Friday, October 30, 2015

Improved Fractal Lorenz Curve



Four years ago I conducted a 'loose' experiment on a Christmas tree to test the weight distribution of branches for Lorenz curve wealth distribution similarities in an economy. This week I finished the Figure 3 chart (below) after modelling the Koch Snowflake fractal for (Lorenz) area distribution. Took me hours. 
I found the area distribution not only follows what we observe with wealth distribution, but expands as the fractal grows (or develops) with time (Table 1). I also found different area groups (triangle sizes) grow with time (from an arbitrary size), and accelerate apart from each other with time. This is a geometry and can be observed in any fractal structure. I have updated my post at academia.edu
Abstract:

Global income has increased exponentially over the last two hundred years; while, and at the same time respective Gini coefficients have also increased: this investigation tested whether this pattern is a property of the mathematical geometry termed a fractal attractor. The Koch Snowflake fractal was selected and inverted to best model economic production and growth: all triangle area sizes in the fractal grew with iteration-time from an arbitrary size – growing the total set. Area of triangle the ‘bits’ represented wealth. Kinematic analysis – velocity and acceleration – was undertaken, and it was noted growing triangles propagate in a sinusoidal spiral. Using Lorenz curve and Gini methods, bit size distribution – for each iteration-time – was graphed. The curves produced matched the regular Lorenz curve shape and expanded out to the right with fractal growth – increasing the corresponding Gini coefficients: contradicting Kuznets cycles. The ‘gap’ between iteration triangle sizes (wealth) was found to accelerate apart, just as it is conjectured to do so in reality. It was concluded the wealth (and income) Lorenz distribution – along with acceleration properties – is an aspect of the fractal. Form and change of the Lorenz curve are inextricably linked to the growth and development of a fractal attractor; and from this – given real economic data – it can be deduced an economy – whether cultural or not – behaves as a fractal and can be explained as a fractal. Questions of the discrete and wave properties and the accelerated expansion – similar to that of trees and the conjectured growth of universe at large – of the fractal growth, were discussed.













Sunday, September 13, 2015

Fractspansion Prediction

I was thinking the other night, after watching a lecture on the distribution of galaxies in the observable universe, if my fractspansion model is correct then there should be a (regular) lateral shift in galaxies by distance time and not just Hubble recession. It should also be increasing with distance-time as with Hubble's Law.



Thursday, June 4, 2015

Best Black Swan event - black swans are native to New Zealand too

In a conversation yesterday, I was asked whether I has read the book Black Swans by Nassim Nicholas Taleb? Yeah, I replied, and then said: ‘You know, the best Black Swan example to me (probably not in Taleb's book if I recall) is that Black Swans once lived in New Zealand too (and its islands 'Chaptam'), and not only Australia as commonly thought. They went extinct (by the Maori), were reintroduced, but have been found, in recent times, to have flown there on their own. They also have similar genetics.  That's the Black Swan of Black Swans I say.

http://www.teara.govt.nz/en/wetland-birds/page-4

Sunday, May 24, 2015

The M.A.D gun

In memory of John Nash, may I share with you my M.A.D. gun - something I have been thinking about a lot, even today before I learned of John Nash's death.
My ideas come not directly from him, but from Thomas Schelling - another economics game theory laureate, this time in the area of cold war nuclear deterrents . I was at his lecture in 2005: the same year that paradoxically the I.A.E.A. got the Nobel peace prize "for their efforts to prevent nuclear energy from being used for military purposes and to .."

The M.A.D. gun.
What if (just say) all firearms, all guns, had two barrels: one that shot your target - your adversary; and the other - at the same time - shot you. So, to use it, would mean you both die (or at least you die trying).  Question is, would it ever be used?  No, but you could argue: yes it would - to save the (your) group.

Well then, make a bigger gun - scale it up - so you get the group too. A cold war, nuclear stand off - as we still have (of sorts) today (even if we don't think about it).

So then, with that logic - and the near 70 years of no 'conventional' use of them, and the likes of Pakistan and India playing cricket and cooperating together again - why don't we, instead of cleaning up, riding the world of nuclear weapons, hand them out. Say 10 each (Middle East and all), with telephones to communicate.  

What would happen? Is it M.A.D, or is it peace.

 If you don't know what M.A.D. is ....google.

If you listen to part of Schelling's lecture, the last 5 minutes of it are most worth, at least for me.
http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2005/schelling-lecture.html

Fuck I love economics.

In memory of John Nash

A great mind died today, a Newton of our time. His idea 'the Nash Equilibrium' offers explanation to likes of why we do not need deities to explain why we’re good (or not) to each other; why in the 69 (soon 70) years of nuclear weapons - all the many thousands of them - they’ve only been used twice in anger (that is amazing!); and even why Sweden didn’t get invaded during WWII, its global monopoly on the ball bearing was so important to both sides, any conflict on its soils would be a lose-lose outcome for both sides – a Nash Equilibrium, fight your battle some where else, not Sweden. There are many more, and I love spotting them.
It seems ironic he died in a car: one of the simplest examples of a Nash equilibrium is the explanation as to why we drive on one side of the road, and not both.

Monday, February 9, 2015

Natural fractal lake, Arethusa Pool, the worlds only?

Is Arethusa Pool (New Zealand) and its island's the worlds only natural fractal lake?

I was there with my family in January: it was a wonderful day, and very exciting for me - mathematically speaking.

Arethusa Pool (and its island) is on Mou Waho Island, which is on Lake Wanaka, which is on the South Island of New Zealand, which is in the South Pacific Ocean.

Water (the South Pacific Ocean), land (South Island New Zealand), water (lake Wanaka), land (Mou Waho Island) , water (Arethusa Pool), land (islands on Arethusa Pool); water in a puddle after rain (or when I filled it), land as small as a square centimeter inside the puddle, .....water??



 
Arethusa Pool, and Lake Wanaka New Zealand 2015.