Wednesday, December 29, 2010

1.8 Sustainability and the Fractal

Sustainability and the fractal:
update: 2011-01-04
This entry follows on from my fractal growth and development entries - published earlier.
There is never one snowflake alike, but there are snowflakes.

The fractal offers insights and helps us understand growth and development, change and evolution, then it should also help us understand sustainability. It should clarify what sustainability is. Is it real? Is it possible? Is it an illusion, or is it a delusion?

Fractals, by definition are patterns that show: 'same' but 'different', or regular irregularity - at all scales.
Fractals do support sustainability in one way; but not in another or the way 'we' currently associate sustainability with, the notion of keeping the environment or the economy today without compromising future generations. It maybe that the notion of sustainability is a (mathematically) non-sense. Here's why.
Fractals and sustainability analysis
To see why sustainability is a false statement - and doesn't hold -  at  least in the way it is commonly used - we need to split the above definition to the 'same' and the 'different'.

'same'
The 'same' or the 'regular' part of the fractal definition suggests that patterns, rules, and knowledge all repeat, at all scales: this part is sustainable or constant, it will happen, it does happen. This feature of fractals is explained by strange attractors found in the study of chaos and fractals; the repeating of a rule.
An example of the 'same' component - what I term lines of fractility - is exposed within the study of biology with 'evolutionary convergence' or 'analogous structures' - as shown in example diagram below. 'Same' pattern - a wing,  but 'different' forms (Bat, Bird, and Insect). The line of fractility is clearly flight by wing, and this is a repeating pattern, repeating at all scales. Today, we could add to this (at least) the human developed aircraft wing . 
repeating evolutionary patterns: same (function) but different (form)

'different'
The 'different' or 'irregular' part of the definition alludes to change, roughness or variety, it alludes to evolution: this component part of the fractal definition is not a sustainable, or fixed notion. This is where sustainability is a nonsense.
Fractals show us how there will never be a repeat of anything again:  there isn't, or has never been, another snowflake the same; there will also never be another 'me', or another 'you'; there will never be another repeated moment. Things come and go, for a complexity of reasons.
As objects (species) evolve, so to will they become extinct, whether we like it, or not; but rules or functions the 'same') will not (not to suggest they can't, else I will be breaking the laws of fractility).
In the wing diagram example; we see that there are many different variates of wing, at least Bat, Bird and Insect; but there is more to this than just that: the 'different' suggests a superposition all the wings that have ever been, and will ever be. Patterns repeat, there will again be winged flight,  it is a part of 'life'.

It is with this I suggest that the fractal shows us that the political notion of sustainability is a nonsense. The thought that humans, for whatever (moral) reason, can hold the likes of life, development, or an economy constant forever, when 'scientific' observation and knowledge shows us evidence only to the contrary, is a nonsense.

As an after thought: it is as if this part of the definition (different)  is a flow concept - the coming and going of something: the other 'same' or 'function' part maybe a stock, or standing (wave) concept.

Monday, December 13, 2010

On fractals and statistics

Just what's on my mind today:
What is the connection between the Mandelbrot set and the bell shaped normal distribution curve, or any distribution for that matter?

This is something I have been thinking about for sometime. I am surprised that fractals are not used to describe patterns.
It came to me today while on my bike to work: Fractals are an object thing, and describe the object through all scales; normal distribution or statistics need a parameter to function.
example :Stars are fractal, and will not distribute without a parameter : when we add say star size, star colour or distance, we get a distribution.
So I believe there is a very close relationship between the two - what is interesting is that distribution patterns are very  fractal, absolutely universal.

It is a goal of mine to understand this more: for there is more to it.

Thursday, December 9, 2010

The (fractal) God Illusion - the feeling of being watched.

The (fractal) God Illusion:
This applies to the Koch Curve zoom and links to my early blog on Inflation.

The following video inspired me for this insight, but the insight actually came to me while waiting in a doctors surgery - funny enough.
This is a great video on fractals and the Mandelbrot set : at 4:20 min Arthur C Clark explains the infinite size of the Mandelbrot set.




Two people stand at the edge of the fractal ( the Koch Snowflake), pairing into it - as if it were a tunnel or a computer screen.
What if one of the people (the walker) were able to walk out into the zoom, while the other stayed out and watched (the viewer).
For the walker, it would be like walking into a tunnel, and the viewer would see him or her get smaller and smaller as they walk in.
Now, what if the walker were to stop, turn, and look behind. What would they see?
A tunnel - with the viewer at the entrance, very small, and watching?
NO.
They would see infinity: they would see the infinite eye of the viewer - who is actually only looking into what they both know and see is a simple (triangle making Koch Snowflake) fractal.