Lets continue our discussion (see "The Recession is Over Or is it? - Fractals") and enhance our world economics model further.
The best tool available to us is the Lattice theory.
I will try to explain it without using any complex mathematical solutions (which is NOT an easy job).
Simple lattice consists of "nodes" connected to each other, something you would see in science books when they talk about crystal structure.
The simplest, or one dimensional, lattice is a line with nodes something like this: -o-o-o-o-o- As you can see each node is connected to the two neighbouring nodes.
If we add another dimension then every node will have 4 connections.
Three-dimensional will resemble "crystal structure" with 8 connections.
If we go above 3-dimensional lattice then you would need to use your mathematical imagination, but number of connections would grow at the power of 2, e.
g.
16, 32, 64, etc.
If each and every node has the same number of connections then the lattice is called regular, but if some connections are broken - then the lattice becomes irregular.
In this case the nodes with maximum number of connections are called supernodes.
Now, when we know what the lattice is, we would apply this structure to economics.
Every node would be an "economy unit" from individual to the multinational corporation or government.
Each node would have a set number of "economy connections" (we should choose only essential ones otherwise we will be using too many dimensions), for example individual is connected to his employer (salary), bank (service) and government (tax).
Company would be connected to customers, suppliers, banks and government and so on.
Even from the above you can see that bank and government are always present therefore they are our supernodes.
We have described our lattice in as much details as possible but have not used any mathematics, which is not bad for a mathematical model.
The best tool available to us is the Lattice theory.
I will try to explain it without using any complex mathematical solutions (which is NOT an easy job).
Simple lattice consists of "nodes" connected to each other, something you would see in science books when they talk about crystal structure.
The simplest, or one dimensional, lattice is a line with nodes something like this: -o-o-o-o-o- As you can see each node is connected to the two neighbouring nodes.
If we add another dimension then every node will have 4 connections.
Three-dimensional will resemble "crystal structure" with 8 connections.
If we go above 3-dimensional lattice then you would need to use your mathematical imagination, but number of connections would grow at the power of 2, e.
g.
16, 32, 64, etc.
If each and every node has the same number of connections then the lattice is called regular, but if some connections are broken - then the lattice becomes irregular.
In this case the nodes with maximum number of connections are called supernodes.
Now, when we know what the lattice is, we would apply this structure to economics.
Every node would be an "economy unit" from individual to the multinational corporation or government.
Each node would have a set number of "economy connections" (we should choose only essential ones otherwise we will be using too many dimensions), for example individual is connected to his employer (salary), bank (service) and government (tax).
Company would be connected to customers, suppliers, banks and government and so on.
Even from the above you can see that bank and government are always present therefore they are our supernodes.
We have described our lattice in as much details as possible but have not used any mathematics, which is not bad for a mathematical model.
Source...