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.

## Wednesday, March 26, 2014

## 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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