Thursday, March 31, 2011

Uniformitarianism and the Fractal

Uniformitarianism: The key to the past can be found in the present.

I have a strong interest in geography and geology and it was here where I first read of Hutton’s uniformity, I soon found – after teaching development economics - that this principle maybe more universal, and may show in economics too.

The law of uniformitarianism reveals itself in the fractal. To describe a fractal, one would eventually cover the principle, only instead of reading as above - the key the past can be found in the present - it would read as the key to the present (scale) can be found in the small scale – or conversely the large scale, assuming. ceteris paribus approach, (holding all else constant or frozen).
In the below tree fractal, the new (present) cross section line b-b will share the same, (but different) as the old (past) cross section line a-a. Scale is the only difference - both in time (age) and size.
Fractal Demonstration of Uniformity

It is another insight from the fundamental characteristic of the fractal – the same but different – at all scales.
For example - which on the surface may seem a ridiculous - if you want to know how you were as a child, all you need to do see the children around us - the same may be said for growing old.
This may sound obvious, but it is only obvious because off the fractal nature of the universe.
Applications in Economics
If you want to know how it may have been to live in the past (social-economically speaking), say the middle ages, you need only search a country in the present that is developing and that has poverty to see it today.
A fractal thinker would see the child in the first application, and the developing country, as the same thing.
In any system you would not even have to find another country, it should be evident everywhere – every (healthy) system has diversity - rich and poor, young and old..change.

Wednesday, March 30, 2011

Macro and Micro and the Fractal

Updated 29th Nov 2012

There are many insights - in relation to macro/micro - that can be taken from the fractal .
Firstly, and importantly, when viewing a fractal (in isolation) scale cannot be discerned, the object maybe any size at all, from infinity small to infinitly large; the object shares the fractal charactoristic of being 'same' but 'different' at every scale. What can be discerned is the shape of the object, and from this an attempt can be made to deduce an understanding of the process to produce it.
The object is the 'same', the examples infinitly 'different'.
Examples: income, wealth, trade, selection, reproduction, specialisation and so on.
We see the same but different - at all scales. These principles repeat throughout the universe and are central too to biology, and maybe even chemistry and physics also.

This observation sheds light on whether there is a distinction between micro and macro : the fractal shows us that there maybe no real separation between the micro and the macro - they maybe one and the same. This is not to say shapes repeat exactly, it is to say rules repeat, principles repeat.  The rule is universal, and this rule will be in the micro, the small, as it will be in the macro, the large. 
If there appears to be a separation, it maybe just a matter of perspective, a matter of the point of observation.  The fractal does demonstrate relativity.
Macro micro: supply and demand
Fractality is evident in the supply and demand diagrams we draw.
From a distance, without looking at the labels and such, they look the same. Downward sloping demand, (and both for much the reasons), and upward sloping supply; price and output on the axis.





The fractal demonstrates imergence behaviour: one to many relationships -as shown above in the Koch curve development (or Growth). From one triangle to an infinity of them, and in so doing, creating a new shape. The new shape in the context of economics, is the economy itself, or what every we term it - the ecosystem ..eg.

Fractal Long Run Short Run

The fractal demonstrates the economic Short Run and the Long Run
In line with the classical economic view of short run and the long run - best demonstrated by images of  cost curves - the fractal is the math of the said phenomena.

Short Run:
The development and growth of the fractal – from iteration 1 to the equilibrium iteration is the fractal (economic) Short Run. The Short Run is the effect of the starting rule, e.g. branching, or adding of triangles.



The Long Run:
The Long Run is the end state, the total superpostition, where all the infinite possibilities are shown : the state where equilibrium iteration shape is set – to the fully developed tree, or snowflake.



Sunday, March 13, 2011

cosmoclimatology: CO2 production by photodegradation

I recently listened to this radio New Zealand science podcast on CO2 production by photodegradation and immediately though of a connection between it and cosmoclimatology.
If this CO2 production works at the small scale, it should  - at least in part - explain the long term carbon dioxide trend through time and its lagging behind temperature. But maybe it's not temperature that it lags behind at all, but rather, indirectly, the shading of clouds, caused by variation of cosmic waves - that also effect the temperature. Of course I am no expert, but at least it cannot be over looked, and I have now passed it on to those in the know. See what happens?

Have a listen, it is a wonderful story of discovery, and I have played it over and over like some good music.

I can only think of those who found the cosmic microwave background, well done Susanna.