It important to distinguish the primary and secondary interpretations of both structures and states respectively. While recognising the importance of secondary interpretations - and their necessary interaction with the primary - the holistic mathematical approach is directly concerned with their primary nature.
In the context in which I define them, primary structures relate to fundamental coherent patterns of dynamic relationships, which can be precisely encoded in a holistic mathematical format at all stages of development.
Now I would contend that this approach in turn provides the basis for a fully scientific universal appreciation of these structures (which is greatly missing in existing translations).
Secondary structures would refer to specific phenomenal expressions whereby the primary aspect is implicitly transmitted.
For example in a primary sense the structures associated with "high" level spiritual understanding are universal (which the holistic mathematical approach attempts to encode).
However the specific phenomenal expressions of these structures can vary greatly over time and from culture to culture.
Therefore in a particular society at a certain period in history the specific expressions of a mystical tradition may well be successful in (implicitly) transmitting these primary structures to its spiritual followers.
However great difficulties may then be experienced in attempting to translate this understanding into a very different culture at a later period in history.
Indeed this is one of the great obstacles that the various mystical traditions generally face in keeping their teaching relevant in a fast changing world. Equally it is the same obstacle that is faced in trying to reconcile the symbols and practices of distinctive traditions. For example the Bardo teachings - which may be deeply meaningful to a Tibetan Buddhist in communicating the nature of involution - would carry little or no resonance for a Christian.
So though the various mystical traditions have undoubtedly accumulated a great deal of wisdom and experience enabling the successful transmission of "higher" structures, unfortunately they are generally dealing with their secondary - rather than their direct primary - nature.
I am not saying that such secondary structures are unimportant. Indeed they remain vitally relevant. However a more scientific universal type understanding would greatly facilitate their appreciation though a common set of symbols that would widely apply in different circumstances (and help ease the artificial divisions dividing traditions).
It would then be possible to apply these primary structures through a variety of secondary phenomenal expressions suited to individual cultural and personality requirements.
So it should be possible therefore say for a Christian and Buddhist - while fully agreeing on the scientific universal nature of "higher" spiritual structures - to choose very distinctive secondary methods for developing such understanding.
States can also be of a primary or secondary nature.
In a primary sense, the states refer to a fundamental manner of spiritually "seeing" reality, which again is unique for each stage of development.
In a dynamic sense a stage is always characterised by the dynamic interaction as between structure and state (which ultimately reaches out to embrace all other stages).
However again states can have a secondary interpretation through the phenomenal circumstances through which the primary spiritual disposition is expressed.
So we can speak of numerous emotional states e.g. joy, happiness, grief, compassion etc. which in various ways transmit the primary spiritual disposition of a stage (and its relationship with other stages).
Equally we can have a series of cognitive states e.g. discipline, control, alertness etc. which again can help transmit the primary spiritual disposition. Indeed in strict dynamic terms the primary spiritual state is indirectly transmitted through a complex interaction of secondary emotional and cognitive states.
Again in the context of the holistic mathematical approach the primary nature of states is paramount.
However the relationship between primary and secondary states is very important.
The precise means however through which a particular individual will indirectly transmit the primary spiritual states may vary considerably depending for example on personality and environmental circumstances.