In dealing with the nature of 2, 4 and 8 dimensions of time (and space) respectively, we saw how that in each case they are characterised by the complementarity of opposite poles.
So 2-dimensional reality is characterised by the complementarity of the "real" poles (i.e. external and internal).
4-dimensional is then characterised by the additional complementarity of the "imaginary" poles (i.e. whole and part).
8-dimensional is finally chracterised by the additional complementarity of special complex poles where both real and imaginary parts are of equal magnitude. This can then be understood as relating to the ultimate interaction as between form and emptiness (i.e. where the dynamic interaction of phnomena are so refined that they do not even appear to arise). So in this sense the dynamic nature of form becomes inseparable from emptiness.
Now it must be understood that further distinct structures with respect to the nature of time (and space) are associated with all other even numbered integers.
However they all possess one important common feature in that they are characterised - however intricately - by the complemenentarity of opposite poles.
This can be simply appreciated with reference to the fact that the qualitative dimension entailed (for each even integer) is inversely related to its corresponding number of roots of 1 (in quantitative terms).
And as all even numbered roots can be arranged in a complementary manner (with half of the roots expressed as the negative of the other half) this entails in turn that the dynamic dimensional structure for all even numbers applying to time (and space) is based directly on the complementarity of opposites.
However this principle clearly does not apply to the odd integer dimensions.
For example in the important case of 1 i.e. the linear mode, which again characterises conventional scientific understanding, time is not understand in dynamic complementary terms (where its ultimate nature is paradoxical).
And in an important more refined manner, this linear view likewise characterises all the odd integer dimensions.
For example, to examine the dimensional structure associated with 3, we need to look at the corresponding three roots of 1 i.e. 1, - .5 + .866i, and - .5 + .866i (expressed correct to 3 decimal places).
As we can see the first root here is 1, which in a sense stands out on its own (as independent of the other roots). The remaining roots - necessarily of an even number - always appear as pairings of complex conjugates (with the imaginary part arranged in a complementary manner).
So how do we explain the nature of such odd numbered dimensions? How do we, for example, attempt to describe the nature of time as experienced in 3 dimensions?
Now this is an issue that I have given an enormous amount of thought to over the last 30 years or so. However suffice it to say that the odd numbered dimensions (apart from 1) are much more difficult to clearly explain than their even counterparts.
I would describe it this way.
The standard dualistic rational approach - where phenomena are treated as independent - is of a linear (1-dimensional) nature.
The standard nondual contemplative approach - where phenomena are treated in merely relative - and ultimately illusory - fashion is based on the complementarity of opposites. So associated with the ascending scale of even integers are ever more refined contemplative (nondual) experiences of reality.
However the odd integers (≥ 1) are associated with a hybrid of both approaches (and ultimately are incompatible with each other).
In this respect I can draw on my own experience of 3 dimensions. Indeed I remember suggesting a proposal for a thesis on a dynamic methodology for Economics (that I only realised many years later, was, in holistic mathematical terms, of a 3-dimensional nature).
On the one hand I was here trying to preserve the validity of the standard conventional model (i.e. 1-dimensional). On the other hand I was trying to reconcile this with the 2-dimensional approach based on the complementarity of opposites. So I was attempting to balance the traditional linear with a new dynamic 2-dimensional approach (based on a circular logic). However from an experiential perspective this led to inevitable conflict. Commitment to the linear aspect fostered - what in spiritual terms is referred to as - dualistic attachment; meanwhile the 2-dimensional aspect experientially required the very erosion of such attachment. So in the end I abandoned that approach (though later was able to return to it from a more refined perspective).
So this led me to the view that it in experience odd dimensional structures are necessarily asymmetrical in nature and ultimately inconsistent with the nondual perspective.
So in terms of psycho spiritual growth, one starts with dualistic 1-dimensional understanding, which is of a strongly differentiated nature. Then 2-dimensional understanding provides the "lowest" level with respect to integrated experience (of a nondual contemplative kind). However because both dual and nondual are dynamically related, to reach higher levels of integration represented by the even dimensions, one must equally embrace higher levels of differentiation represented by the odd dimensions (which inevitably are of an inconsistent temporary nature).
So in terms of space and time the very nature of the odd numbered dimensions entails that space and time can no longer be experienced in a complementary manner. This means that new forms of phenomenal rigidity i.e. new forms of matter, necessarily arise with the odd numbered dimensions.
If we apply this understanding to the dynamic nature of "lower" physical reality, this implies that associated with each higher odd dimension are new matter particles, whereas with the appropriate even dimensions these quickly dissolve in the creation of energy.
And as all dimensions in a sense co-exist simultaneously, there is an unending trail of matter as it were waiting to be discovered. In other words the higher the dimensions we can access (which in a sense is the task of particle accelerators) the more new forms of matter will arise.
Equally from a psycho spiritual perspective, the higher the dimensions one can access through advanced contemplation, the more refined one's experience can become so that one can actually now "see" such matter arising from a deep unconscious level of experience.
From a physical perspective, the interaction of odd with even integer dimensions relates to the continual transformation of matter into energy (and gravity). And there is no limit to this process with ever more dynamic short-lived transformations associated with the higher dimensions.
From a corresponding psychological perspective, the interaction of odd with even integer dimensions relates to the continual transformation of dualistic matter phenomena into (contemplative) spiritual energy. And again there is no strict limit to this process with ever more dynamic short-lived transformations associated with the higher number dimensions.