I am setting down a few notes about the conception of time and space common in the west. Axiom 2 declares that these are fractals. It is important to distinguish time because this is a fractal used as a foundational scale like length but is based on movement in space. The fractals that i am looking at are therefore space and movement in space.

Like all conceptions there is an inate sense of the fractal we call time, but what i am sensing is the iteration process or procedure. Axiom 3 declares that i am able to have multiple orientations on this inate sense and my chief sense is how personal to me the iterations are. Then as i look out or sense other bounded regions i can experience a different iteration process happening there within or including the boundary region. I can also find similar iteration procedures going on at a larger scale and at larger scales than that. These larger scale iteration procedures imply that the iterations processes within smaller scale boundaries are not isolated from each other by the perceived boundaries but may in fact be entrained to the larger scale ones. This causative relationship is perceived but as "chaotic" or complex. To this list of descriptors i may now add fractal. But it is not just a descriptor it is a fundamental reorganisation of any notions of cause and effect i have formerly introduced.

Axiom 9 therefore i sketch out here as: large scale and small scale iteration procedures in FS are fractally entrained at any scale size i wish to examine.

When i take a large scale iterative process such as a solar cycle as a standard or the rotaton of the earth about its axis, i can then subdivide it into smaller and smaller segments and use it as a measure or metric. Measures or metrics are some of the most obvious fractals that i can create or design in FS, but as such they are abstracts. Each iteration process i use as standard has to include the sub iterations within its "orbit" to imply any useful iteration link. So to become so abstract that a metric is applied "outside" of its defining iteration procedure is likely to lead to problems of scale.

When i experience a fractal zoom it reminds me so strongly of the differences in structure which scale changes reveal and therefore it is a wisdom to me not to generalise in an assumption of a "smooth" continuous development beyond a certain iteration procedures defining region of operation. Rather i should expect discontinuity and discrete regionalised developments. So for example the quantum physics and classical physics are fractally entrained by axiom 9 so they will operate on each other,but there will not be a smooth continuous link between them. However i can approach iteratively close to the "boundary" between them in a wada "point" sense. I could refer to this as asymptopic, but i am not assuming a smooth continuous progression.

So using the movement of space in space i have traditionally accepted an abstract conception of iteration procedures and caled this "time". What i have perceived within the iterations is movement, and in movement the speed or rate of movement. So using my own visual sensors and the inate notions of sequence position/location and my own internal iteration procedures i am able to develop a sense of speed or rate. Even within my own body if i take my heart beat as a standard i can develop a rate assessment of say how fast i am breathing. This is a useful example as it reveals that many iterative internal procedures are combined in developing this sense of rate of breathing besides heart beat, and again axiom 3 leads me to expect this.

Space and movement of space in space under an iterative procedure is what i will look at next post.

This has been a most rewarding experience. This is math as it should be, not hidebound by snobbish conventionality but collaborative and egalitarian and inclusive as well as playful. The use of the processor and algorithms for visualisation, shading , rendering etc show the mathematical toolset benefits by innovation and extension.

mathematic

c.1380 as singular, replaced by early 17c. by mathematics (1581), from L. mathematica (pl.), from Gk. mathematike tekhne "mathematical science," fem. sing. of mathematikos (adj.) "relating to mathematics, scientific," from mathema (gen. mathematos) "science, knowledge, mathematical knowledge," related to manthanein "to learn," from PIE base *mn-/*men-/*mon- "to think, have one's mind aroused" (cf. Gk. menthere "to care," Lith. mandras "wide-awake," O.C.S. madru "wise, sage," Goth. mundonsis "to look at," Ger. munter "awake, lively"). Mathematics (pl.) originally denoted the mathematical sciences collectively, including geometry, astronomy, optics. Math is the Amer.Eng. shortening, attested from 1890; the British preference, maths is attested from 1911.

Online Etymology Dictionary free

So really! congratulations!! As you may know i think the foundations of maths can now be revised, but not in terms of unifying, an old value and goal.RATHER IN TERMS OF THE ITERATIVE NATURE of all things i perceive. I find you practitioners more stimulating than dry elegant text.

The following are candidates for Axioms of set FS but i have just considered them so i have yet to assess them.

Inertia, Equilibrium, Syntax, Parsing and Equivalence.

By Equivalence i mean that things `are not the same despite the objects being seemingly identical. Every thing is unique but some things are apparently the same, that is perceived similarity, or apparently identical, that is perceived congruency. The class of sets of "things" for which these relationships are a good description i am calling equivalence, and the specified sets within that class i am calling equivalences. The specification of a set in Equivalence is those aspects of a "thing" which are perceivable as the same in all elements of that set. These sets are in general containing similar elements. A set which is consisting of similar elememts which upon further iterative investigation are found to be the same for any arbitrary new rule imposed on the set is defined as a set of identical elements and called a congruence.

For a given set in Equivalence we can form ratios of its elements specific properties such that for a property p in the set the ratio of p for element i [ pi] to the same property p for element j [pj] is pi : pj or alternatively . This ratio wherever it makes sense for elements i and j will be a constant value in the sense that the ratio will always be reducible to the smallest numerals by "dividing out" common multiples.

I can establish a system of ratios based on the same property for many elements in a specific equivalence and these allow me to represent an operation or an action or a relation that applies to many elements at once. This also enables me to represent the many levels of a fractal system by one convenient ratio.

Between specific equivalences there may also be a property that allows a ratio to be formed. Such ratios between equivalences are in the Equivalence class and may represent relationships of one equivalence acting on another. The action of an equivalence on another may be indicated and a property linking the two equivalences be implied by the ratio between the equivalences being constant.

Thus the iterative process of enquiry may be characterised by the forming of Equivalences, the forming of ratios around a common property, and the seeking of properties to link found constant ratios.

Many things i take for granted are equivalences. For example mass is an equivalence. My mass is the equivalent mass of water at a certain temperature that has the same moment on a balance scale as i do. The specific property is the moment on a balance scale. By this property many equivalences can be put into ratio with each other. However these properties may not specify the set of the participating equivalences, rather they define a new set a new equivalence.

Before i continue i want to sketch out a possible universal iteration procedure. I am thinking of a relative vortex for each individual. So the entire experiential continuum i have constructed is based on a procedural vortex relative to myself. Each iteration applying the vortex results in motion within my experiential continuum. At each fractal level fractal entrainment across the boundary generate motion on the other side of the boundary and either side of the boundary. The vortex procedure moves a region at each iteration to a new position, and regions within regions to new positions within the regions. The universal application does not imply uniformity, it implies fractality at all scales, which is to say that the product of the iteration under the vortex procedure is a fractal with infinite levels, and these products would be vortex motions at all scales. Wile this may appear to one observer to be chaotic to myself it would appear fractal, and would generate a search for the self similarity ratios the boundaries of regionalisation and the evidence of fractal entrainment. As this vortex procedure is universal, all motion that results will be voticular to scale. Thus i would expect to find that all forms of motion from seemingly straight line motion to hyperbolic parabolic elliptic circular, cardioidal and spiral and even brownian would be apparent in its region of operation, which is universal and thus at all scales.

Since we use elliptical and circular motion to define periodicity i would expect periodical forms of motion to be linked to the iteration cycle of the universal vortex iteration in some way.

I would also expect brownian motion to be linked to vorticular motion and fractal entrainment both ways across a boundary with a wada basin condition.

Whatever descriptions we have of vorticular procedures should have this fractal nature if this is a universal iteration, and boundary conditions will need to be generalised to reflect the wada nature of all boundaries in a fractal.

The vortex procedure in the set FS will have properties demonstrated above. Thus regions around the vortex will be moved in a coherent way and at different scales. Within the layer generated at each scale by fractal entrainment, regions that are in sympathetic vibratory lock , that is resonance move as a whole with gradual sheer representing growth. Those regions not in resonance move in a way that dissipates them rather like evaporation. Evaporation and condensation can be expected within the layers and across the layer boundaries. Within the layers vortex motion will be evident again fractally entrained by the vortex procedure driving the layer system.

The coherent motion generated by the vortex procedure with these stationary boundary systems and a smooth and flexible boundary condition (at least on a normal everyday scale) exists everywhere even in the twist of the vortex. Only the sheer that cuts spirally down the eye wall of the vortex induces chaotic motion always and spirally on the wall of the eye, Elsewhere resonance induces coherent modes of motion some conformal some sheer, some growth some contraction. Dissonance generates evaporative destructive motion on a region assonance and resonance a conformal motion on a region and euphony a condensing motion on a region. Notice this coherency in the following

The coherency demonstrated here under these conditions allows me to posit that the coherent light produced in a laser or a coherent maser are evidence of vorticular procedures within the generating crystals under the influence of fractal entrainment by a changing electromagnetic field which itself is vorticular in operation.

With this extreme level of coherency the wada basins for the vorticular motions should have a definite axial shape which demonstrates concentration of the motion along that direction. Also the boundary of a region as a wada basin may be significant in the propogation of fractal entrainment across a boundary at any scale. It may be that all boundaries are wada basins in some sense.

http:"//video.google.com/videoplay?docid=4532767129040787318&ei=NixUSveREYqUqQL1gMGqDw&hl=en#QL1gMGqDw&hl=en#

This tendentious video nevertheless illustrates the conceptual basics but much has to be sifted to get the insight. {copy and paste in the address bar removing the "}

The navier stokes equations for fluid flow of compressible and non compressible fluids have vortex solutions that describe the propogation of vortices in interrupted flows, but the point is not the flow of vortices but the vortex procedure which they describe. This procedure is one model for the universal procedure in setFS and helps to understand the propogation of wave forms as vortices in this space. For example a vortex or vortex formation can establish a sinusoidal type vibration that is propogated radially or in a flow.

Complicated standing forms can be produced from vortex motion at specific resonances to the medium

http://www.climateaudit.org/?p=466

The calculated solution and the photographed image show not only compliance but other effects due to non resonance.