The fundamental subjective process interaction with space is the accepting of semeia. This is the only distinguishing element between subjective lead processing (and thus internal) and objective led subjective processing(external).
In accepting semeia we engage in a recursive, iterative process of assignment. The assignment process is instantaneous for all intents and purposes, but in actual signal processing it may be due to massive parallel processing input and output streams, and thus sequential at some stage in the processing, especially the convolutional processing networks which underpin combination or synaesthesia.
Thus , instantaneously semeia are assigned, but certain significant (more intense) semiotic signals dominate the return information processing. Thus the recursion/iteration tends to separate out the semia into distinct clusters which are patterned, but not seuenced. I call this an "initial scatter pattern", which is primed for sequencing.
My observation here s tha prior to sequencing, processing at an initial level has occurred which results in a scatter pattern output for further processing. This scatter pattern output is in fact the inherent and initial assignment of semeia to regional space as a compass multivector network relative to the subjective processing centre.
Along with intensity of signal from the assigned semeia recursively evoking the scatter pattern, motion of semeia also recursively evokes sequencing in the scatter pattern. Thus an initial scatter pattern is primed for processing to simultaneously evoke the "path" of moving semeia. This is the spur to all sequence processing in the subjective processing centre, and reveals that if the scatter pattern is not an instantaneous assignment of semeia then at least it is a very much fsster assignment than the output "frames" for moving semeia. I phrase it this way because the whole programming and technology of video and audio capture informs this analysis of the subjective -objective processing that occurs in my experiencing "consciousness", or the subjective experience as dynamic form.
In any recording medium there is a delay between the input signal and the record of that signal being accessible. This is due to processing sequence, and the very sequence underpins any fundamental notions of "time" while at the same instance making "time" a meaningless concept. Sequence and rhythm are the precursors which give birth to time in Pythagorean philosophy. Thus we may ponder on the pont that we never can live in the "now", as we are hostages to fortune of our processing sequences, and thus our individual,subjective experience of anything that we may agree to call time is unique and not synchronous with anyone elses!
Path therefore represents the combination of compass multivector networks, as "frames" of individual scatter patterns are combined by a recursive or iterative process. This type of combinatorics is essentially the field of study of the calculus, both integral and differential. But i hope hat the reader can immediately see that the results of the calculus must confirm the dynamic forms we subjectively experience, and that alternatives to calculus exist in film making, video editing etc which give instant and accessible results that all can follow and understand/apprehend.
The calculus therefore represents a category within the field of combinatorics which deals with these dynamic forms by "instantaneous" capture and combination of the scatter patterns. Essentially , to describe the combinatorics in an ongoing , changing experience requires the calculus tool, but is no more accurate than filming a sequence of changeand watching it frame by frame. This is what the calculus was designed to do by Newton et al.
The sheer number of instances is what overwhelms the "comprehension " processes, but we are readily equipped to apprehend and process this "experience" to interpret and react in real time to a continual flow of such "instances". We should not feel dumb cos we do not like the notation and fulminations of the mathematicians.
The question is whether these instances are as is or are just the output from the subjective processing centre.
So combinations always involve sequences in the subjective scatter patterns that present as subjective experience. These sequences are "stored " in memory where they are accessible for analysis, comparison and processing for creativity.
We resolve our subjective experience into fundamental orientations(compass multivector networks or scatter patterns), Paths(the calculus of variations) and directions( the experience of traveling along a path), and this is all resolvable relative to the subjective processing centre in contra forms.
We may then "drill down" to individual instances which lead to specific notions like vectors, division,subtraction multiplication,addition,comparison, measurement,scalar, monad…
Combinatorics deals with all these things, but its remit is to take magnitude and bind it in some way. The bindings are called boundaries, and the boundaries represent the forms of regional space. Within the boundaries subjective processing assigns semeia either static or dynamic. This scatter pattern of assignments marks the dynamic sequencing of the scatter pattern variations,and stores the variations in a memory structure or arrangement. At the same time real time processing gives rise to a subjective experience of the dynamic combination of all these structures and substructures. The processing is only possible if the whole recursive activity is based on fractal pronciples. Inthis way the processing can be expanded on demand to deal with scale boundary condiions. Fractal image compession is an example of how scale can be handled without loss of quality.
Comics maintain and explain the role of myth in culture
It is clear that combinatorics is far richer than a bunch of formulae for dealing with cards for example,and the use of /,-,*,+ needs to reflect that, along with a host of other symbols.
For example ai+bj is a combination of vectors which results in another vector, But we could rethink this as two paths Ωi +Ωj, and this "generalises" the vector combination process, it is usually expressed. In fact it announces the combination process for paths.
Most Algebras, group theories begin with a set of rules and axioms which are in fact the combinatorics for the "forms" under study. With that observation it is worth examining the combinatorics for completeness and relevance. For example, most combinatorics do not address the calculus combinatorics, or more importantly the trigonometric combinatorics.
For those who have wondered about motion sequents, this is a version of motion sequents arrived at by the "dialectic" approach, which i am about to study with Grassmann. This dialectic is usually expressed as opposites or contra or polar relationships. In fact, it represents the cyclical relationships between all things, the relative relationships between all things, the vorticular relationship between dynamic forms.