Thursday, September 29, 2011

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.

.




Wednesday, September 28, 2011

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




Monday, September 19, 2011

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.




Thursday, September 15, 2011

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













Monday, September 5, 2011

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.




Thursday, September 1, 2011

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).