashion (which continually altenate).

However once again this dynamic view of physical reality must be complemented by an equally dynamic interpretative mode (that combines real and imaginary aspects).

The huge problem with present attempted understanding is that is confined formally to merely real modes of interpretation. This is the very reason therefore why physicists finds it so difficult to properly incorporate dimensions within string theory.

To do this satisfactorily will require a radical new scientific approach that combines both conventional (linear) and new integral (circular) modes of interpretation.

This relates to a deeper problem with the whole area in that theorists and practitioners seem unable to bridge the gap as between mathematically satisfying results and a coherent explanation of the physical concepts involved (that can evoke any acceptable resonance with the manner in which people understand reality).

So at the moment string theory resembles a kind of secret code that undoubtedly can generate many exciting mathematical results (suggestive of deep physical connections). However without a much more coherent philosophical decoding of the nature of its concepts it cannot really qualify as a true physical explanation of reality.

So the problem with strings not alone relates to the present difficulties in finding ways of experimentally testing its mathematical findings; perhaps more significantly, it also relates to even greater difficulties in providing an intuitively satisfying means of the nature of its concepts.

From my own perspective the root of this problem is easy enough to state. Once again conventional scientific method is based formally on mere 1-dimensional interpretation of reality (which conforms best with everyday intuitive notions of the nature of macro reality).

However when we probe at the extreme margins of reality, 1-dimensional interpretation breaks down as a means of adequately conveying the nature of reality investigated.

What is needed in effect are progressively higher dimensional interpretations that incorporate both (analytic) linear and (holistic) circular notions in ever more refined fashion.

So my own investigations with respect to Integral Science are designed with a view to providing - in basic fashion - this much needed holistic dimension. It is not properly geared to developing quantitative theories (that can in principle be tested experimentally). Rather it is designed to provide the holistic framework within which concepts - such as in string theory - can be given an appropriate philosophical explanation (that intuitively concurs with the new understanding adopted).

It must be apparent to conventional physicists that the attempted definition of a string is unsatisfactory.

We are led to believe that a string is an object with one spatial dimension of length (but lacking any other dimensions).

Though it might indeed be useful in mathematical terms to characterise a string in such a fashion, clearly it does not stand up in philosophical terms.

In conventional terms we cannot conceive of an object that is 1-dimensional. Once again though in geometrical terms we can represent a line that is 1-dimensional, this is simply an idealisation that does not strictly hold in physical terms. So any line that we actually try to represent must inevitably possess a degree of width (for its phenomenal identity to be established).

So if a string has length (without any thickness) how can its phenomenal identity be established? Also what about time in such a characterisation? Surely, again a string to have phenomenal meaning must have some sort of existence in time!

Also to even talk about a string is to attempt to give it a distinct identity (which is a merely linear notion of interpretation). And this presupposes that we can somehow place the string in a pre-established dimensional framework (of space and time). But even physicists will accept that realistically speaking, that the string must in some way embody these very dimensions (as contained in the same entity).

The best way of moving towards a more satisfactory explanation is initially with reference to the conventional piece of string. As we know we can stretch a string out in a linear manner. We can also if we wish fold it around in circular fashion. Or we can equally bend and twist the string in variety of configurations (in both linear and circular fashion).

So in philosophical terms the basic starting point for a coherent definition of strings is the realisation that we must combine both linear (analytic) and circular (holistic) notions. From a psychological perspective this entails that interpretation must necessarily entail meaning pertaining to both conscious and unconscious. Whereas in direct sense the conscious (analytic) aspect corresponds to rational understanding, the unconscious (holistic) properly relates to intuitive appreciation.

Therefore in corresponding physical fashion we must conceive of reality itself entailing the interaction of two distinct modes that are real and imaginary with respect to each other.

Therefore a string (and indeed combined group of strings) must be rooted in a dynamically conceived complex notion of reality (with - relatively - switching, real and imaginary aspects)

In this way both the (whole) dimensional and (part) object aspects of the strings can be viewed in dynamic interacting real and imaginary fashion (which continually altenate).

However once again this dynamic view of physical reality must be complemented by an equally dynamic interpretative mode (that combines real and imaginary aspects).

The huge problem with present attempted understanding is that is confined formally to merely real modes of interpretation. This is the very reason therefore why physicists finds it so difficult to properly incorporate dimensions within string theory.

To do this satisfactorily will require a radical new scientific approach that combines both conventional (linear) and new integral (circular) modes of interpretation.

### Ramanujan and Strings

In the previous post, I demonstrated the interesting fact that with respect to root quantitative values (and corresponding dimensional qualitative values) that both n = 8 and n = 24 play a special role.

Here with respect to the relationship cos(360/n) + i sin(360/n) the square of sum of (absolute) real and imaginary values = 2, for n = 8, and = 1.5, for n = 24 (where all possible values range from 1 to 2).

So the former represents the maximum that can be attained whereas the latter represents the mean average (of all possible values).

Let us remind ourselves of the context out of which this has arisen!

Earlier I explained how the original Jungian Theory of Personality Types was based on 8 distinctive types.

Then in the holistic mathematical extension of this approach (based on permutations the four key coordinate points on the complex plane) 24 distinctive types could be defined.

One way of looking on each Personality Type is that it provides a unique way of configuring characteristic experience of the 4 dimensions of space and time.

So in this dynamic interactive sense, a dimension is now understood as representing - not a separate entity - but rather uniquely distinctive arrangements of all 4 dimensions.

However the holistic mathematical approach that yields fundamental "Personality Types" (in psychological terms) equally yields corresponding "Impersonality Types" (in physical terms).

Now this is where the connection with string reality can be made. As - properly speaking - at this level, physical phenomena are inseparable from the dimensions with which they interact, we cannot view the notion of dimension (as at the macro level) as an independent entity but rather as a configuration of - as yet - entangled embryonic dimensions (where matter cannot be properly distinguished from its holistic background environment).

Some years ago I was reading "Hyperspace" by Michio Kaku. In a Chapter on "Superstrings" to refers to Ramanujan Functions and how the number 24 repeatedly appears in his work. Also the number 24 is also the origin of the mysterious cancellations occurring in string theory (thus enabling its consistency).

So in string theory each of the 24 modes in the Ramanujan function corresponds to a physical vibration of the string.

We could of course equally say that each of the 24 modes (with respect to Personality Types) correspond to a unique psychological vibration relating to a distinct personality type.

Now the very rationale of Integral - as opposed to Conventional - Science is that we can always establish a complementary psychological interpretation for every physical notion (or alternatively physical for every psychological notion). So the very means of achieving integration in experience derives from successfully establishing at the deepest levels such complementary links!

So we now are we seeing a way here through which the very notion of "a string" can be given both complementary physical and psychological interpretations.

So once again in physical terms each of the 24 modes (in the Ramanujan Function) corresponds to a unique vibration of the string!

Now in corresponding psychological fashion, we see that each of the 24 modes corresponds to a unique vibration of the string!

Thus whereas in the former, a string is designed to represent a basic physical entity, in the latter a string now represents a basic means of psychological interpretation of reality!

The significance of this is quite momentous.

Conventional Science is conducted within just one standard mode of interpretation i.e. the default linear (1-dimensional mode). The very essence of this mode is that qualitative is reduced to quantitative meaning.

However once we allow for true qualitative - as opposed to strict quantitative - meaning we then see that parallel psychological holistic interpretations exist for all analytically defined concepts (in physical terms).

When the Ramanujan function is generalised, the number 24 is replaced by the number 8. Now physicists customarily include two additional dimensions.

Thus earlier superstring theories were based on 24 + 2 = 26 dimensions, and in generalised terms 8 + 2 = 10 dimensions.

Now Kaku gives an explanation at the end of the Chapter for the inclusion of these two additional dimensions. Basically the extra dimensions are included to allow for symmetrical (as well as asymmetrical) states so that the 8 and 24 respectively relate to the asymmetrical vibrations of the string.

In corresponding psychological terms we could equally include two additional symmetrical states (relating to attainment of a pure state of spiritual unity and alternatively pure state of nothingness respectively).

Recent developments with M-theory would suggest 11 dimensions (9 + 2) as the ultimate arrangement.

Interestingly, perhaps the best known Personality System (The Enneagram) is based on 9 distinctive types. So this would complement the new physical understanding.

However this is not the important issue. What I am anxious to demonstrate here is that we need to use a distinctive notion of dimension (in string theory) as the dynamic configuration of - yet - not properly formed dimensions (where matter particles cannot be clearly distinguished from these dimensions).

Secondly the very notion of a string needs to be significantly extended to include complementary physical and psychological aspects.

Whereas in physical terms the vibration of a string results uniquely in distinctive matter particles, in corresponding psychological terms the vibration of a string results uniquely in distinctive qualitative interpretations of this reality. Linear interpretation (i.e. 1-dimensional) simply characterises the lowest mode of vibration of the psychological string (where dynamic interaction as between psychological and physical aspects of reality is ignored). This then results in the illusion that we can somehow "objectively" understand physical reality in a comprehensive manner.

As Conventional Science by its very nature simply reduces the qualitative to the quantitative aspect, it can never (by itself) unravel the true mystery of string reality. Indeed, even the very hope in an eventual quantitative TOE reveals its reductionist nature.

Here with respect to the relationship cos(360/n) + i sin(360/n) the square of sum of (absolute) real and imaginary values = 2, for n = 8, and = 1.5, for n = 24 (where all possible values range from 1 to 2).

So the former represents the maximum that can be attained whereas the latter represents the mean average (of all possible values).

Let us remind ourselves of the context out of which this has arisen!

Earlier I explained how the original Jungian Theory of Personality Types was based on 8 distinctive types.

Then in the holistic mathematical extension of this approach (based on permutations the four key coordinate points on the complex plane) 24 distinctive types could be defined.

One way of looking on each Personality Type is that it provides a unique way of configuring characteristic experience of the 4 dimensions of space and time.

So in this dynamic interactive sense, a dimension is now understood as representing - not a separate entity - but rather uniquely distinctive arrangements of all 4 dimensions.

However the holistic mathematical approach that yields fundamental "Personality Types" (in psychological terms) equally yields corresponding "Impersonality Types" (in physical terms).

Now this is where the connection with string reality can be made. As - properly speaking - at this level, physical phenomena are inseparable from the dimensions with which they interact, we cannot view the notion of dimension (as at the macro level) as an independent entity but rather as a configuration of - as yet - entangled embryonic dimensions (where matter cannot be properly distinguished from its holistic background environment).

Some years ago I was reading "Hyperspace" by Michio Kaku. In a Chapter on "Superstrings" to refers to Ramanujan Functions and how the number 24 repeatedly appears in his work. Also the number 24 is also the origin of the mysterious cancellations occurring in string theory (thus enabling its consistency).

So in string theory each of the 24 modes in the Ramanujan function corresponds to a physical vibration of the string.

We could of course equally say that each of the 24 modes (with respect to Personality Types) correspond to a unique psychological vibration relating to a distinct personality type.

Now the very rationale of Integral - as opposed to Conventional - Science is that we can always establish a complementary psychological interpretation for every physical notion (or alternatively physical for every psychological notion). So the very means of achieving integration in experience derives from successfully establishing at the deepest levels such complementary links!

So we now are we seeing a way here through which the very notion of "a string" can be given both complementary physical and psychological interpretations.

So once again in physical terms each of the 24 modes (in the Ramanujan Function) corresponds to a unique vibration of the string!

Now in corresponding psychological fashion, we see that each of the 24 modes corresponds to a unique vibration of the string!

Thus whereas in the former, a string is designed to represent a basic physical entity, in the latter a string now represents a basic means of psychological interpretation of reality!

The significance of this is quite momentous.

Conventional Science is conducted within just one standard mode of interpretation i.e. the default linear (1-dimensional mode). The very essence of this mode is that qualitative is reduced to quantitative meaning.

However once we allow for true qualitative - as opposed to strict quantitative - meaning we then see that parallel psychological holistic interpretations exist for all analytically defined concepts (in physical terms).

When the Ramanujan function is generalised, the number 24 is replaced by the number 8. Now physicists customarily include two additional dimensions.

Thus earlier superstring theories were based on 24 + 2 = 26 dimensions, and in generalised terms 8 + 2 = 10 dimensions.

Now Kaku gives an explanation at the end of the Chapter for the inclusion of these two additional dimensions. Basically the extra dimensions are included to allow for symmetrical (as well as asymmetrical) states so that the 8 and 24 respectively relate to the asymmetrical vibrations of the string.

In corresponding psychological terms we could equally include two additional symmetrical states (relating to attainment of a pure state of spiritual unity and alternatively pure state of nothingness respectively).

Recent developments with M-theory would suggest 11 dimensions (9 + 2) as the ultimate arrangement.

Interestingly, perhaps the best known Personality System (The Enneagram) is based on 9 distinctive types. So this would complement the new physical understanding.

However this is not the important issue. What I am anxious to demonstrate here is that we need to use a distinctive notion of dimension (in string theory) as the dynamic configuration of - yet - not properly formed dimensions (where matter particles cannot be clearly distinguished from these dimensions).

Secondly the very notion of a string needs to be significantly extended to include complementary physical and psychological aspects.

Whereas in physical terms the vibration of a string results uniquely in distinctive matter particles, in corresponding psychological terms the vibration of a string results uniquely in distinctive qualitative interpretations of this reality. Linear interpretation (i.e. 1-dimensional) simply characterises the lowest mode of vibration of the psychological string (where dynamic interaction as between psychological and physical aspects of reality is ignored). This then results in the illusion that we can somehow "objectively" understand physical reality in a comprehensive manner.

As Conventional Science by its very nature simply reduces the qualitative to the quantitative aspect, it can never (by itself) unravel the true mystery of string reality. Indeed, even the very hope in an eventual quantitative TOE reveals its reductionist nature.

## Sunday, January 10, 2010

### The Number 24

24 in its own right is a fascinating number.

Firstly it represents all the permutations of 4 (containing 4 elements) that can be made from 4 which is 4 * 3 * 2 * 1.

However there is another very interesting property that if we add up the squares of the consecutive numbers from 1 to 24 (inclusive) that the result 4900 will be the square of an exact whole number i.e (70).

This is the only case known where the sum of squares of successive natural numbers is equal to the square of another whole number!

Interestingly the sum of 1 + 2 + 3 +....+ 24 = 300, while the sum of the prime numbers between 1 and 24 = 100!

24 - as we shall see - plays a key role in Ramanujan functions, which in turn provides a direct link to the number of dimensions in one of the earlier string theories.

24 also plays a crucial role in the search for the Monster Group (the largest known symmetrical object) which again provides a direct connection with string theory.

As we know, if the proper divisors of a perfect number are summed, the total is the same number. So for example 1, 2 and 3 are the proper divisors of 6 and the sume of 1 + 2 + 3 = 6. So the ratio here of proper divisors to the number = 1

Now 24 is not a perfect number. However interestingly the ratio of its proper divisors to the number = 1.5.

Another highly interesting relationship to 24 that equally results in 1.5 is worth commenting on in greater length.

I mentioned in an earlier contribution that I had found a mathematical justification as to why the 1, 2, 4 and 8 dimensions play an especially important role in an overall integral approach.

Once again the holistic qualitative notion of dimension is directly linked to the quantitative structure of its corresponding root (of unity).

So 1 qualitatively is related directly to the 1st root (of unity) which is identical. Thus in effect, no clear distinction exists as between qualitative and quantitative interpretation with respect to the 1st dimension.

To obtain the nth root of any number (which in qualitative terms corresponds with its nth dimension) we simply obtain cos (360/n) + i sin (360/n)

The value of both cos and sin will range in absolute terms as between 0 and 1.

Then when we add both terms and square the result, the absolute value will range between 1 and 2.

Now when the root and dimension is 1 the value is 1 + i (0) = 1.

So here we have a maximum in terms of the real part representing the absolute dominance of rational understanding according to one dimensional i.e. linear interpretation. Equally we have a minimum in terms of the square of sum of sin and cos values = 1.

When root and dimension is 2 the value is cos 180 + i sin 180 = - 1 + i (0) = - 1.

Now we have a maximum in terms of the negative real part. This reflects in turn the dominance of negative linear (i.e. intuitive) understanding.

Equally again the square of the absolute sum of sin and cos values = 1 (which again is a minimum in terms of what can be achieved).

When root and dimension is 4 the value is cos 90 + i sin 90 = 0 + i (1) = i.

Now we have a maximum in terms of the positive imaginary part. This reflects in turn the dominance of imaginary linear (i.e. the indirect rational expression of intuitive) understanding.

Equally again the square of the absolute sum of cos and sin values = 1 (which again is a minimum in terms of what can be achieved).

Finally when root and dimension is 8, the value is cos 45 + i sin 45 = 1/(sq. root of 2) + i/(sq. root of 2).

Now we have a balanced equality in terms of real and imaginary parts. This reflects in turn the harmonisation of rational (conscious) and intuitive (unconscious) understanding.

Equally again the square of the absolute sum of cos and sin values = 2 (which now is a maximum in terms of what can be achieved, representing the limit in terms of pure contemplative integration of experience).

So what we see is that 1, 2, 4 and 8 dimensional interpretation represent specialised extremes in terms of rational (real), intuitive, rational (imaginary) and empty understanding (as the equality of conscious and unconscious) respectively.

One could perhaps suggest therefore that the ideal radial balance (in terms of overall understanding) should come at the midpoint between the two extreme values i.e. 1 and 2 (for the square of absolute sum of cos and sin values).

Now this in fact happens when n = 24.

Therefore from this perspective, 24-dimensional understanding represents the ideal in terms of overall balanced understanding.

Coming back to the previous post on Personality Types, this would suggest that for truly balanced radial understanding of reality, one would need to successfully combine attributes of all 24 Personality Types.

So when we look at development from a radial perspective , the key goal is to successfully differentiate (to a degree) traits associated with each Personality Type before then integrating all in a simultaneous manner.

Firstly it represents all the permutations of 4 (containing 4 elements) that can be made from 4 which is 4 * 3 * 2 * 1.

However there is another very interesting property that if we add up the squares of the consecutive numbers from 1 to 24 (inclusive) that the result 4900 will be the square of an exact whole number i.e (70).

This is the only case known where the sum of squares of successive natural numbers is equal to the square of another whole number!

Interestingly the sum of 1 + 2 + 3 +....+ 24 = 300, while the sum of the prime numbers between 1 and 24 = 100!

24 - as we shall see - plays a key role in Ramanujan functions, which in turn provides a direct link to the number of dimensions in one of the earlier string theories.

24 also plays a crucial role in the search for the Monster Group (the largest known symmetrical object) which again provides a direct connection with string theory.

As we know, if the proper divisors of a perfect number are summed, the total is the same number. So for example 1, 2 and 3 are the proper divisors of 6 and the sume of 1 + 2 + 3 = 6. So the ratio here of proper divisors to the number = 1

Now 24 is not a perfect number. However interestingly the ratio of its proper divisors to the number = 1.5.

Another highly interesting relationship to 24 that equally results in 1.5 is worth commenting on in greater length.

I mentioned in an earlier contribution that I had found a mathematical justification as to why the 1, 2, 4 and 8 dimensions play an especially important role in an overall integral approach.

Once again the holistic qualitative notion of dimension is directly linked to the quantitative structure of its corresponding root (of unity).

So 1 qualitatively is related directly to the 1st root (of unity) which is identical. Thus in effect, no clear distinction exists as between qualitative and quantitative interpretation with respect to the 1st dimension.

To obtain the nth root of any number (which in qualitative terms corresponds with its nth dimension) we simply obtain cos (360/n) + i sin (360/n)

The value of both cos and sin will range in absolute terms as between 0 and 1.

Then when we add both terms and square the result, the absolute value will range between 1 and 2.

Now when the root and dimension is 1 the value is 1 + i (0) = 1.

So here we have a maximum in terms of the real part representing the absolute dominance of rational understanding according to one dimensional i.e. linear interpretation. Equally we have a minimum in terms of the square of sum of sin and cos values = 1.

When root and dimension is 2 the value is cos 180 + i sin 180 = - 1 + i (0) = - 1.

Now we have a maximum in terms of the negative real part. This reflects in turn the dominance of negative linear (i.e. intuitive) understanding.

Equally again the square of the absolute sum of sin and cos values = 1 (which again is a minimum in terms of what can be achieved).

When root and dimension is 4 the value is cos 90 + i sin 90 = 0 + i (1) = i.

Now we have a maximum in terms of the positive imaginary part. This reflects in turn the dominance of imaginary linear (i.e. the indirect rational expression of intuitive) understanding.

Equally again the square of the absolute sum of cos and sin values = 1 (which again is a minimum in terms of what can be achieved).

Finally when root and dimension is 8, the value is cos 45 + i sin 45 = 1/(sq. root of 2) + i/(sq. root of 2).

Now we have a balanced equality in terms of real and imaginary parts. This reflects in turn the harmonisation of rational (conscious) and intuitive (unconscious) understanding.

Equally again the square of the absolute sum of cos and sin values = 2 (which now is a maximum in terms of what can be achieved, representing the limit in terms of pure contemplative integration of experience).

So what we see is that 1, 2, 4 and 8 dimensional interpretation represent specialised extremes in terms of rational (real), intuitive, rational (imaginary) and empty understanding (as the equality of conscious and unconscious) respectively.

One could perhaps suggest therefore that the ideal radial balance (in terms of overall understanding) should come at the midpoint between the two extreme values i.e. 1 and 2 (for the square of absolute sum of cos and sin values).

Now this in fact happens when n = 24.

Therefore from this perspective, 24-dimensional understanding represents the ideal in terms of overall balanced understanding.

Coming back to the previous post on Personality Types, this would suggest that for truly balanced radial understanding of reality, one would need to successfully combine attributes of all 24 Personality Types.

So when we look at development from a radial perspective , the key goal is to successfully differentiate (to a degree) traits associated with each Personality Type before then integrating all in a simultaneous manner.

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