System Reaction to Looming Criticality

On approach to a phase transition, the system begins to contemplate and move violently between states of existence. The system feels the torment of the critical point, and in turn sways and jerks between the two states not knowing how it should behave. Large variability is inherent and upon reaching the critical point, the system loses its character. No longer is it described accurately by any usual metric. Instead, the scales of its measures are its only useful description. In the end, despite all of its torment and rebelious swings, the system falls into place. Only its struggle at criticality is named due to their universal features.

Graph theory and economies.

I've been teaching myself about graph theory and network dynamics lately. The topics are some of the most fascinating I've come across. I've been thinking about how the predictions of different graphs may be applied. One application that I think may be useful for their application is an economy. How to apply graph theory to an economy may be tricky, though. Here, I'll try to explain how I think a model might be developed (which has probably already been done, so this is purely my own intellect at work).

The basic pieces of a graph are vertices and edges. Edges connect vertices, so paths may be determined by following edges between nodes. If a path cannot be found between two nodes, then those two nodes belong to separate, disconnected components. So, a graph may contain multiple components which are disconnected. Furthermore, directed graphs contain edges which define how two nodes are connected, that is, there is a one-way path from one node to it's neighbor, but there may not exist a way to make a path from the neighbor back to the starting node. Lastly, edges may be weighted in that there can be a greater "flow" of something between two nodes. However, the topology of a graph is what most people study since knowing the weight of a graph's edges is not usually available.

I think a model for an economy could be determined by individuals or organizations who make trades and the resource flow between them. In this case, a business would be a node, and the people and businesses they pay (for one reason or another) defines a directed edge between the business and the recipient. If available, then these edges may be weighted by the amount of a resource, let's go with money, is exchanged from the business to it's partners, employees, and governments. Nodes which grow due to interest, like banks, may have an edge which is directed back into the bank according to the inward edges. Corporations which have multiple companies within their umbrella could be represented as black-box node. Edges may go into the node, but each edge may really go to specific portions of the corporation. This could result in corporations being sub-graph containers, where they are still a node, but the inward and outward edges ping around it's companies. Black-box nodes might also be useful for looking at different scaling levels of very large graph. Organization of government levels may provide a decent scaling definition. Individuals live within a town, a town in a county, a county in a state, a state in a country, etc. Metropolitan areas, provinces, territories, etc. may be included similarly at appropriate levels. For business side organization, a similar approach may be taken. Governments may act as apexes to their respective levels (city government to towns, county governments to counties, etc.) since they receive tax revenue from all other nodes within their level. An anarchy style economy would have no apex.

Some predictions I wish I could explore are:
There could be a huge difference in just the topology between capitalist and communist economies. Consider the US; there may be less flow to the central government and less flow from the central government. Alternatively, consider China; there may be greater flow to the central government along with greater flow from the central government. Both of these would be coupled with a greater number of edges between non-government nodes in the US than in China. In terms of the apex nodes, the US should have a smaller (outward/inward edge weights) apex than China.

Transportation networks are structured similarly with a greater number of transactions (edges) being local (physically shorter paths). Therefore, transportation networks may help determine a framework for an economic network.

Internet companies receive more inward edges (receive money from others) on a greater physical scale. These nodes may occasionally be nearly disconnected, so they may be representative of bridges within an economic graph.

Changes to economic and tax policy almost always causes disruptions to network structure and the ability for edge creation. Edge creation and strengthening inward edges should be a sign of strengthening and/or desirable economies. It'd be interesting to see if there is a measure of these two aspects of edges relative to the possible number of edges within an economy graph which determines a desirable economy (matching subjective interpretations of current measures like unemployment rate). Essentially, economies perform best when the rules are consistent.

Turmoil within a black-box may call for a swell in that level's apex node. That is, governments may need to grow to help settle the inner workings of it's level. However, when a government should swell may depend on the extent of weakening throughout it's level. This may extend considerations for some times it may be useful to take a larger government model for some time if it's constituent nodes are too weak. However, stronger economies may require smaller government/apex nodes (in the case of capitalism). Therefore, economic policy might be best implemented conditionally. The difference between big v small government is due to viewing greater trust in the control granted to an apex vs less control.

I have other predictions I've thought of, but I've exhausted my mental capacity for now.