In the last blog entry, I introduced a new dynamic holistic way for viewing the nature of time (and space) which is based on interaction of the fundamental poles of experience.

So from one perspective external (objective) and internal (subjective) aspects always dynamically interact in experience; from an equally important perspective whole (collective) and part (individual) aspects likewise interact.

When we appreciate time ( and space) in the dynamic context of complementary external and internal aspects, time is revealed as possessing two dimensions (or directions) that are positive and negative with respect to each other; likewise space has also two dimensions (or directions) that are positive and negative with respect to each other.

In a similar manner to left and right turns at a crossroads, what is positive or negative is of a relative arbitrary nature, dependent on context.

Now when looked at from the appropriate perspective, time and space (as possessing both positive and negative directions) necessarily directly relates to the very nature of experience.

However customary interpretation of space and time is heavily based on limited linear (1-dimensional) notions.

Here space and time are separated in an asymmetrical manner (with 3 dimensions of space and 1 dimension of time). Likewise the spatial dimensions are readily identified with rigid notions of form (in quantitative terms). Though time necessarily has an also indirect nature, capable of quantitative measurement, it is appreciated in a more qualitative manner.

So the very notion of linear (1-dimensional) understanding based on single separate frames of reference is directly related to the customary interpretation of time, as likewise 1-dimensional, with a single positive (i.e. forward) direction.

In philosophical terms, this is directly equated with the nature of dualistic understanding (which always implies independent poles as frames of reference).

However in the various contemplative traditions the possibility of "higher" dimensional appreciation has long been recognised, where rigid dual notions increasingly give way to a more refined nondual form of awareness, which is directly of a spiritual intuitive nature.

What however has not been properly appreciated are the huge implications of such awareness for intellectual appreciation of the world (especially our most fundamental mathematical and scientific notions).

Nondual experience relates directly to spiritual intuitive awareness of the present moment. So once phenomenal identity arises in experience, a framework of relative space and time is necessarily involved (with directions that are paradoxical from an overall perspective).

So the very appreciation of the nondual (in a direct awareness of the present moment) provides the appropriate means for enabling the more refined switching as between opposite external and internal polarities, with a deepening appreciation of the merely relative nature of all phenomenal truth.

Thus in a very real experiential sense, positive and negative polarities, with respect to space and time, keep cancelling each other in experience, leading to a deeper spiritual awareness of the underlying absolute nature of reality that is always in the present moment.

In general terms the earliest stages with respect to the mature development of spiritual contemplative awareness relate to the movement from the somewhat dualistic appreciation of external and internal poles as separate, to a deepening realisation of their nondual nature, as dynamically complementary with each other (and ultimately identical in an ineffable manner).

This correspondingly leads to a breakdown with respect to the customary linear experience of space and time.

For example during the (positive) illuminative stages of such development one tends to look on the external world in an expansive manner with endless possibilities for further refined engagement in phenomenal terms.

However this leads inevitably to a problem of growing attachment to the secondary symbols through which spiritual truth is mediated, eventually leading to the need for a substantial period of purgation (spiritual cleansing) whereby the focus is directly on the eradication of undue attachment.

This purgation is then is associated with a profound experience of the negative direction of both space and time. It feels as if space and time undergo extreme compression so that - literally - the dimensional framework no longer exists to carry out one's customary activities. So as one sees the undoing of many skills and activities, with which one was previously associated, it genuinely is experienced in psychological terms as backward movement in space and time.

So the direction now switches dramatically from external (conscious) to internal (unconscious) activity.

Then growing development of the unconscious in a new internal environment of space and time starts to take place with the same problems of undue attachment gradually arising leading to the need for a new more internal purgation.

This now leads to marked compression of one's internal framework of space and time with eventually sufficient harmony restored, so that a new even more refined expansive phase of illumination (with respect to the external world) eventually takes place.

Thus what happens during these periods is that absolute linear notions of space and time gradually break down to be replaced by understanding of an increasingly relative nature. So one better appreciates that both external and internal directions of experience are positive and negative (and ultimately completely paradoxical) with respect to each other.

Thus refined phenomenal notions of space and time, of an increasingly relative form, are experienced against an underlying background of the absolute present moment (that is directly of a spiritual intuitive nature).

# Number and Spacetime

A radical new interpretation of the true holistic nature of space and time

## Wednesday, June 18, 2014

## Wednesday, April 2, 2014

### Paradox of Time

I mentioned in the last blog entry how the conventional notion of time as linear, directly reflects a corresponding linear mode of rational understanding, where the objective aspect of experience is abstracted in an absolute manner.

However it is quite easy to show the limitations of this notion of time.

Once again in this context it is helpful to consider the simple example of a crossroads. If one travels in the direction N up a straight road, one can unambiguously identify the left turn (at this crossroads). If now travelling in the opposite S direction, one encounters the crossroads, again one can again unambiguously identify the left turn. However both of these turns (in terms of isolated N and S reference frames) are thereby identified as left!

However we can immediately recognise a problem in that relative to each other these turns are left and right and right and left respectively.

Now we have exactly the same situation with respect to the identification of time.

So whereas in the crossroads example we used the polar opposite of N and S as reference frames, in the experiential context now of the experience of time, we use E (external) and I (internal) frames.

Then again whereas we used the unambiguous polarised identification of a left turn, in this corresponding experiential context we use the unambiguous polarised identification of the positive (i.e. forward) movement of time.

Thus when we attempt to isolate the external (objective) aspect of experience in physical terms, the movement of time is indeed positive (i.e. forward).

Likewise now with respect to isolated internal) subjective aspect of experience viewed in a corresponding psychological manner, the movement of time is identified in a positive (i.e forward) manner.

Thus, because of the abstract assumption of both isolated external and internal aspects, we thereby identify - just as in crossroads example both turns as left - the movement of time for the external and internal aspects of experience as positive in both cases.

But just as with a crossroads, the two turns are necessarily left and right (and right and left) in relation to each other, likewise once we recognise the interdependent nature of external and internal, then the movement of time is necessarily positive and negative (and negative and positive) with respect to these two aspects of experience.

In other words, if time has a positive (forward) direction with respect to the external objective aspect of physical reality, then - in relative terms - it thereby has a negative (backward) direction with respect to the internal subject aspect of psychological experience.

Also from the opposite perspective, if time now has a positive (forward) direction with respect to the internal psychological self, then - in relative terms - it has a negative (backward) direction with respect to the external physical experience of the world.

Therefore from a dynamic interactive perspective, based on these two polarities of external and internal, time is necessarily of a two-dimensional relative nature (with positive and negative directions respectively).

This fundamentally alters the corresponding experience of space, which is now likewise understood in 2-dimensional relative manner.

So if we identify the positive (forward) movement of space with the external physical aspect of experience, then - relatively - the negative (backward) movement is associated with the internal psychological aspect.

And again in a reverse manner, if we then identify the positive movement of space with the internal aspect, then the negative movement - relatively - will be thereby identified with the external physical aspect.

Thus from this new dynamic interactive perspective - which properly corresponds with actual experience - time and space are now understood in a truly relative symmetrical manner, whereby both dimensions are understood as possessing two complementary directions that are positive and negative with respect to each other.

This has dramatic implications for science at all levels.

What is conventionally known as science represents but a limited special case where the external aspect of experience is treated in an absolute independent manner (as existing independently of the inquiring mind).

But properly speaking the external aspect has no strict meaning in the absence of corresponding interpretation which is - relatively - of an internal nature.

So the clear realisation of this interdependence changes the very paradigm of science and our corresponding understanding of the nature of space and time.

From this new perspective space and time are intimately related to the fundamental polarities that dynamically condition the nature of all phenomena.

The first of these relates to the interaction of external and internal aspects. In this sense all phenomena have both an outside and an inside aspect!

The second relates to the interaction of whole and part aspects (which we will deal with later).

Once again the conventional notions of space as 3 dimensional and time as 1-dimensional (viewed in a slowly positive manner) directly reflects the limited - and ultimately untenable - assumption that external and internal aspects of experience can be completely abstracted from each other.

However it is quite easy to show the limitations of this notion of time.

Once again in this context it is helpful to consider the simple example of a crossroads. If one travels in the direction N up a straight road, one can unambiguously identify the left turn (at this crossroads). If now travelling in the opposite S direction, one encounters the crossroads, again one can again unambiguously identify the left turn. However both of these turns (in terms of isolated N and S reference frames) are thereby identified as left!

However we can immediately recognise a problem in that relative to each other these turns are left and right and right and left respectively.

Now we have exactly the same situation with respect to the identification of time.

So whereas in the crossroads example we used the polar opposite of N and S as reference frames, in the experiential context now of the experience of time, we use E (external) and I (internal) frames.

Then again whereas we used the unambiguous polarised identification of a left turn, in this corresponding experiential context we use the unambiguous polarised identification of the positive (i.e. forward) movement of time.

Thus when we attempt to isolate the external (objective) aspect of experience in physical terms, the movement of time is indeed positive (i.e. forward).

Likewise now with respect to isolated internal) subjective aspect of experience viewed in a corresponding psychological manner, the movement of time is identified in a positive (i.e forward) manner.

Thus, because of the abstract assumption of both isolated external and internal aspects, we thereby identify - just as in crossroads example both turns as left - the movement of time for the external and internal aspects of experience as positive in both cases.

But just as with a crossroads, the two turns are necessarily left and right (and right and left) in relation to each other, likewise once we recognise the interdependent nature of external and internal, then the movement of time is necessarily positive and negative (and negative and positive) with respect to these two aspects of experience.

In other words, if time has a positive (forward) direction with respect to the external objective aspect of physical reality, then - in relative terms - it thereby has a negative (backward) direction with respect to the internal subject aspect of psychological experience.

Also from the opposite perspective, if time now has a positive (forward) direction with respect to the internal psychological self, then - in relative terms - it has a negative (backward) direction with respect to the external physical experience of the world.

Therefore from a dynamic interactive perspective, based on these two polarities of external and internal, time is necessarily of a two-dimensional relative nature (with positive and negative directions respectively).

This fundamentally alters the corresponding experience of space, which is now likewise understood in 2-dimensional relative manner.

So if we identify the positive (forward) movement of space with the external physical aspect of experience, then - relatively - the negative (backward) movement is associated with the internal psychological aspect.

And again in a reverse manner, if we then identify the positive movement of space with the internal aspect, then the negative movement - relatively - will be thereby identified with the external physical aspect.

Thus from this new dynamic interactive perspective - which properly corresponds with actual experience - time and space are now understood in a truly relative symmetrical manner, whereby both dimensions are understood as possessing two complementary directions that are positive and negative with respect to each other.

This has dramatic implications for science at all levels.

What is conventionally known as science represents but a limited special case where the external aspect of experience is treated in an absolute independent manner (as existing independently of the inquiring mind).

But properly speaking the external aspect has no strict meaning in the absence of corresponding interpretation which is - relatively - of an internal nature.

So the clear realisation of this interdependence changes the very paradigm of science and our corresponding understanding of the nature of space and time.

From this new perspective space and time are intimately related to the fundamental polarities that dynamically condition the nature of all phenomena.

The first of these relates to the interaction of external and internal aspects. In this sense all phenomena have both an outside and an inside aspect!

The second relates to the interaction of whole and part aspects (which we will deal with later).

Once again the conventional notions of space as 3 dimensional and time as 1-dimensional (viewed in a slowly positive manner) directly reflects the limited - and ultimately untenable - assumption that external and internal aspects of experience can be completely abstracted from each other.

## Wednesday, March 26, 2014

### Linear Time

Our common sense intuitions have long accustomed us to a linear (i.e. 1-dimensional) notion of time.

What is not however commonly appreciated is that accepted nature of time is itself but the direct reflection of the linear (1-dimensional) mode of understanding on which conventional scientific interpretation is based.

In yesterday's blog I defined the precise nature of 1-dimensional interpretation as that which is based on isolated polar frames of reference.

So once again with respect to the key polarity sets, conventional science is based on the notion that objective (external) reality can be viewed independent of its subjective (internal) means of interpretation. Essentially this thereby removes consideration of the dynamic relationship in the assumption of a direct fixed correspondence as between both polarities.

Likewise conventional science is based on the notion that the quantitative features of such reality can be viewed independent of corresponding qualitative considerations. So rather than a unique dynamic interaction as between both poles, once again qualitative notions are assumed to directly correspond with their quantitative counterparts.

Now of course in such science, ultimately the existence of an independent observer must be accepted.

So effectively this leads to an interpretation of the external observed world of space (with which objects are directly identified) in rigid terms as 3-dimensional. The remaining dimension of time is is then isolated in 1-dimensional manner.

Thus right away the very mode of interpretation associated with conventional science leads to an asymmetrical treatment of space and time understood in a merely (1-dimensional) linear manner.

The rigid nature of objects in space corresponds to 3 (separate) linear dimensions of length, width and depth which can be directly quantified in tangible terms.

The nature of time then appears more intangible and mysterious directly relating to a qualitative identity. However indirectly it too can then become subject to precise quantitative measurement.

Though Einstein's Theory of Relativity leads to a much closer integration of space and time in a 4-dimensional spacetime, significantly the asymmetrical nature of space and time is still preserved (with 3 recognised space and 1 time dimension).

Indeed here time is considered as an imaginary space dimension. So the contrast of the "real" dimensions of space with the "imaginary" dimension of time once again highlights the somewhat mysterious nature of time

Likewise in String Theory though many more dimensions of space (with 11 now postulated in M-theory), in most approached just one dimension of time is still recognised.

Now time can equally be viewed in both a physical and psychological sense.

Thus from the conventional scientific perspective events move forward in time (and space).

Once again our common sense intuitions seem to be strongly identified with this solely positive movement of time.

One important example of this is in the manner in which we attempt to view the origin of the universe.

Present scientific wisdom tells us that our universe started with a Big Bang some 13.7 bl. years ago.

So this implies a strictly linear view of the nature of time (which is quite untenable). However, so strongly rooted is this conventional notion of time that few scientists seem to question the validity the Big Bang hypothesis. In other words if we truly accept relative notions of space and time with respect to the cosmos, then it makes no sense to apply a linear (absolute) notion of time to its origins and overall evolution.

We also tend to view the psychological movement of time in a similar manner.

Thus the life span of an human individual is commonly represented in a decidedly linear fashion.

So for one born today with an expected life-span of 80 years, time is set to move relentlessly forward in a linear manner (with each day bringing one inevitably closer to one's end).

This linear view of time however represents but one limited view of its nature.

Once again it is based on isolated frames of polar reference (which is not in keeping with the true interactive nature of experience). It is also of a merely conscious nature based on rational interpretation.

So we can already perhaps see a connection here with the nature of number.

The rational represent just one important component of the overall set of numbers. And even with respect to the rational numbers we can have negative as well as positive members.

So the position with respect to the conventional understanding of time is akin to a number line in which solely rational members (that are positive) are recognised.

However as we shall see we have alternative notions of time corresponding to all numbers and number types.

So in the next blog entry we will look more closely at the important significance of the 2-dimensional (as opposed to the 1-dimensional) notion of time.

What is not however commonly appreciated is that accepted nature of time is itself but the direct reflection of the linear (1-dimensional) mode of understanding on which conventional scientific interpretation is based.

In yesterday's blog I defined the precise nature of 1-dimensional interpretation as that which is based on isolated polar frames of reference.

So once again with respect to the key polarity sets, conventional science is based on the notion that objective (external) reality can be viewed independent of its subjective (internal) means of interpretation. Essentially this thereby removes consideration of the dynamic relationship in the assumption of a direct fixed correspondence as between both polarities.

Likewise conventional science is based on the notion that the quantitative features of such reality can be viewed independent of corresponding qualitative considerations. So rather than a unique dynamic interaction as between both poles, once again qualitative notions are assumed to directly correspond with their quantitative counterparts.

Now of course in such science, ultimately the existence of an independent observer must be accepted.

So effectively this leads to an interpretation of the external observed world of space (with which objects are directly identified) in rigid terms as 3-dimensional. The remaining dimension of time is is then isolated in 1-dimensional manner.

Thus right away the very mode of interpretation associated with conventional science leads to an asymmetrical treatment of space and time understood in a merely (1-dimensional) linear manner.

The rigid nature of objects in space corresponds to 3 (separate) linear dimensions of length, width and depth which can be directly quantified in tangible terms.

The nature of time then appears more intangible and mysterious directly relating to a qualitative identity. However indirectly it too can then become subject to precise quantitative measurement.

Though Einstein's Theory of Relativity leads to a much closer integration of space and time in a 4-dimensional spacetime, significantly the asymmetrical nature of space and time is still preserved (with 3 recognised space and 1 time dimension).

Indeed here time is considered as an imaginary space dimension. So the contrast of the "real" dimensions of space with the "imaginary" dimension of time once again highlights the somewhat mysterious nature of time

Likewise in String Theory though many more dimensions of space (with 11 now postulated in M-theory), in most approached just one dimension of time is still recognised.

Now time can equally be viewed in both a physical and psychological sense.

Thus from the conventional scientific perspective events move forward in time (and space).

Once again our common sense intuitions seem to be strongly identified with this solely positive movement of time.

One important example of this is in the manner in which we attempt to view the origin of the universe.

Present scientific wisdom tells us that our universe started with a Big Bang some 13.7 bl. years ago.

So this implies a strictly linear view of the nature of time (which is quite untenable). However, so strongly rooted is this conventional notion of time that few scientists seem to question the validity the Big Bang hypothesis. In other words if we truly accept relative notions of space and time with respect to the cosmos, then it makes no sense to apply a linear (absolute) notion of time to its origins and overall evolution.

We also tend to view the psychological movement of time in a similar manner.

Thus the life span of an human individual is commonly represented in a decidedly linear fashion.

So for one born today with an expected life-span of 80 years, time is set to move relentlessly forward in a linear manner (with each day bringing one inevitably closer to one's end).

This linear view of time however represents but one limited view of its nature.

Once again it is based on isolated frames of polar reference (which is not in keeping with the true interactive nature of experience). It is also of a merely conscious nature based on rational interpretation.

So we can already perhaps see a connection here with the nature of number.

The rational represent just one important component of the overall set of numbers. And even with respect to the rational numbers we can have negative as well as positive members.

So the position with respect to the conventional understanding of time is akin to a number line in which solely rational members (that are positive) are recognised.

However as we shall see we have alternative notions of time corresponding to all numbers and number types.

So in the next blog entry we will look more closely at the important significance of the 2-dimensional (as opposed to the 1-dimensional) notion of time.

## Tuesday, March 25, 2014

### Introduction

I have already approached this important topic in other contexts. See for example the 20 articles in the series "Multidimensional Nature of Time and Space" on my companion "Integral Science" blog.

However because of its importance, I have decided to give the topic a new dedicated blog where the issues involved can be explored in greater depth.

Put simply, I believe that a radical new understanding of the nature of space and time is now required in our culture. Furthermore I believe that such understanding is intimately related to the holistic notion of number.

Now right away this creates a major problem with respect to the accepted mathematical interpretation of number which in formal terms gives no recognition whatsoever to its holistic aspect.

Conventional Mathematics - as formally understood - is based solely on the analytic interpretation of an abstract independent identity.

In a very precise holistic manner this in fact reflects 1-dimensional understanding.

Let me clarify once again briefly!

All experience (which necessarily includes mathematical) is based on the interaction of opposite polarities which dynamically interact.

Chief among these are - what I refer to as - the horizontal polarities of external and internal.

Therefore in mathematical terms, the recognition of an external object such as a number necessarily requires the relationship with a corresponding mental perception which - relatively - is of an internal nature.

Thus understanding here is strictly dynamic in nature, with the external aspect inseparable from its corresponding internal interpretation.

However in conventional mathematical terms the attempt is then made to reduce such dynamic interaction in a static absolute manner. So the (external) object is thereby abstracted (as independent) with (internal) interpretation assumed to be then in direct correspondence with the object.

So the true interdependence as between object and (mental) perception - which intrinsically is of a qualitative nature - is thereby broken and reduced in a merely quantitative manner.

Thus quite remarkably, Conventional Mathematics has no means of dealing with the very notion of interdependence except in a reduced quantitative manner!

The second key set underlying all experience (i.e. the vertical polarities) relates to the dynamic interaction of whole and part.

We can again see this clearly with respect to the notion of number. There are in fact two aspects which dynamically interact in experience that are whole and part with respect to each other.

The cardinal notion relates to number as a homogeneous whole identity (where individual units have no distinct identity).

So 4 in this sense is a whole number (i.e. integer) that would be represented in terms of its individual units as lacking any qualitative distinction i.e. 4 = 1 + 1 + 1 + 1.

The ordinal notion relates by contrast to the distinct individual (part) members of a number group.

So 4 in this part number sense is made up of individually distinct 1st, 2nd, 3rd and 4th members (that strictly lack thereby a distinctive whole identity).

Thus once again our actual experience of number entails a dynamic interaction as between whole (cardinal) and (part) ordinal notions. However once again in conventional mathematical terms, the cardinal aspect is abstracted in an absolute static manner, with the ordinal then misleadingly assumed to correspond directly with the cardinal.

Put more generally the 1-dimensional (i.e. linear) interpretation of mathematical symbols is based on the use of isolated single poles as reference frames for all subsequent interpretation.

Now I identify this abstract interpretation of mathematical symbols as analytic..

So all accepted mathematical interpretation in formal terms is thereby analytic in this sense.

The holistic interpretation of symbols by contrast arises directly from their consideration in a dynamic interactive context. So holistic meaning (which directly is of an intuitive nature) arises directly to the degree to which the interdependence of opposite polarities is recognised.

Normally, the dynamic understanding of symbols in this sense entails both quantitative (analytic) notions of independence and qualitative (holistic) notions of interdependence.

Pure holistic appreciation would thereby approximate the highly refined experience where a separate independent existence can no longer be distinguished.

In psychological terms this would entail approximation to a purely psycho spiritual energy state (as intuition). In corresponding physical terms it would entail approximation to a purely physical energy state.

When appropriately understood the number system ranges between its pure absolute analytic expression in rational terms (i.e. the primes and natural numbers as fixed entities of form) and the corresponding pure holistic expression (where numbers approximate pure energy states through the zeta zeros in physical and psychological terms).

The great importance of the holistic interpretation of number is that it directly lends itself to a completely new interpretation of the nature of space and time which concurs directly with actual experience.

Because of the complete lack of such holistic appreciation, we remain greatly hampered by extremely limited physical notions of space and time (that themselves have been derived from an inadequate mathematical understanding).

Quite remarkably - though not recognised - whereas the analytic appreciation of number lends itself directly to quantitative type interpretation with respect to objects, the holistic appreciation lends itself directly to qualitative appreciation with respect to dimensions thereby facilitating a true appreciation of the nature of space and time.

However because of its importance, I have decided to give the topic a new dedicated blog where the issues involved can be explored in greater depth.

Put simply, I believe that a radical new understanding of the nature of space and time is now required in our culture. Furthermore I believe that such understanding is intimately related to the holistic notion of number.

Now right away this creates a major problem with respect to the accepted mathematical interpretation of number which in formal terms gives no recognition whatsoever to its holistic aspect.

Conventional Mathematics - as formally understood - is based solely on the analytic interpretation of an abstract independent identity.

In a very precise holistic manner this in fact reflects 1-dimensional understanding.

Let me clarify once again briefly!

All experience (which necessarily includes mathematical) is based on the interaction of opposite polarities which dynamically interact.

Chief among these are - what I refer to as - the horizontal polarities of external and internal.

Therefore in mathematical terms, the recognition of an external object such as a number necessarily requires the relationship with a corresponding mental perception which - relatively - is of an internal nature.

Thus understanding here is strictly dynamic in nature, with the external aspect inseparable from its corresponding internal interpretation.

However in conventional mathematical terms the attempt is then made to reduce such dynamic interaction in a static absolute manner. So the (external) object is thereby abstracted (as independent) with (internal) interpretation assumed to be then in direct correspondence with the object.

So the true interdependence as between object and (mental) perception - which intrinsically is of a qualitative nature - is thereby broken and reduced in a merely quantitative manner.

Thus quite remarkably, Conventional Mathematics has no means of dealing with the very notion of interdependence except in a reduced quantitative manner!

The second key set underlying all experience (i.e. the vertical polarities) relates to the dynamic interaction of whole and part.

We can again see this clearly with respect to the notion of number. There are in fact two aspects which dynamically interact in experience that are whole and part with respect to each other.

The cardinal notion relates to number as a homogeneous whole identity (where individual units have no distinct identity).

So 4 in this sense is a whole number (i.e. integer) that would be represented in terms of its individual units as lacking any qualitative distinction i.e. 4 = 1 + 1 + 1 + 1.

The ordinal notion relates by contrast to the distinct individual (part) members of a number group.

So 4 in this part number sense is made up of individually distinct 1st, 2nd, 3rd and 4th members (that strictly lack thereby a distinctive whole identity).

Thus once again our actual experience of number entails a dynamic interaction as between whole (cardinal) and (part) ordinal notions. However once again in conventional mathematical terms, the cardinal aspect is abstracted in an absolute static manner, with the ordinal then misleadingly assumed to correspond directly with the cardinal.

Put more generally the 1-dimensional (i.e. linear) interpretation of mathematical symbols is based on the use of isolated single poles as reference frames for all subsequent interpretation.

Now I identify this abstract interpretation of mathematical symbols as analytic..

So all accepted mathematical interpretation in formal terms is thereby analytic in this sense.

The holistic interpretation of symbols by contrast arises directly from their consideration in a dynamic interactive context. So holistic meaning (which directly is of an intuitive nature) arises directly to the degree to which the interdependence of opposite polarities is recognised.

Normally, the dynamic understanding of symbols in this sense entails both quantitative (analytic) notions of independence and qualitative (holistic) notions of interdependence.

Pure holistic appreciation would thereby approximate the highly refined experience where a separate independent existence can no longer be distinguished.

In psychological terms this would entail approximation to a purely psycho spiritual energy state (as intuition). In corresponding physical terms it would entail approximation to a purely physical energy state.

When appropriately understood the number system ranges between its pure absolute analytic expression in rational terms (i.e. the primes and natural numbers as fixed entities of form) and the corresponding pure holistic expression (where numbers approximate pure energy states through the zeta zeros in physical and psychological terms).

The great importance of the holistic interpretation of number is that it directly lends itself to a completely new interpretation of the nature of space and time which concurs directly with actual experience.

Because of the complete lack of such holistic appreciation, we remain greatly hampered by extremely limited physical notions of space and time (that themselves have been derived from an inadequate mathematical understanding).

Quite remarkably - though not recognised - whereas the analytic appreciation of number lends itself directly to quantitative type interpretation with respect to objects, the holistic appreciation lends itself directly to qualitative appreciation with respect to dimensions thereby facilitating a true appreciation of the nature of space and time.

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