[Mike 5]

GUILLE has asked for more details of Fractal Dialectics, as mathematics, and I sense some impatience.

So I will just jump straight in.

Take a cake. It is a totality. It is finite. It is complete.

So this is essentially very different from Cartesian co-ordinates, which take a "random" starting point – Paris or Greenwich, or some lumpiness in the data, some "landmark" and measure regular "distances" out from there.

In Fractal Dialectics, you start with a finite total and you must already be … interacting with things enough to decide, this is the entire area for my data, and beyond that I am not concerned.

So in a way the primary "dialectic" or decision is figure and ground. The starting point is What are we looking at, and that must be explicit to allow others to later say, aha, I disagree, I’m going to look at a different totality.

Next there is the first arbitrary division into two. I am going straight for an example – and clearly the old distinction of quantity and quality is merged and re-drawn in Fractal Dialectics. The lumpiness of qualities will generally be where you divide the totality.

Here is my example, it will be banal to get the underlying points across: DAY vs NIGHT.

Or NIGHT vs DAY. There is no political comment as to which is 0, which is 1, the opposition is always reversible and that is the essence of the sequencing and recursion to follow.

In Fractal Dialectics, all real things are in motion, and this means that TWO mid points arise – DAWN and DUSK. People often speak of a spectrum of Greys, between some extremes of Black and White. This is not really possible in Fractal Dialectics because motion and change are essential qualities of all real things. Every grey is in truth fading or darkening. That may be irrelevent today, but for example my Roland TR505 drum machine was made of two beige plastics, and over the years one darkened and the other faded, so now it is a stripy drum machine. Impossible for a museum visitor to really know the original colours and and appearance of things in their original context.

WHITE – DARKENING – LIGHTENING – BLACK

NIGHT – DAWN – DUSK – DAY

Now normally I place these in a circle. Night is opposite day, and dawn is opposite dusk. Then again the garden swing resolve essentially circular motion into a sine wave, or a back and forth, depending on your viewpoint. An essence of Fractal Dialectic Analysis is finding simple harmonic motion and using Fourier analysis to reduce complex motions fractally (recursively) to layers of simple harmonic motion.

In flattening this obvious circle, I deliberately left the original extremes at each end. Because to list them going around the circle is incomplete – firstly either clockwise or anti-clockwise is selected and depending on the data you may introduce some bias. Then again we have use some bias – unless we start alternately DAY – DUSK – DAWN – NIGHT. But to list it sequentially, there is no beginning nor end to the loop and I would enter and leave with "…" as follows:

… DUSK … NIGHT … DAWN … DAY … DUSK … NIGHT … and so on. It is a loop.

Because of the axiom of Fractal Dialectics that All Material Things are in Motion, specifically curved motion (or rotation), there always will be this four way split if you care to look for it. But it does not stop at four, the basic qualities number six! As follows.

I am using text so please imagine this letter O is the circle made by these four elements in a continuous analogue loop. The loop contains an area, which is the fifth – ness, of … well I have to make up words here. This is a form of Analogue Binary, but a very structured form. I am tempted to call it Recursive Analogue Binary, but maybe someone else has a better name? For now RAB always implies a recursively layered structure of complete loops, and each loop essentially will be binary, even if that divergence is utterly arbitrary; that binary will have two mid points, even if they are not used in this or that application; and the enclosed area ( I call this the tetrahedron, for obvious reasons I hope) is a fifth … a fifth … what word to use? It literally emerges in the juxtaposition of these four (or even just three) labelled points in any continuous flow. Finally beyond that O outside is the context, the background to this figure, the skin and what ever this structure is not.

Before we apply this recursively to further cut up each slice of cake, the sixness is a maximum. There is no more than six, and normally we will use just two (digital binary) or four (what the hell to call this – Virtual Analogue Binary?). This is rapidly becoming a nomenclature.

Occasionally we will just use the fifth … shit what can I call these. They are not numbers, and the problem is the fifth and sixth transcend the loop or cake and step into a duality beyond it.

So many flippant words come to mind that are already used, and I must protest these are not number simply because numbers go to 7 and beyond and these CANNOT. They are qualities, but in a specific structure, that is always the same.

Innocently we have strayed into linguistics because unlike mathematics, where quality is discarded, and quantity exists esoterically without the shoes or sheep you are counting, here in Fractal Dialectics we have a grey area that is not quite quality and not quite quantity.

Up until now numbers spoke for quantity and we were very happy to say yes, numbers "exists", which is poppycock.

Numbers do not "exist" at all, they are esoteric fabrications in our minds. But I say that knowing in Fractal Dialectics, real material things rotate. Numbers do not rotate. They therefore do not exist on this planet nor any other, nor is space, they are not "real" in the way Supernova 1987A is. Sure, I take both numbers and Supernova 1987A on trust by mere symbols from teachers and the internet, but ultimately I feel I could take a large telescope and SEE it for myself. There is no telescope to see numbers, because they exist inside our minds only.

Until now WORDS had the exclusive rights to quality. Now I come barging in and upset the applecart.

OK. Here is an interesting thing about these six … shit … I have no word yet. It is possible the ancient Chinese already were familiar with all this., The YiJing (formedly spelt I Ching in the days Beijing was spelt Peking) has 64 "hexagrams" each with 6 "lines". There are some versions of the esoteric theory about the qualities of each of these lines. To some extent, with plenty of lube, these six lines could be said to correspond to the six quality-quantity things I am talking about here. Romantic thought.

And on that thought I’ll end for now except to say, fractally, recursively, this structure is applied to each of the portions you have. Using just the four portions, each of these then is cut into four again, there are specific challenges to resolve. Ultimately you have a finite system with a loop of elements that need a notation – I use a double notation, so one element for example would be called day/dawn and so on.

One final thing, Maths is said to be about number, structure, change and space. What I am doing here is not number as we know it. Truly it is Data, number, change and space, because with data you have to know what is the realm you are measuring, how are you measuring it, and what are the limits, algorithmic or otherwise, to expected maximum. Infinity is impossible in data, and zero is just an item in the list of possibilities, without the attributes of calculation.

Numboids. What else could I call these 6. Hexoids. Hexameter. That has a cetain rhythm. I love to speak in iambic pentameter verse. But since I started it's going from bad to worse....