Given the eight general, exponentially-derived, categories it is obvious that they are too general to be truly useful other than as generalisations. Thus we need to extend the categories and the logical thing to do is to keep applying recursion and so exponentiation of the D/I dichotomy. This will take us step-by-step through qualities derived from powers of 2.
This process of exponentiation is a process that is a member of a set of processes all relating to self-referencing. This set contains four members - addition, multiplication, exponentiation, and tetration - with the latter two of interest in the form of exponential growth, N qualities become 2N qualities, and hyperbolic growth where N qualities become N2 These processes all lead to the same results but the differences is in the speed in which the result is obtained as well as the bandwidth obtained where bandwidth affects how much information it is possible to express at any moment.
It is from hyperbolic growth where N qualities turn into N2 that we can quickly achieve the widest bandwidth to give us a rich set of qualities and it is from hyperbolic growth that we can 'stay in the box' of D/I categorisations, we do not have to step out of the box to use elements of other boxes to aid in our categorisations.
The hyperbolic process, as applied to our species development categorisations, works like this:
Once the basic set of general qualities has been derived, to a level where they are generally useful, we need to flesh-out the qualities of each quality. By this I mean that a universal quality linked to a particular context can express itself in subtly different ways when compared to its 'purest' expression where the text and the context are the same.
How do we do identify these differences? The process of hyperbolic growth reflects the taking of ALL of the members of the general set of qualities and using them as sources of analogy to describe the qualitative differences of expression WITHIN a particular general quality. Thus for each of the eight qualities derived above we derive eight analogies. This gives us eight octets, each octet containing the eight analogies applicable for each of the original eight qualities.
Symbolically we can extend the binary values we used to identify the general qualities by adding-on the binary values of all of the qualities. For example, the DDD quality, converted to its binary value format becomes 111. This binary value is the GENERAL quality and as such represents a CONTEXT, a universe of discourse, within which we make our analogies. Thus for the context of 111 we can make the following symbolic representations of the analogies:
context-text
111-111 DDD within a DDD context.
111-110 DDI within a DDD context.
111-101 DID within a DDD context.
111-100 DII within a DDD context.
111-011 IDD within a DDD context.
111-010 IDI within a DDD context.
111-001 IID within a DDD context.
111-000 III within a DDD context.
The next step is, once the analogies are made we can recruit them and abstract them to become autonomous units, descriptions of 'unique' qualities themselves rather than as analogies. Thus from a set of eight general qualities we have derived a set of 64 (8 x 8) more particular qualities (symbolically we remove the hyphen, thus the analogy expressed as 111-000 becomes the 'pure' quality of 111000)
We can do this literal-to-analogous-to-recruit/abstract-to-literal process ad infinitum such that we move from 8 to 64 to 4096 to 16+ million qualities of D/I processing very quickly (where N qualities become N2. and these become the new value of N and so on) But this can lead to an excessively long string of binary digits! For the sake of demonstration, as well as there being no real need at the moment to go to using high values, we will stick to the use of three to six binary digits and so to the use of 8 to 64 qualities in describing 'reality'. (4096 will become the norm later, but for now we stick to 64). This process of hyperbolic growth reflects the refinement from a perspective that is GENERAL to one that is increasingly PARTICULAR.