In this entry, I will probe further the deeper psychological basis for the holistic synchronistic aspect of number.
All experience - including of course mathematical - is conditioned by fundamental sets of twin dynamically interacting polarities.
The simplest of these relates to the objective/subjective (alternatively external/internal or outside inside) set of polarities.
Therefore in psychological terms, whenever we recognise a number - say the number 2 - both external and internal aspects are necessarily involved.
Thus corresponding to the external number object, is a corresponding subjective mental perception of a - relatively - internal nature.
Strictly speaking therefore, recognition of a number is a dynamic experience entailing the interaction of both an external aspect (as object) and corresponding internal aspect (as mental perception). And properly understood, like the left and right designations of a turn at a crossroads, external and internal likewise have a purely relative meaning!
However normal experience - especially with mathematical interpretation - is considerably reduced in a conscious rational manner .
What this entails is the explicit separation of the two polarities involved.
Thus rather than the dynamic recognition of an interactive process, phenomenal experience - in this case of the number 2 - is rigidly reduced in a static manner with respect to just one pole.
So in this reduced manner, there are now two absolute ways in expressing the number experience.
1) We can identify the number absolutely with its (external) objective aspect in the (erroneous) belief that the number objectively exists (independent of our subjective mental relationship with it). Here, the implicit assumption is then made that the (internal) mental perception directly corresponds with the number object (i.e. as an exact copy as it were of the object).
2) We can identify the number absolutely with its (internal) subjective aspect, again in the (erroneous) belief that the number has a mental existence (independent of any objective reality). When this is the case, again an implicit assumption is made that the (external) number object directly corresponds with its mental perception (i.e. as an exact projection of this perception).
In effect in does not matter from this absolute perspective whether one adopts the realistic (objective) or idealist (subjective) perspective as to the nature of number existence for the interaction is thereby reduced in an absolute in terms of just one pole. So we can reduce the internal aspect in terms of the external; alternatively we can reduce the external in terms of the internal resulting effectively in the same absolute interpretation of number existing.
Such absolute interpretation of number (as independently existing) likewise explicitly coincides with the equal reduction of unconscious type intuitive appreciation in a conscious rational manner.
Equally this could be expressed as the reduction of the holistic aspect of appreciation in a merely analytic manner.
It is important to realise that Conventional Mathematics is explicitly based in every formal context on such gross reductionism.
So what properly represents the dynamic interaction of external and internal poles of experience (both of which properly enjoy a distinct relative validity) is explicitly interpreted in a reduced - and thereby distorted - static manner, whereby they are separated as absolutely independent of each other.
Thus an interactive experience that properly entails both conscious (analytic) and unconscious (holistic) modes of understanding is formally interpreted in a merely conscious (analytic) manner.
Putting it simply therefore, the conventional belief in the abstract nature of number, which has come to dominate accepted thinking over the past few millennia, fundamentally distorts its true nature.
So in truth number - and by extension all mathematical constructs - entails a dynamic interactive process with a merely relative validity.
From this perspective opposite poles cannot be directly reduced in terms of each other in an absolute manner. Rather they enjoy an existence of relative independence (where opposite poles are considered as separate) together with relative interdependence (where the poles are considered as complementary).
The independent aspect corresponds directly to rational (conscious) understanding of an analytic nature; the interdependent aspect corresponds directly with intuitive (unconscious) understanding that is by contrast holistic.
Now looking at the psychological process through which we understand phenomena such as number, we can indeed go more deeply into the dynamics involved.
What is vital to appreciate here is that unconscious is necessary to enable switching as between opposite poles.
So for example when we form knowledge of a number e.g. 2 as an (external) object, the conscious rational mind is directly involved. However the switch to the corresponding recognition of the (internal) perception of 2 requires the intervention of the unconscious. Now as the unconscious is inherently based on the complementarity and ultimate unity of opposite poles such as external and internal, it thereby acts to counteract the unbalanced emphasis on just one pole. So the positing of 2 as an (external) object is thereby to a degree negated, enabling the switch to the corresponding (internal) recognition of 2 as a mental perception. Once again unbalanced identification with the positing of this pole (in a rigid phenomenal manner), will gain be counteracted to a degree by the unconscious leading to its corresponding negation.
Thus when the holistic unconscious in sufficiently developed very flexible switching continually takes place as between both external and internal polarities, which are identified in an increasingly relative manner.
However when the unconscious is not recognised understanding becomes increasingly rigid with both external and internal poles confirming each other in an absolute manner.
Thus the distorted interpretation of mathematical symbols such as numbers (which represents accepted mathematical understanding in our culture) inevitably leads to confirmation of its reduced findings in an increasingly absolute manner.
Looking at this from a Jungian perspective, this reveals that an enormous collective shadow hangs over the Mathematics profession in a total failure to recognise its own unconscious identity.
Objective truth does not exist in abstraction (even in Mathematics); rather what we understand as objectively true (in external terms), always reflects a corresponding means of mental interpretation (in an internal manner).
So the apparent absolute nature of mathematical truth simply confirms the distorted nature of conventional interpretation (where external and internal poles are reduced in terms of each other).
However once we properly allow for the dynamic interaction of poles an unlimited number of mathematical interpretations - each with a limited relative validity - are seen to exist.
So Conventional Mathematics is decidedly 1-dimensional in nature (based in any context on just one absolute pole of reference).
However when we allow for the interaction of opposite poles Mathematics becomes multi-dimensional (with a potentially unlimited number of relative interpretations).