A theory of everything: to blog, or to publish?

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 publish them, and shut down my blog .

On the other hand, yesterday I discussed with another group of colleagues - and my students:
express myself through this blog, - I don't see anyone else out there with a similar theory, otherwise we would know it - take my chances with it, use the new information technology we have.
Is a blog is a claim?

I am not in this for fame and fortune, I'm in it for the truth.

Blair.

Adaptation and the fractal

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.

fractal: A theory of mind, shape, objects knowing

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 recognisable humanly shape - but nothing else.
The mind doesn't need take in all the information we see – that is too costly:  it only needs shapes or objects: to know more, we can 'zoom in' to get more detail.
More to come.

.

The Paradox of Value, fractal

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 marginal area or satisfaction. If the object is fully developed 'fractally', it is positioned to the right on the fractal MA curve - another iteration returns a very small gain in satisfaction.

So, from the fractal it can be explained how we value goods differently: 
We value goods differently because in our 'mind’s' we experience objects in different stages or position of fractal development. The stage of development also determines the elasticity of the good, which is fundamental to value determination theory. The later is demonstrated in Fig. 2 with elasticity changing as the object develops. 

Fig. 1

Fig. 2

Pareto Efficiency, fractal

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.

Universal ceteris paribus: fractal

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 the 'sciences'. We may have theories, but we cannot predict precise outcomes with these theores.

With the Koch Snowflake (below) - or any fractal in isolation - there are no other factors (or, other fractals) in the image. The shape is a pure (sterile) function - it is pure Ceteris Paribus. 
Scale and location are impossible to discern.

 I am convinced that this problem of no scale or position is the problem we call (in reality) being lost.  In reality, ceteris paribus locations or situations are ones where there are no reference points, no discernible scale, and where we literally feel lost. All we have is shape (or knowledge) and as the perimeter of the Koch frontier is infinite we have ourselves a reference point or positional problem.
 Crators on the Moon
Ceteris Paribus exists in reality too - in monotonic 'landscapes'. Snow-scapes, dunes, waves and the like..
One example I picked up on - and demonstrates this observation - is the craters on the surface of the moon.
Watching the moon landings (yes they did land on the moon!) it must have been next to impossible for the pilots to discern height, there are no other reference points. It must be like this flying in cloud -without the aid of instruments. They relied on their radar - their instruments.
From (Fig. 1) below, ask yourself, what is the distance between these craters?
Is is 1:1?
Is 1:1,000,000?
We can't tell, can we. Height, scale, or location cannot be discerned - with the information provided.
Interestingly, one cannot even discern if it is the moon? It could be a tray of flour - with craters?
What we can discern though is that it at least looks like a crater landscape.

Fig. 1

For us to know more, we need reference points.
In Fig. 2 we now have references: 'eye at 104.10km  - it is very large.
Is is the moon - I trust NASA and Google, and the two dominant  craters in Fig 1. are at the top of the image. We actually get another reference, time: 11:27 2010-12-29, and it is in the age of Google.
This is how these craters looked around that time - and have done for many millions of years.

Fig. 2

In Fig. 3 we can see that the large crater has a name, Lambert. This is another reference. Those 'in the know' will know Lambert, and of course the other craters in Fig 1.

Fig. 3

Fig 4. Lambert at 210km - it could still be a tray of flour, yes? Take a look now at  Fig 4.a of Earth from 210 km's.

Fig. 4

Fig 4.a

 Below in Fig. 5 is an moon image without reference point taken at 3.75Km above the Moon, and Fig. 6 is taken from 3.79km above the Earth. Which one do we know more? Which one would you be confident with in making a decision like, touching or walking on. The Earth right? We can tell the altitude of the

Fig. 5

Fig.6

Conclusion.
Fractal Ceteris Paribus is where we can know, and understand the object in question; it is where we do 'science'; it is clean of all the 'chaos' of other influences.

The paradox is of this, is that in 'ceteris paribus' we don't know position or scale.
And this leads me to believe that there is a direct relationship between the fractal and the atom - for this is the language I hear when the quantum world is described to me. Something I will pick up on soon.

Thank you.
Blair

1.2a Negative Marginal Utility is misattributed

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.

paradigm: fractal

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) - leaving the past behind - as it decays away.

As and example, what have microscopes, and telescopes done for our understanding? Changed us forever.

Thank you Amanda  (with permission).



Fractal (Information) Decay

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 sensitivity),  and the below the logarithmic line of the above - exposing the (economic) elasticities.

Benefit Decay Curve

Rising blue benefit decay curve:

This curve is the opposite to the downward sloping benefit curve and demonstrates that benefit increases as the fractal (snowflake) decays. It is the marginal or change in the Total Area of the snowflake (Total Area is not shown here, see my early posts to see this). It is not to say that the Total benefit of loss gets greater, but that the change gets greater - the change (or loss) is small in the beginning and greater later.

Decreasing green decay cost curve

The cost, the pain, is highest at the beginning (assuming beginning is at equilibrium) and there after falls away.

Decay Elasticity

Elasticity of Blue decay curve:

Inelastic at (or near) the centre (the equilibrium point) suggests another iteration (or one less iteration in the case of decay) will not change the shape or Area greatly. Conversely, elastic at the end of decay suggests noticeable, or sensitivity to change in Area.

Elasticity of green decay curve

Inelastic suggests insensitive to change in the beginning - the pain, the cost remains, it lingers, the shape remains, the memory remains.

Elastic suggests after time the converse to the above. The shape is a distant memory and is changing - no pain.

Where do we see or experience this decay in reality?

• Think of a dying tree - the branches wasting away to expose only the 'trunk'.
• What do we remember after time - just the basics,
• the pain is in the beginning.
• The melting of a snowflake.
• It makes me think of Lord Rutherford's radioactive decay, carbon dating and transmutation??
• Viewing something from a distance.
• Is this what is termed entropy?

The credit card effect

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.'

Object: transformation, formation, creation

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.

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.

(Christmas) tree Lorenz 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 would not change the shape as they were so light. So, I counted and averaged the final 2 levels (sorry, things to do).

Conclusion and reflection

The conifer tree has a very large Gini coefficient - similar to that of the Koch snowflake (below) and that of the standard wealth distribution.

The question is, is this how an economy is? Is this disribution universal? Yes it is.

Is improving this gini coefficient impossible? Do we see Chrismas trees with branches as big a the trunk? No - the branches will break.

This does make me think of cacti, but I still think the trunk is dominant.

http://kalaalog.com/2007/07/15/how-to-paint-cactus/ 

That was fun; I would like to thank my family who promised not to laugh while I counted branches on the floor :)  ..  and to my school math. teacher colleagues for their support, and of course - always - to my students.

Update 2017, I have published/posted.
I have found; Lorenz distribution is a fractal phenomenon;  the fractal models the Lorenz Curve; Gini coefficients increase as the fractal grows and develops; and the distribution between groups accelerates with growth and development. Lorenz distribution is universal: income and wealth inequality one aspect of a universal phenomenon, and is scale invariant. 
 https://www.academia.edu Demonstrating_Lorenz_Wealth_Distribution_and_Increasing_Gini_Coefficient_with_the_Iterating_Koch_Snowflake_Fractal_Attractor

1 + 1 does not equal 2

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

Decades of Common Agriculture Policy leave Europe with little future hope.

Update: 01-11-2011

I have been thinking of a metaphor to sum up this issue, and thought of this:
"Cutting off the nose to spite the face"

Original entry:
This is the perfect fractal (or scale) example of 'no such thing as a free lunch'.

Decades of agriculture protectionism - strangling the death out of developing economies - has (ironically) hindered any prospects for Europe trading itself out of this (next to) bankrupt financial crisis it is currently in.
 One of the saddest topics in the subject of economics is that of the impacts of farm and agriculture protectionism, namely the Common Agricultural Policy, or the CAP.  For decades it has favoured a very  few – some 1  to 2% on average of EU GDP  – at the expense of the EU tax payer, and has almost systematically destroyed –  through the act of dumping –  any hopes of developing counties (LDC’s) producing and importantly trading food themselves. It has gotten so bad, and out of hand, these countries are now net importers of food.

Is it now 'Africa', that could save the EU?  - trade your way out - rather than bail /print yourself out.

In principle, had EU bought African sugar (cotton, corn, chocolate bars and T-shirts best), Africa would have in turn bought EU trucks, EU make trucks, and Africa they will need trucks to move the sugar – both would have won. Through CAP, this principle has been distorted (and still is, even with the austerity in Europe right now, CAP has hardly changed!! ) to the extent where Europe produce both sugar and trucks, and have then dumped the surplus sugar on African market, destroying their production chances and their self sufficiency.  To add salt, EU then expect them to buy the trucks anyway! - with the little they have.

This absurdity has survived due to more than one reason, but it is interesting how rich nations have been able to trade with each other, the same goods – trucks for trucks in this case - as Professor Krugman described in his 2008 Nobel Prize lecture (here).  This has been successful, up until recently, but now rich countries (with the exception of a few, Norway and the like) are broke! 

The only method to kick-start these economies has been extreme monetary policy (printing), with negative interest rates (from around 2014) and fiscal policy. I call this act of printing and deficit spending to improve yourself, Economic incest.  Do it with yourself, your own family.

Europe wouldn’t have had to do this, had they'd traded - freely!  Win Win.

Too late, China is in ahead.
Today, we see China making its way into Africa, and in doing so growing Africa for the first time in 50 (odd) years.  Europe never did that, and thought the only solution for Africa was aid. Wrong!

EU, what a mess you have made for yourself. "Cutting off the nose to spite the face".
From a distance, it is almost as if Europe is racist. Economic apartheid.


http://www.oxfam.org.nz/sites/default/files/reports/DairyPaper.pdf

Rationality and Chaos

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 of rationality, to read as: rational but irrational at all scales. This is to say, that even the axe murder will weigh up cost over benefit - before throwing the axe; their choice is rational to them, at that time of throwing, but relative to someone else watching (the fractal demonstrates relativity), it would appear extremely irrational. It is just to say they are reasoning 'differently', but they are using the 'same' method.
Again,  all Science uses the notion of  ceteris paribus -  with its laboratories, and control experiments, it 'freezes' out the chaos. Science can know (can derive a law, but, with that knowledge it cannot predict.  We can know the likes of Newton's laws of gravity, and use them to describe a pen falling from a table; but could we every repeat the event so as the pen falls in exactly the same place, over and over?  Theoretically, yes. Practically, no. I know I am contravening some 'deternimistic' understanding here, but I say no.  Even if we had all the information, I still say no: the reason being, it is infinity costly to get full information - this is demonstrated in the fractal, and is the key principle of chaos theory.
Not being able to predict, does not stop the work of science. And in the same way, not being rational does not stop the work of economics. We are searching for patterns.
Ignore the chaos, find the order.



So I would conclude that if we are to understand, we must treat all as rational, so that we can find the rational behaviour. But understand, when all is put together in the reality, we will observe 'irrationality' - or chaos.

Fractal Monopoly vs Perfect Competition or Knowledge

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 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

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 in the fractal - it is a law of the fractal. 

Evolution is a record of the chaotic or 'different' component of the fractal definition; where the object in question is the 'same' component, and time is the scale.

Evolution can been seen in the fractal and is a core component of the mechanics of the fractal: a universal repeating pattern or algorithm. From the simple to the complex, an emergence, as demonstrated in the following 'development' of the koch snowflake fractal. In principle, as the fractal is infinite, so to is evolution.

The relationship between evolution and development:
Development may be seen as a 'short run' or short term observation - the development or emergence of an object, from iteration 1, in the fractal, to fractal equilibrium - iteration 6: the development of a tree for example.

Evolution may be seen as a long run observation, tracing 'development' of the object, the tree, through (greater) time, and is best demonstrated by the fractal zoom.  Evolution shows the 'chaos'  the complexity or the influences on the 'developed' object.

Evolution and development are, fractaly speaking, of the same principle, and may well be indistinguishable from each other without a (time) scale reference. The tree, becomes the tree of life. 'Nested' development within evolution.

The fossil record traces or records these changes through time - the fossil record is a fractal record:  'cataloging' the infinity of ('different') combinations.

Can, in the long run, something become fully evolved, as we can say something can be fully developed?
Yes, and no. In the same way as there are limits to (fractal) growth and development, the object will evolve to a formed shape; but no, because there will always be change, an infinity of changes - never one object the same.
Evolution and Quantum Mechanics:
From an analysis of the fractal, we can see that evolution and quantum mechanics are related. More to come.

Evolution a fractal wave?
The below diagram(s) demonstrate a change to one of the triangles during the development of the fractal.
Insights from this are many:
A pulse, or wave is demonstrated - is evolution a wave phenomena?
Branching is also demonstrated, which is key to evolution.
More to come.

I am very interested in Biology, particularly the fossil record:  here is one of my favourite lectures where the only word left out is fractility. Here the Professor describes key principles of economics at the smallest of scales. It is worth a listen.

clip Lecture 2:
Professor Paul Rainey FRSNZ, Massey University
Professor Rainey paints a picture of life's evolution from the perspective of major evolutionary transitions, including that from solitary organisms to societies.
Recorded 28 July in New Plymouth

Butterfly Effect a flawed argument; Credit Card Effect better

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.
This is the perfect fractal in action: note the principle or idea is the same and that scale is irrelevant.


Today it is countries that are getting bailed out.

The perfect storm.

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.

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.

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.

Fractal equilibrium count

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 is the first protrusion, then there is a chimney on the building - 2, then a brick on the chimney -3, then there is, I can just see, an icicle (it is winter) -4.
See my entry on fractal paradigm

(http://www.musanim.com/miller1956/ )

It can be observed everywhere - if you open your eyes.

In the image of a tree to the left, if you follow out from the trunk of the tree, until it first forks, then follow that branch until it forks again, and then go on repeating, following the 'first' branch on the branch, until you cannot see any more branches, you will find you can only fork 7 + or - 2 times.

Iteration No 6 is the optimal or perfect viewing iteration of the (fractal) Koch Snowflake - from the viewers perspective.

I believe it is also the number of iterations, or feedback's, to gain market equilibrium.

The following cases are of interest to me:

• 6 degrees of separation - between knowing everybody on the earth: I have heard that the reality is around 4 before the link ends, fades away.
• How many times can one fold a piece of paper - 7, 8,9, maybe 13 - but not more (??)
• The food-chain: How many links between the top and the bottom of the food-chain. With whales and plankton, not many, but I have been told the max is 6. After that there is nothing to be gained, and what is comes at too higher cost. 

Fractal: Equilibrium Perfect Knowledge and Output

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 information or shape -  and it will come at a great cost.
Perfect knowledge, or the perfect shape, is gained where MA =MC.  This, it taken directly from  economics theory, resembles where allocative efficiency is maximized - at the equilibrium point in market theory. Competition gives the best shape or knowledge, opposed to a monopolist that would produce or output somewhere left of equilibrium.
Notice Total knowledge will never be gained - the cost is too high.
*I am aware that the fractal demonstrates infinity, and thus shows the infinity of knowledge - of the rule. To say perfect information may well be a relative statement, said in context, or in a  paradigm.

A theory of knowing?
Development of the little man is my attempt at understanding how we know: check out my theory of mind

http://www.fractalnomics.com/2011/09/paradigm-fractal.html

Equilibrium Output (quantity)

Of course, iteration number is not the output or quantity ( as in classical economics). So, what then is it?

It came to me that it is the number of triangles - that are added after each iteration.

In the below diagrams below (fig.3 and 3b), shown in orange is the increase in the quantity of triangles, after each iteration. I have recently learned that this curve is exponential.

 Equilibrium quantity or output at fractal equilibrium is  ..... triangles or point 'a', on the diagram.
Update May 2017
This is by far my best idea; I have written it up in a working paper at my academia.edu 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, followed by the paper. I hope to have some collaborate and review my work in time.

Abstract

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.  

 Keywords

Marginal, Fractal, Elasticity, Utility, Cost, Production, Price, Growth and Development, Say’s Law