[Mike 5]

BEZIER & the Umbilical cord

It is obvious that I have found it immensely difficult to express Fractal Dialectics clearly.

If there is anyone with any patience left to read this, I’d like to thank you and ignoring the salt being rubbed into the whiplash wounds, comment on the significance of the Bezier curve.

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Imagine vector A, which is defined by a position in space and it’s direction and force, represented here by an arrow. B is a totally separate position with it’s own direction and its own force. They are each minding their own business, and will continue to do so, blissfully unaware of any other existence

These exist in their own realms. We see both. But through the genius of a Swiss mathematician, by viewing these independent vectors by a mechanical process while each remains oblivious to our new interpretation, something else is also there.

A single flowing curve, and there is only one curve possible, joins these two vectors and is known as a Bezier curve after the mathematician Paul Bezier. Vector graphics use Bezier curves, and the Adobe company – famous for Fonts, Adobe Acrobat and its pdf files, and Adobe Photoshop – were among the first to revolutionise graphic capabilities with the way so few positions, each with their own STRAIGHT length, efficiently map curves. Bezier released computer fonts from the dot matrix.

I want to use Bezier to express for now what I mean by DIALECTICS.

The point is that each of the vectors remains untarnished, untouched, taken alone. But something beyond the straight line vector occurs through JUXTAPOSITION.

Now JUXTAPOSITION is the central fact of Fractal Dialectics. For as soon as I had a theory of how things can divide up, JUXTAPOSITION – the way things touched or influenced each other – this was the key that made it all come to life.

So something that was not there before, is there immeidately two different things are juxtaposed. Yet each thing remains unmixed – and take away vector B, and there is our friend vector A, as always, minding his own business. This is very different from normal ways of thinking. Guilty until proven innocent. Dead or alive. Girl or Boy. Normal thinking is not dialectic but binary digital. Fractal Dialectics remains analogue, the search is always on beneath the appearance for the underlying tension and extremes that must be there to form the appearance. Someone could be both guilty and innocent, it actually depends on how you view it or word the accusation. A person could perhaps exist as a zombie or a vegetable on life support. A boy may truly feel he is a girl to the point of suicidal tendencies. Even so, take away the dialectic, the tension, take away the pressure as it were to be this or that, and the person exists in their own style, the flow is there, and you can even find new reference points to discuss what phenomena are and how they may connect together.

Once you grasp this, can you apply this recursively as an algorithm? Certainly. The recursive or fractal process is difficult for most people to imagine, but I wonder if the word UMBILICAL helps us to grasp the essence here. Babies emerge from the womb linked umbilically to their mother for nutrition and so on. That link is then cut, but it is a very real thing – I cut through two of them for my own children and it is like cutting a rubber tube on a bunsen burner. Very physical. And we do not tend to think of Fractals as physical but for me, they are. I don’t know if that analogy helps – I am seeking the actual mathematics of the Gods, of nature, whatever, of reality, and have to say the existing models are inadequate and anthropomorphic to specifically trade and war and little else. Maths as we know it reduces our world to things to be traded or fought over, but the umbilical worldview of the tribal shaman linked every birth back and back and back ultimately to the tribal creation myth, and everybody has VALUE and a place within the whole.

So in summary, I am not sure if I have been distracted by my earlier insistence on oscillation as sine waves (because all material things rotate and sine waves map rotation). And Fourrier analysis to reduce all analogue data to nested (fractal) sinewaves.

When I came to draw those sine waves I used Bezier curves, it is close enough if you arrange the vectors A and B to form any diamond or rhombus.

However the use of Vector graphics in computing shows their application, efficience, and power.

I still think I have not explained this adequately.