The Stock Market, Forest Fires and the Fermi Paradox

On May 1st, Brandon quoted a theoretical physicist, Mark Buchanan, in this blog. My curiosity was piqued, as it often is when questions of applications of physics to real-life are concerned. I had kitten pull Buchanan’s Ubiquity and Nexus from the University stacks and I dove in….

And was transfixed. Buchanan is an expert on Non-equilibrium Critical States. These are conditions where there are literally millions of different factors and interactions working on something–far too many to count and examine separately. This is a new field in theoretical physics–less than forty years old, really, and like chaos theory has only been possible to study with the advent of large-scale parallel processing and tools like Wolfram’s Mathematica.

One of the Holy Grails of geology has been earthquake prediction. Countless millions of dollars are at stake and hundreds or thousands of lives could be saved if we could know when a quake is liable to hit San Francisco, Tokyo or St. Louis. Therefore, a lot of time and effort has been expended to attempt to learn how to make accurate predictions.

They all failed. No matter what models were used, statistics recorded or physical measurements made, any predictions were useless. Some, like the false predictions of “The Big One” in the St. Louis area, caused a great deal of consternation and panic. At the same time, the scientists completely missed predicting the San Francisco earthquake of 1989.

It was too complex. An interesting discovery came out of their research, however, concerning the magnitudes of earthquakes. Current methods of recording earthquakes are accurate over about 6 or 7 orders of magnitude. This is a huge range in science–sort of the equivalent of the mass range of a shrew to a blue whale.

When one graphed the number of earthquakes versus their Richter value on the scale of 2 through 8 on a logarithmic scale, a straight line was found. This was called the Gutenberg-Richter Law. Here’s a wiki on Power Laws, for those of you who want more information about them.

This caught the interest of theoretical physicists who were interested in Game Theory, which is a method of examining real-world situations by making simple mathematical models with certain rules and then turning a computer loose with those rules and some initial conditions and seeing what happens next. They were successfuly in modelling the data by using blocks and springs with connections between them.

However, the physicists were more creative than that, as per usual. They began looking for other examples of this type of power law occurance and found them everywhere.

There are power-law relationships found in the distribution of wealth in society, how large a forest fire grows, the historical extinction of species in the earth’s biosphere over the last billion years and how many people are killed per week in historical wars.

All of the systems examined had several things in common:

1) There were large-scale (orders of magnitude) differences between the low end numbers and the high-end results of a perturbation.

2) There were uncountable numbers of factors working on the items examined.

3) It was impossible to predict what the result would be of the next perturbation of the system.

The type of system involved can best be visualized by thinking of a pile of rice grains. You add a grain at a time to the pile. Usually, nothing big happens, but every once in a while, a huge avalanche of grains occurs, changing the condition of the pile drastically.

One discovery that would be of immediate interest to you, Billy Joe, is that fluctuations in the Stock Market indexes are one of these cases. If you go back for the last eighty years and feed in the day-to-day fluctuations of the Dow Index adjusted for inflation, you find that there’s a power-law relationship between the size of the change and the number of times that it occurs.

My research in this respect is nothing new. Evidently, physicists have been watching this for some time, as these papers indicate. Assuming that the market really is a non-equilibrium critical system, one major result can be deduced:

One cannot predict the magnitude of the stock market’s change from one time period to the next on any scale.

This means that my earlier prediction in Urbanagora of a large-drop in value is utter nonsense. The laws of Physics dictate that it is impossible to predict the size of either a fall or a rise in the market, period.

Side note–everyone always talks about what a great long-term investment the Stock Market is. One of the things I found during my search is the actual, inflation-adjusted return on long-term investment over the course of the market. Can anyone guess what it is?

Now, I want to get to the last point in this article–the relationship of these systems to the Fermi Paradox. In order to do this, I need to start with Forest Fires.

Physicists found that, in spite of the uncountable factors in the spread of an individual forest fire, they were easy to model. They made a grid of squares and began having trees grow in them over a period of time. Every so often, a match would be dropped on a tree and the rules of the game said that the fire could only spread to an adjacent square.

The size of the area that burned in a given fire ended up being a power-law relationship, just as happens in real-life. They also found an interesting corrolary, however. If someone or something had a tendency to put out the fires and the number of trees available to burn increased greatly, the entire line moved upward on the graph. In other words, if you put out small fires (and perserve a lot of the trees), when you do get a fire, it has a tendency to burn a lot larger area than if you didn’t. This was demonstrated in the devestating Yellowstone fires a couple decades ago, as well as the brush fires currently burning in the LA Basin and in Florida where housing developments have precluded the small fires that used to remove brush and trees.

So, the impatient of you who are still awake are asking, “What the hell does all this have to do with Alien Civilizations?”

Here’s the deal: Let’s assume that one cannot go faster than light, as Fermi did years ago and that an alien civilization has a finite lifetime. Let’s also assume that there is a maximum distance in light-years to the nearest habitable planet that is practical for a civilization to colonize. (This is an analogue of the distance between trees exhibited in the forest-fire model.) Therefore, the size to which a civilization grows before dying out becomes a power-law distribution. As one looks out over the galaxy in the electromagnetic spectrum at any given time, one sees silence for a large part of the time, just as a park ranger in a fire tower usually sees no smoke over his forest.

From time to time, a civilization will arise and colonize a portion of the galaxy, but the area involved will not be very large (for a vast majority of the cases), so it would be unlikely to leave artifacts in our solar system, for example, just as one usually doesn’t see burned trees along the sides of roads as you drive through Colorado.

The discovery of a red-dwarf with a planet in its habitable zone adds an interesting note to this analogy, however. If you remember, during my article on Gliese 581c, I noted that the period of time that the planet would be within the habitable zone would be much larger than that of a solar-type sun.

With our Sun, our civilization appeared at about the 80% mark of habitability as far as time goes. Yellow stars come and go at a swift rate in the galaxy. However, red dwarfs are stable in the long-term. This means that as time goes on, more and more of them come into being, and continue providing a stable home base for a colony of a civilization for a long time.

This is another analogy to the forest fires becoming larger with additional trees being added to the forest.

Therefore, my solution to the Fermi Paradox is as follows:

Aliens have existed and may currently exist, but their extent of colonized worlds follow a power-law distribution. We, as observers, have a privileged postion within the history of the galaxy because the number of red-dwarf stars has not yet reached a critical value which would push the power-law line upward and encourage large, easily visible galactic empires.

Anyone have any ideas of testable observations that could disprove this hypothesis?

Tom