1.8 Sustainability and the Fractal

Sustainability and the fractal:


This entry follows on from my fractal growth and development entries, which were 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. 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 support sustainability in one way but not in another or the way we currently associate sustainability with keeping the environment or the economy today without compromising future generations. It may be that the notion of sustainability is (mathematically) nonsense. 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 into the 'same' and the 'different'.

'same'
The 'same' or '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. Strange attractors found in the study of chaos and fractals explain this feature of fractals: the repeating of a rule.
An example of the 'same' component - what I term lines of fractality - is exposed within the study of biology with 'evolutionary convergence' or 'analogous structures' - as shown in the example diagram below. 'Same' pattern - a wing,  but 'different' forms (Bat, Bird, and Insect). The line of fractality is clear flight by wing, which is a repeating pattern 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 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 will they become extinct, whether we like it or not, but rules or functions the 'same') will (not to suggest they can't, or else I will be breaking the laws of fractality).
In the wing diagram example, we see that there are many different variations of wings, at least Bat, Bird, and Insect, but there is more to this than just that: the 'different' suggests a superposition of all the wings that have ever been and will ever be. Patterns repeat, and winged flight will again be a part of 'life'.

I suggest that the fractal shows us that the political notion of sustainability is 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 show us evidence only to the contrary, is nonsense.

As an afterthought, 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 may be a stock or standing (wave) concept.

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