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.