FRACTAL ECONOMICS

Update: I have published on this blog, read here. I have been having a very difficult time recently , and I am not totally sure what to do? What do you suggest? I have taken down my many entries on the fractal because I am afraid they will not stand as an official claim to knowledge. Do I publish here on my own, using the low cost technology of the web, or go through usual costly slow peer review process? The thing is, my discoveries with the fractal, have led me to - what I believe - a straight forward theory of Quantum Mechanics, or what might be called 'a theory of everything'. When I listen to the 'experts' on the subject of quantum mechanics, it is as if they are speaking about the same things as I have discovered - but not yet published - in the fractal. Everything!: duality, uncertainty and entanglement, and even time and relativity included. What am I to do? I have been advised by a 'highly' academic colleague to write articles, and publi

This entry adds to my entry on the evolution of the fractal. It should go without saying - but it does require a mention. Adaptation is demonstrated by (or in) the fractal as a change in the shape; it is a change in the 'different' component of what makes a fractal - 'same' but 'different' through all scales. If we substitute or add time, this may be read as, 'same' but 'different' through all time scales. This is to say that the same rule or shape will repeat in different ways - through time -  as a result of outside influences, it will adapt, or it will change. This adaptation is best demonstrated in the fossil record - 'same' but 'different' through time.   It maybe useful to reflect on the elasticity of the shape; the elasticity or senitivity to change, changes through scale, and or time. This is shown in the below diagram and is described in an earlier entry on Decay.

Is our mind a fractal object or pattern collector, and if so, does the fractal explain laughter, and sadness - as the object changes shape changes? This entry follows on from my earlier blogs on equilibrium, particularly from the shape being set at or around iteration 7. Fractal development: Koch snowflake and equilibrium at iteration 7 Could it be that this is how our minds recognise  –  and know  –  objects or shapes? If the universe is full of repeating patterns, then to know something, all we need is a collection patterns; we don't need any detail at all. This can be demonstrated (below) by Koch snowflake development: as the snowflake develops, the 'stickman' develops; at some point  –  around 7 plus or minus 2 iterations  – the shape is known, the stickman is defined. At iteration one, we know nothing. In the above diagram we see the fractal development of a humanly figure. At iteration 1 the shape is not known; by iteration 5 we know it is a recognisab

The paradox of value or the diamond water paradox is well established and it is not my intent to challenge it but rather show that the fractal complements it. – explains it.  As I have shown earlier, the demand curve is derived from the fractal, it follows that if there is any substance of truth to my thinking it must address the likes of this paradox too. The answer to this paradox of value goes: diamonds are valued highly as they are assumed scarce, they have low Total Utility and a high Marginal Utility (or value). Goods similar to this are positioned to the left of any Marginal analysis diagram. Water is less valued than diamonds a it is (assumed) abundant. Water has high total utility and low marginal utility. The fractal offers an explanation to this paradox - or at least demonstrates.   If the object is not developed – fractally speaking – then it is positioned to the elastic left end of the fractal MA curve in Fig. 1: another iteration will return similarly high

Fractal Pareto Efficiency In a comment made on my fractalnomics youtube clip, Pareto and the fractal came up – is there a connection? Not to take the creativity from the person with the question, I began to think about it myself.   Pareto efficiency is where: one cannot be made better off without making another worse off.  It is said to be achieved at your full potential or market equilibrium. Fractal Pareto Efficiency Since the fractal demonstrates and shows market equilibrium (see my earlier work), fractal equilibrium is also the point of Pareto efficiency. Further to this - and trying to be in line with the Pareto efficiency definition (above) -  the merging of  fractal development with fractal decay (as seen below), shows fractal Pareto Efficiency, where: ('new') information cannot be gained, with losing ('old')information. or, put another way - we cannot go forward or grow without leaving something behind.

Ceteris Paribus - keeping all other factors equal or constant. Fractal Isolation This entry is to show that fractal demonstrates and shows us that Ceteris Paribus exists in reality, and has connections directly to our understanding of reality - even possibly at the atomic scale.   Ceteris Paribus  is a central assumption behind economic models and analysis - and of course, unbeknown to others, all science itself. It assumes, or sets, all other factors equal or constant; this allows us to study the pattern of the object in question. Without it, the 'cause' and the 'effect' would not be discernible - or would be confused in the 'chaos'. I often explain it to those outside economics that this is our way of achieving a controlled laboratory experiment. Alas it is also seen as the weakness of economics, as we don't (really) live in a 'ceteris paribus' world, we live in the chaos.  I would strongly argue - again -  that this is the weakness of all t

This entry is an addition to my earlier work on fractal marginal utility, something I have been reluctant to add due to the consequences of such a statement. I am convinced that that negative  marginal utility  is misattributed: that the MU curve does not go negative as shown below. Wikipedia. The fractal shows us that production and benefit go together are never seperated, you cannot have one without the other. The increasing  marginal cost (MC)  after fractal equilibrium, (green in Fig. 2 and 2b below), is more than enough to account for this 'negative marginal utility'. The cost rises - greater than the satisfaction or benefit  -after fractal equilibrium : this is feeling of being ill after excess consumption, of having had too much of something.

I put it out there, paradigms are a fractal phenomena. This insight is only a day old (2011-09-02): It was inspired by talking to one of my students. Last year I saw that she (not knowing it) drew or doodled  Sierpinski  fractals (below) in the corner of her work books - and I thought it was pretty cool. I pointed out to her  - at the time - that she could only draw down to 7 plus or minus 2 different triangle sizes in one doodle. Yesterday, she came back to me and questioned me again on this: Is that the limit? 7?  I went on to explain that 7 plus or minus 2 at one one standing or view, or perspective ; but if we zoom in, we will see more and more - as they come into focus; but there will always be 7 - yes. It came to me later, this standing or perspective is a paradigm, and is demonstrated by the fractal development below. The paradigm is the view from the first iteration to fractal equilibrium. A change in paradigm comes with a  zoom into the fractal (universe) - le

Fractal Decay As shown in the animation below, and described in my earlier entries, the fractal demonstrates development and growth: but if this reversed, it also demonstrates decay. Developing from the  first simple iteration to the complex, and in reverse, decay from the complex to the simple; from the snowflake to the triangle. fractal growth and development Analysis Below are two diagrams that analyse the Koch Snowflake fractal: the top diagram shows the exponential, and the lower the log. Both are split vertically (with a 'black' line of reflection) - showing development on the left side and decay on the right side.  - keep your eye on the snowflake..  The blue curve  shows the extra benefit of another iteration (in terms of Area), and  green - the extra cost of  producing or iterating.  As fractal development is exponential, it follows that so is decay. The above diagram of the two shows the exponential curve - with a constant elasticity (or sens

The credit card effect (as opposed to 'the butterfly effect') - one persons (credit card) debt could bankrupt a country - or even the world's economy. This is the perfect economic fractal example where dangerous massive debt burdens have migrated from the small scale (individual) to the large scale (country);  the principle or idea (of debt) is the same, the scale is irrelevant. I explained the world's economic problems to my 10 year old daughter by reducing the problem to her scale - it was very easy. Today - through the mechanism of (moral hazard) bank bail-outs - it is countries that are getting burdened. Where to next? This is the perfect storm. '

From a triangle, to the formation of a snowflake, this is a (universal) demonstration of creation: this is transformation, the creation of an object. Many to make one. Emergence Q. Is the original triangle the big bang? Animation of Koch Snowflake development

Fractal Elasticity - along the straight line curve. Click to see most recent developements that complement this entry. After discovering in my early blog that the elasticity of the Koch Snowflake fractal  is constant, I have since pondered on what is the meaning of all this? Economic theory suggests that all objects have this constant elasticity or are logarithmic in nature. The next thing to to is to straighten out the fractal curves. I produced the following diagrams to do just that and to demonstrate the change in fractal elasticity as the fractal developments. The above diagram shows constant elasticity, and the below variable elasticity along the straight (log) curve.

After completing my  Lorenz analysis of the Koch Snowflake fractal  I set upon analysing a real life fractal and chose a Christmas tree. This has been a side interest from my core fractal work and thinking so I have not written it up as a 'science report'. I am not sure of the species of tree I selected, but it is typical conifer of Northern hemisphere. Method I trimmed all the branches off the tree, counted them, weighed them, recorded results, then ranked the branches from lightest to heaviest; completed a cumulative percentage rank of weight and count table, and finally graphed the results. Branches everywhere: Below is the Christmas tree Lorenz Curve in terms of weight. Note that 'cumulative percentage of triangle weight' should read branch rather than triangle. I found that there were 5 levels of branches. I will be honest with you, I did not continue counting and weighing the branches in detail after the 3 level - the time cost was just so high and it

It came to me yesterday - in an epiphany: 1 + 1 does not equal 2 : if it does it is only half the answer, the other half lies in understanding chaos and fractals. The definition of (or insight from) the fractal is: same but different (or regular irregularity) - at all scales. Fractals show us how no one object is the same, they are complex, they are different . The 'same ' component of the definition is quantitative, and met or described as the 1 + 1. The different is qualitative and describes (at least) the diversity, complexity or unpredictability of the object. Update 2015 I have long thought about the my early entry and now know more. If 2 identical objects are added together, they equal 1. They are indistinguishable. I have also leant this is an assumption at the quantum level where particles are assumed to be identical; more support to my fractal quantum theory. I plan to write all this up in one paper as soon as I can. Blair

Updated: 29th Nov. 2012 This is an entry I have been wanting to do for some time, and is the first of three on fractal insights I have discovered on the economic assumptions (rationality, ceteris paribus, and perfect knowledge). This is a very difficult subject to describe, I hope I give it justice. I strongly believe that the issue of understanding of rationality is closely related to - if not the same as - that of understanding 'chaos': that is to say, complex systems are unpredictable. If we are to understand rationality, then should understand chaos, and thus, fractals. The definition of the fractal (attractor) is: same but different , at all scales. In our Economic models we use the assumption ceteris paribus: we hold all other variables constant,  and treat all persons as rational, so as to see the order (or the 'same', as in the definition), amongst complexity -  just as other science's do.  This definition maybe adapted or interpreted in this context

Fractal analysis demonstrates  Information asymmetry :  Monopoly and Perfect Competition The diagram below shows the development of the fractal Koch Snowflake. Shape equilibrium (Perfect Knowledge) - but not absolute information as the fractal is infinite in detail or size - is reached at iteration 4 -  where the marginal benefit is equal to marginal cost.  Perfect Knowledge or ‘perfect information'  is achieved only with free, open, competitive, or unobstructed feedback. Any obstruction to 'iteration' in achieving this equilibrium - due to what may be termed a knowledge monopoly - will produce an incomplete fractal shape, imperfect knowledge, asymmetric information. At some stage in the future, when things calm down, I plan to come back to this entry and update and further explain it: there is just so much to do.

Evolution and the fractal It is implied from many references, from leading biologist's, and mathematicians: 'that evolution has (often) found fractal ways, or has used fractal ways'.  This is totally misleading. Evolution is a feature of the fractal. Evolution is always, and everywhere, fractal.   Dictionary Search Results ev·o·lu·tion noun  /ˌevəˈlo͞oSHən/  evolutions, plural The process by which different kinds of living organisms are thought to have developed and diversified from earlier forms during the history of the earth The gradual development of something, esp. from a simple to a more complex form - the forms of written languages undergo constant  evolution Synonyms noun:  development ,  growth ,  progress If evolution is defined as change through time: and  fractality: as the ' same', but 'different' - at all scales then evolution is a (universal) fractal process, and can be demonstrated

I think the 'Butterfly effect' has a flaw, or is at least misleading. It suggests two attractors: the (flying) butterfly - which is governed by aerodynamics, and the (blowing and turbulent) typhoon - governed by thermodynamics.  Chaos theory suggests that each and every attractor demonstrates 'chaos' in a system; that a system (an attractor) in isolation will experience chaos - without any other influences. The real butterfly effect maybe more like.. 'the flapping of a butterflies wings could explain the presence, or existence, of the large (747) jet aircraft flying today - which is aerodynamics; or the heat emitted from the butterflies breath, could explain the typhoon, which is thermodynamics. What do you think? The credit card effect - one persons credit card debt could bankrupt a country - or the world. Dangerous debt burdens migrate from the small scale  - individual  - to the large scale - country - through moral hazard bail-outs

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 may be 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 ch

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 n

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.

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.

Continuing on from my earlier blog on fractal equilibrium : Koch Curve Animation From a fixed view point: all fractals ('attractors')  form their shape (are at fractal equilibrium) at and around 7 plus or minus 2  iterations - any more than this will come at too high a cost, and with no extra benefit - as shown in the animation of the Koch Snowflake development above. The 5 iterations to develop the fractal Koch snowflake in fig. 1 (below) - the point where the blue extra (Marginal) area (MA) and green extra (Marginal) cost (MC) intersect, corresponds with where the shape of the snowflake is fully developed.  This,  I believe, is not only a demonstration but is an explanation for  The Magical Number - Seven, Plus or Minus Two , but is also observable through-out our reality. From any stand-point, there will be around 4,5,6,7,or 8 levels of protrusion. For example, from where I am writing, I can see out my window where there is a park and some buildings. The building

Fractal Equilibrium: This entry follows on from 'production of the fractal'. Here I am suggesting that equilibrium - in any sense - is a fundamental of the fractal. Koch Snowflake development: source, Wikipedia The above animation shows the development of the fractal, at iteration 5 or 6 fractal equilibrium is reached - where the shape (of the snowflake) is made; or where benefit production is equal to cost of production. Fig. 2b below, shows a closeup analysis of the fractal equilibrium, at least from a static point of view.  MC  intersects, or is equal to MA, at iteration 5 where the Area is equal to 1, due to the reciprocal of 1 itself being equal 1. Equilibrium - Perfect Knowledge* http://en.wikipedia.org/wiki/Perfect_information Any iteration less than fractal equilibrium will result in an imperfect (snowflake) shape or incomplete knowledge or information. Any iteration point greater fractal equilibrium will result with little added gain in informa