The Mathematics of Despair and Hope

The following theory is mine alone. Others may have posed similar ideas, but I have never encountered them if they exist. I have been looking at the general ideas behind network theory and “percolation theory.”  In percolation theory, imagine a porous rock containing oil or gas. The network through the rock is the collection of pores or blockages. The oil and gas driller and the mathematician are concerned whether there is a path through the rock to extract the oil contained in it. At the most basic level, networks are just collections of things joined together by something in common. For example, you could have the network of all parents of students at Sally Smith Junior High, or the network of all sparrows in Missouri, or all the people in Tinytown USA who earn $50,000 a year. These are finite networks with a limited number of members of each set. Mathematicians find it much easier to work on infinite sets, but we’ll deal with that later.

A community the size of Muskogee might have dozens or hundreds of networks where each person in the town may belong to many different sets such as all people between the ages of 40 and 43, all married persons, all parents of children at Muskogee High School, all who attend ABC Baptist Church, and so on. As the number of people or members of a set grows larger and the number of different relationships (sets) increases, the large numbers begin to mimic the results mathematicians find with infinite sets. The mathematics for these percolation networks apply to phenomena as disparate as extraction of oil and gas from rock, to economic bubbles in the market, to dissemination of false information.

But I am more concerned about the nature of the relationships between people that form all the tangled webs of networks that define our lives. I am concerned about how people at one side of a large network are able to connect or not to those on the other side. My theory is that the distribution of income overlaid on the web of social networks for a given community will determine whether that community is filled with hope or despair.

Imagine a curve representing the distribution of income from below poverty to folks making millions. It may not be a classic bell curve. A typical community will have far more people on the low-income side than the high side.  But a community of hope will have an income distribution that has only one hump. In this case, people on the low side of the distribution always have a connection straight through a collection of people earning more than they are that stretches all the way over to the high side of the curve. Hope is present because people can see through others they know the possibility of doing better.

But woe to the community with a double hump income distribution. In the case of a double hump, the middle class has been hollowed out to a tiny minority leaving a huge peak of low-income people on the left and a tiny hump of very wealthy families on the right. The hollowed-out middle class might be what Luke has in mind in Luke 16:19-26, the “chasm between the rich man and Lazarus.” Double hump communities are in despair because people in the low-income side have zero connections with people on the wealthy side. When there are no relational connections between the poor and the wealthy, the poor have no incentive to try because the message of the system is, “You will always be kept in that low-income place.”

History has proved that such systems are unstable in the long run. Or as W. B. Yeats put it,

“Things fall apart; the centre cannot hold
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere the ceremony of innocence is lost
The best lack all conviction, while the worst are filled with passionate intensity.”

Indeed. The centre cannot hold when it has been eliminated.

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