# The axioms and notions.

Axiom !: The Experience "I" have is solely my own and is constructed by "me" within a context that i can only model using cultural "forms".
Note: The structure of "my" experience i have constructed using the paradigm of a continuum between poles that are indefinitely located in a location that has at least an inner region separated by boundarisation processes from an outer region. It is consequential of the construction process that the outer region has no boundary that cannot be enclosed by another constructed boundary.

Axiom 2: All processes within my experiential continuum are iterative or recursive.

One important corollary of Axiom1 is that Everything i construct is necessarily relative to me in "my" model. Hence:
Axiom 3:- i can construct any given number of other reference points within "my" model by iterative processes.

This among other things allows me to rotate {in fact all affine transforms} my model relative to myself so i can gain insights from different vantage points within my model/ experiential continuum. The number of reference points is unbounded. The iterative processes are the basis of "trial and error" within my experiential continuum as i construct the re configured model from my initial assumption of cultural paradigms.

Axiom 4: The "context" in Axiom 1 is not constructed or definable within my model but is perceivable by "me" by a iterative process of negation of all elements within my model.
Basically i can't say what the context is but i can say what it is not by recursive means.

Axiom 5: I stabilise "my" model by an iterative process of "acceptance".

"My" experiential continuum changes with what i "accept" as a basis for the iterative processes of perception and recognition. the cultural forms which i accept from conception are numerous and pervasive and as i alter these my perceptions change as does my experiential continuum. "not altering" then is a nascent notion of acceptance.

Axiom 6: The Set FS is the universal set within which my model/ experiential continuum is defined and has a rule:- all processes on its elements are iterative /recursive and all its elements are determined by iterarive processes. notFS will be the recursive definition of the context in axiom 1. However there is a mapping from notFS onto FS such that FS is a model of notFS.

Axiom 7: Iterative/recursive processes operating on notFS are perceivable.

These processes will be compared with enegetic transfomations within FS.

Axiom 8:All perceived boundaries involve an iterative process or processes.

Definition: Infinfite is unbounded and large Infinitesimal is unbounded and small.

Counting is one of my accepted cultural iterative processes, as is measuring. The perceived boundaries which I count and or measure are the basis of my nascent notion of quantity and support by iterative processes the notion of quality.

The notion of motion within my experiential continuum ls a perception of change in size and relationship to any given boundary or boundaries in a sequential manner. The perception of quickness is that of a sequential boundary change occurring relative to another sequential boundary change. So for example an object identified by its boundary moves past a boundary in the blink of an eyelid.

Boundaries are what i use to define, identify, count, measure etc and so are inputs into many iterative processes. They also seem to be outputs from the perception process which is an iterative process.

Limits are boundaries beyond which a given process has no effect on what it is operating on.

Orientation is notion perceived relative to boundaries and the sequence they occur in either in motion or in enumeration. "I" have many structures which are involved in the perception process of orientation which i call sensors. It is from the The recursive perception of orientation that i derive the notion of direction.

The recursive processes that "I" engage my sensors in to produce these perceptions are assumed within my description of my experiential continuum.

Points lines and planes are abstract limit surfaces for iterative processes operating on regions whose perceived boundaries are those described in fractal geometry. So in my model I start with a bounded region and iterate to define a plane,line,or point;and as these are limits they do not exist other than as abstractions of a limiting process.
It is also the way hypersurfaces will be identified. This means that surfaces in general or objects will be and already are defined as the end result of some iterative process.

The word algorithm is used to describe a symbolic description of a process. The symbols can be in any language with a proper syntax, that is a sequential way of decoding the actions encoded in the symbols.

I just wanted to briefly discuss the important iterative process of metrication, to highlight how we have always been using fractal patterns practically. In establishing a metric we are doing something very simple and repetetive and recursive in fact. By taking a bounded object as a standard for length we quantified our metric for lenghth. By an iterative process of disection we were able to establish a pattern of marks from this standard length which form the patterns found on all measuring rules or tapes, and this we can continue until the thickness of the marks used become significant. By using finer and finer marks we can produce infinitesimal regions on our standard length. but we can also extend the pattern in an infinite collection of standard lengths which are self similar to every other division within the collection and which have the same structure in orders of 10 throughout. So the metric we use every day is a region within an infinite fractal pattern. It is worth noting that the problem of the thickness of the marks on a boundarised object limiting accuracy has led to a laser beam of a certain wavelength being used as the standard but again the boundary conditions for the bouncing beam are iteratively determined.From this the standard has become the space time constant itself, but again the accuracy of this defintion is subject to an iterative process because of the uncertainty principle. So as i indicated we can see that our standard scientific metric is based upon a fractal pattern which is infinite as well as infinitesimal.