*We don’t readily understand our interconnectedness; social matrix algebra, which is a matrix algebra practical application, illustrates the problem.*

## Matrix Algebra

In a former post, I talked about a high school teacher who hectored me constantly. In the post, I also mentioned one of my best friends who used to academically rip my butt in that teacher’s classes.

The one section from her class that I specifically recall was matrix algebra, solving several equations simultaneously. You need to know that this was before hand-held calculators were available. I can still remember the next year, one girl in our physics class had a 4-function calculator her dad had bought her for something like $100 — about $250 dollars today. She instantly became popular.

So solving matrices back then required hand calculations, and a lot of careful attention. One small mistake, and the whole thing fell apart. Most of the matrices were ‘neat’, *i.e*., the solutions resulted in whole numbers. But during the last part of the section, the teacher assigned us homework with a 5×5 matrix — they get much harder the bigger they get — and the results came out in 17^{ths}. It took me three teeth-gritting attempts over a couple of hours to solve it. My friend told me the next day that he solved it on his first attempt.

Hmph.

## A Matrix Algebra Practical Application

At the time, all we were told was that matrix algebra was good for solving equations. With the rise of technology, it turns out that computers can solve very large, highly complex matrices without much problem. Years later in graduate school I found out that a cell in a matrix can be not only a variable, it can also be another equation, even another matrix. With that approach, matrices can be used to model highly complex systems.

For instance, one matrix algebra practical application would be to represent a food/energy matrix. You can take a survey of a pond, calculating out the numbers of plants, animals, and microbes, estimate what they each consume and produce, and then include air, sun, and temperature. The whole system can be laid out in a giant social matrix, where each cell represents a factor in the system, with variables representing how they all relate to one another. Then you can play with it. What happens if the fish population drops? Rises? An invasive species is introduced? And so on.

The concept is powerful. In fact, Wassily Leontif won the 1973 Nobel Prize in economics, largely for producing a very accurate table (*i.e*., a solved matrix) showing what each sector of the economy contributes to every other. Today, economists and mathematicians apply the Leontief input-output analysis to a broad array of problems. It’s not hard to see how you could take Leontif’s tables, and simply insert more complex expressions into each cell, to produce a highly dynamic analysis of the economy, and get some idea of how one sector affects another in real time.

## Oil Slump

For instance, I have noted that Lafayette is not an oil town but it has a thriving petroleum sector. Before the recent slump, oil accounted for about 10% of the jobs in the MSA. From what I can tell, the current oil slump cut that a couple of percentage points, to about 8%. A brief consideration would suggest that the local economy would only drop a couple of points. No big deal. If your boss said he was cutting your pay 2%, you wouldn’t like it but it would hardly affect your lifestyle.

It’s been much worse than that in Lafayette. First, the layoffs did not account for the total drop in revenues; any business with reserves is laying off as few people as possible, and tightening their belts until oil recovers. So a 2% drop in employees represents a much larger drop in revenues. Then there are non-petroleum suppliers that nevertheless cater to the oil patch: office supplies, janitorial, computing, helicopters, and boats. They were hit hard. Some of those businesses don’t have much in reserves, and they had to shutter their operations. Oil jobs provide the best-paying jobs of any major sector here, so a lot of high-end restaurants and stores also saw a drop in revenues, and they had to lay off people. I know of at least one upscale local restaurant that permanently closed early in the slump.

All of this creates a synergy. A 2% drop in the labor force turns into a very large local impact. And that’s in a town where the oil sector is not the largest industry; healthcare, retail, and manufacturing are all larger.

## University Town

People don’t grasp this interconnectedness readily. Years ago, I was in grad school in a college town. The college had 10K students, the town had 10K residents, but the locals treated the students with a fair amount of disdain. One day I was talking to a nurse who was a supporter of the college, and complaining about how badly local businesses treated the kids. I noted that without the college, the town would not be there.

“Oh, I don’t know about that,” she replied. “My husband’s a lawyer here, and almost none of his clients work on the campus.”

## Depression Spending

Our insensitivity to our interconnectedness also turned up some years ago, when a friend insisted that the New Deal did not pull the U.S. out of the Great Depression. WWII did.

I thought about that a moment, and then asked, “So let me get this straight. Moderate government spending to employ our men and women in rebuilding American infrastructure was ineffective for getting us out of the Depression, but massive deficit spending to kill our men and women in destroying European infrastructure, *that* was highly effective?”

## Marshall Plan

Similarly when the Marshall Plan was first proposed, many in Congress opposed it. The U.S. had already funded two post-war aid packages to help Europe, and neither had produced any demonstrable effect.

The Marshall Plan was a much larger financial commitment on our part than those first two packages. But that larger investment worked, although part of the reason was that a large number of our best & brightest worked on the Plan, alongside some of the best and brightest from Europe.

## Pennies from Heaven

It seems that any source of money will work. Sure, Detroit has done it with autos, New York does it with banking & finance, and Houston does it with oil. On the other hand, New Orleans does it with bars and restaurants, Hollywood does it with entertainment, North Carolina does it with tobacco, Reno does it with cathouses and gambling, and Denver’s trying to do it with pot. It’s social matrix algebra: pretty much anything that brings money into a local economy will move through the system, and grow that economy.

I have been wondering if it would even work with a kleptoplutocracy.

*Continued after this important invitation:*

collin237

This assumes that all the eigenvalues are either positive real numbers, or (as in the footnote) zero.

I doubt that this applies even approximately in most cases.