Wednesday, December 29, 2010

1.8 Sustainability and the Fractal

Sustainability and the fractal:

Update May 2017
This is by far my best idea; I have written it up in a working paper at my and vixra, and named it:  Quantum Mechanics, Information and Knowledge, all Aspects of Fractal Geometry and Revealed in an Understanding of Marginal Economics.
I shall post the Abstract, followed by the original post. I hope to have some collaborate and review my work in time.

Fractal geometry is found universally and is said to be one of the best descriptions of our reality – from clouds and trees, to market price behaviour. As a fractal structure emerges – the repeating of a simple rule – it appears to share direct properties familiar to classical economics, including production, consumption, and equilibrium. This paper was an investigation into whether the mathematical principles behind ‘the market’ – known as marginalism – is an aspect or manifestation of a fractal geometry or attractor. Total and marginal areas (assumed to stand for utility) and the cost of production were graphed as the fractal grew and compared to a classical interpretation of diminishing marginal utility theory, and the market supply and demand. PED and PES was also calculated and analysed with respect to (iteration) time and decay.  It was found the fractal attractor demonstrates properties and best models classical economic theory and from this it was deduced the market is a fractal attractor phenomenon where all properties are inextricably linked. The fractal, at equilibrium, appears to be a convergent – zeta function – series, able to be described by Fourier analysis, and involves Pi, i, e, 0, and 1 (of Euler’s identity) in one model. It also demonstrated growth, development, evolution and Say’s Law – production before consumption. Insights from the fractal on knowledge and knowing are also revealed, with implications on the question of what exactly is ‘science’ – and what is ‘art’? A connect between reality and quantum mechanics was identified. It was concluded marginal, classical economics is an aspect of a fractal geometry.  
Marginal, Fractal, Elasticity, Utility, Cost, Production, Price, Growth and Development, Say’s Law

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'.

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)

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 some time. 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.

Update Feb 2020
It was some time ago when I wrote the above; it is coming back to me know as I know more and have more questions.
What I am talking about above is the difference between power laws and normal distribution. And I think through the fractal I can unify them. Power laws are the direct stuff of fractals (scale invariance) and normal distribution, as I tried to claim, to do with parameters. I think I can explain why Pi shows up in normal distribution; it is that systems are fractal.

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?
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.