My discoveries and insights derived from the fractal. Towards a theory of Quantum Chaos. Experts on fractal point out examples of fractals as trees and clouds; I say they are everywhere and everything and it is more interesting finding what is not fractal.
Fractal mechanics: the laws of information and knowledge as derived from the fractal.
Like a fractal itself, these laws will/should - over time - grow, develop and form shape .
1.1The fractal demonstrates the universality of knowledge and information.
1.2Absolute knowledge is unachievable – as information is infinite.
2.1By iterating – using, studying, researching, or experiencing, the same rule the fractal reaches what may be termed shape, knowledge, or fractal equilibrium.
2.2Fractal equilibrium is reached at or around 7 plus or minus 2 iterations.
2.3Fractal equilibrium is a superposition of the information.
2.4The ‘same’ (or regular) component is what is known as a rule – and thus this is the basis of Euclidian mathematics.
2.5The ‘different’ (or irregular) component is the chaos – the diversity of the rule.
2.6A paradigm is the number of iterations from ‘first iteration’ to fractal equilibrium.
3Knowledge development – the demand side
3.1The fractal, and thus knowledge, is developed by repeating (or iterating) information in the ‘same’ regular way.
3.2The extra (marginal) utility or benefit of Knowledge is greatest at the first iteration, and there after in one paradigm diminishes (exponentially) with each and every additional iteration.
3.3Diminishing marginal (or extra) utility of knowledge derived from the fractal:
4Knowledge – supply (production) side
4.1Fractal production of extra knowledge comes at an increasing (exponential) cost or difficulty, and is inverse to demand.
4.2Knowledge claims, and definitions (as demonstrated as a fully developed fractal shape) will ‘appear’ simple – or complete – on the surface, but be complex in the detail. Simple: so as to be able to be refined or generalized into one word. Complex: so as to open more questions – the more we try to investigate (demonstrated in the fractal zoom).
4.3Fractals, attractors, and chaos together demonstrate that we can know (the shape), but (future) outcomes cannot be predicted.
5.1In reality the same information repeats in a ‘different’ (or irregular) way – at all scales. This maybe due to interference from other fractals.
6.1In a fractal ‘monotonic’ state of Ceteris Paribus – where there are no other fractals – only shape can be discerned.
7.1In a state of Ceteris Paribus, scale cannot be discerned.
8.1In a state of Ceteris Paribus, position cannot be discerned.
8.2Other fractals act as reference points – they give position.
9.1.1Transformation, emergence: From being a triangle (in iteration 1) to being something new – a snowflake.
9.1.2From the above, everything ‘real’ has complexity or fractality.
9.1.3From the small (the particular) we induce the large (the general), and conversely from the general we deduce the particular.
10.1Growth is the change in the quantity of units – triangles on the fractal – after iteration.
10.2There are limits to growth:
10.3Area: the fractal area is finite; the (total) area of the fractal will grow at a decreasing rate.
10.4Quantity: though quantity of triangles is exponential, it is limited by the equilibrium of cost over benefit.
11.1Development is related to the complexity of the fractal structure, it is inextricably linked to the growth of the fractal.
11.2Fractal Decay: is the inverse of fractal development, and is also logarithmic.
12.1Inflation is demonstrated to the perimeter of the fractal: the perimeter increases (to infinity) after each and every iteration, while the area of each additional unit decreases – or devalues.
13.1Elasticity is the sensitivity of one variable to a change in another. It is explained and used in classical economics and is made relevant – through the fractal – to all things real.
14Monopoly – Competition
14.1Obstruction to iteration – though (for example) monopoly power – will produce an incomplete fractal shape, or imperfect knowledge. Perfect shape, (perfect knowledge) is achieved with open, and competitive unobstructed feedback.
16.1Evolution is demonstrated in the fractal – by zooming (through time): the ‘same’ (or regular) but ‘different’ (or irregular) through time. Evolution is a universal.
17The fractal record
17.1The fractal record is the set of the ‘same’ rule and its possibilities, the ‘different’.
18.1For something to be real, it will have a (complex) history. This is to say it will demonstrate all the features of the fractal through time.