Exponential Function and Negative Feedback Loops; Bad News!
By Greg Chadwick
The greatest mathematical phenomena affecting mankind’s very existence is unknown to the majority of Americans; that of feedback loops, both positive and negative.
Dr. Albert Bartlett states that our greatest shortcoming as a species is our inability to understand the exponential function. However, it might be that we choose not to understand the exponential function simply because it clearly demonstrates that our economic system is doomed to fail; sooner, rather than later.
As a result, we choose not to factor the function into our calculations. Essentially our position has been, “Why should we stop the party when there is still cold beer on tap?” After all, we’re here for a good time, not for a long time.
Tolkien wrote…. “It does not do to leave a dragon out of your calculations, if you live near him.” However, we leave the mathematical dragons out of our calculations so that we can blissfully continue the party until the cold beer suddenly runs out.
The frightening truth about Professor Bartlett’s explanation is that everything appears fine, right up to the last doubling; then all hell breaks loose. The party ends suddenly.
Those who deal in micro solutions and sound bites may be encouraged that our rate of population growth is slowing; however, it should be noted that our present economic system can’t survive unless the growth continues. It is a classic Catch-22, at this juncture in time, we’re damned if we grow, and we’re damned if we don’t.
As the exponential function has begun to play out, feedback loops have begun to kick-in. These feedback loops work on the upside as well as the down side. In theory, so long as our population is small in relative size to our resource base, feedback loops should not pose a major problem.
However, that is not always the case. During the Great Depression the physical system was more than ready to go, there were lots of resources and not many people using them. However, human greed and stupidity fueled the negative feedback loops that produced and prolonged that historical nightmare.
The Great Depression was the most shocking demonstration of the unrelenting stubbornness of negative feedback loops that the world has ever witnessed. While volumes have been written regarding the cause and length of the Great Depression, let there be no mistake, that terrible event endured due to our inability to break the natural progression of a negative feedback loop!
That being said, man has almost no control over negative feedback loops that are caused by bumping into shortages and the associated cost increases that are due to diminishing resources. Feedback loops accelerate the process of depletion and the situation deteriorates quickly. This is the position we are in today. However, unlike the exponential function, we do get some warnings in the form of shortages and price increases before we hit the proverbial wall.
Now that population and economic growth are slowing, our debt and interest based economic system is failing. As the growth continues to slow, the system will deteriorate at an increasing pace. This is the point where negative feedback loops pick up great momentum.
To better picture this phenomena, let’s look at how towns grow. For an extended period of time the growth is slow and gradual and then it explodes. I have personally seen this happen in two communities that I have lived in. In both instances, sleepy rural communities that had stable populations for decades began to experience growth.
This happened as people fled the big city for an area with less population density and a slower pace of life. At first, the population increase is measured, but over time it picks up momentum and seemingly overnight the residents wake up to find that their lovely little community is now four or five times its original size.
So how does this happen? The short answer is feedback loops. It seems harmless enough when a small subdivision comes to town. Many people like it initially because there is more activity downtown, there are more people walking formerly deserted streets, and business picks up for the local merchants. Tax revenues are up and life is good; temporarily.
But what does it take to support these newcomers? They want the same services and amenities of the big city, but in a small town setting. New schools need to be built, more teachers hired, more housing, larger grocery stores, hardware stores, libraries, roads, sewers, water lines, electrical lines and substations, plus all of the people to build, operate, and manage this new infrastructure. This expanding infrastructure fuels more growth as the positive feedback loop intensifies.
Unfortunately, the positive feedback loops that allowed a seemingly insignificant population to explode overnight (will by their very makeup) turn negative and go into overdrive in the opposite direction. In simplistic terms, anything that can’t go on forever doesn’t.
Now the process reverses. Unemployment reduces spending, local merchants lay people off because of the reduced spending, and now this new unemployment further reduces spending. The reduced spending results in lower tax collections, forcing the city to reduce payrolls. This further reduces consumer spending leading to more unemployment.
Large numbers of homes are put up for sale as the unemployed either fail in their mortgages or are forced to relocate. This balloons the housing inventory and stops nearly all new construction. Those involved in construction now find themselves in the eye of the negative feedback loop. I could go on detailing the chain reaction; however, the picture is already clear.
The point is that once the ball gets rolling, momentum quickly makes it unstoppable. Like it or not, we become spectators when we allow things to reach this threshold. Once again, feedback loops work quickly, everything seems fine until we are on the brink. Consider that throwing Trillions of dollars at the problem has had no noticeable effect.
We had several clear warnings of our current plight in the seventies. Had we done something then, we probably could have made orderly changes and maintained a good quality of life without seriously depleting our resource base. But since we failed to act, feedback loops will now run their course.
The good news is that we still have our lives to lead and choices to make. We can make the best of our circumstances and enjoy ourselves, or we can complain and play the role of victim. We still have that choice; use it wisely.

If you haven’t already seen the videos of Dr. Albert Bartlett discussing exponential growth, I highly recommend them. Here is the link to Bartlett’s videos, there are a total of eight and they are well worth the time.
http://www.youtube.com/watch?v=F-QA2rkpBSY
To explain the enormity of Exponential Growth, let me use a shortened version of my favorite, but very simple example:
If a pond lily doubles everyday and it takes 30 days to completely cover a pond, on what day will the pond be 1/4 covered?
Answer: Day 28. Growth will be barely visible until the final few days. (On the 21st day, the lilies cover 1/512th of the pond; on the 25th day, the lilies cover 1/32nd of the pond).
Exponential growth works the same insidious manner whether it be consumption of natural resources, or population growth or debt or whatever. You go along, thinking that you (or they) have time to work things out and then the final few days of the exponential function plays out and the door slams very hard on reality. Very hard!!! -bb
You are describing the effects of positive feedback loops.
“Large numbers of homes are put up for sale as the unemployed either fail in their mortgages or are forced to relocate. This balloons the housing inventory and stops nearly all new construction. Those involved in construction now find themselves in the eye of the negative feedback loop.”
This is a positive feedback loop, i.e. the hotter it gets, the hotter it gets. Positive feedback occurs when a small change in input to a system produces a large change which reinforces the input. This creates a runaway condition. An example is an uncontrolled fire.
Negative feedback is the opposite. A small change in input to the system is canceled out by an opposing signal fed back from the output. Thus negative feedback loops are stable. An example is a thermostat which keeps the temperature constant.
That was well said.
Another example of a negative feed back loop might be Social Security. I have seen the figure of 10,000 baby boomers retiring PER DAY in the not too distant future. That is 10,000 less people paying into Social Security and 10,000 more people drawing out.
That is also 10,000 people in the prime of their earning years. I am sure that the people that are hired to replace them will be so at a reduced pay - so even less being paid in.
I remember a few months back hearing that Social Security was paying out more than it was receiving. So the exponential growth will be seen soon in red ink. No problem, just add it to the national debt.
I recently turned 62 and applied for my Social Security in advance just to stay ahead of the crowd.
Fred, The Social Security mess can be fixed rather easily. Just void the ceiling or raise it. I think that fica stops at $187k per year. Why not raise it to 3 million? Why not kick it in again when you hit 10 million?
If you want to get money into the hands of the poor, who will spend it rather than hoard it, make the first 10k fica free, and spare the small businesses all the paperwork to boot. I don’t worry about social security, I worry about all the out of control military spending, jeeze do we really need the largest two airforces in the world? The Air Force and secondly, the Navy’s air force, yada, yada, yada..
Military spending.. Now, there’s a whole new topic.. I agree.. Cost way too much.. We do not get value for our money spent, and it is not making us safe..
But, wall street, and the best government money can buy love it, so it’s “untouchable”.. Oops, forgot.. Wall Street’s media loves it also.. Patriotic, don’cha know..
wma..
Bobcat,
Thank you for your correction. You are absolutely accurate in your textbook definition of feedback loops.
Greg’s intention was to demonstrate a positive feedback loop that reverses the amplifier effect in relationship to the desired outcome. In other words, we have a positive feedback loop that is currently producing negative results when applied to a growth based economy.
It should also be stated that “Positive or Negative” in the instance of feedback loops does not mean desirable or undesirable, but merely refers to the sign of the multiplier which either increases or decreases the magnitude of the subject equasion.
When this multiplier is used to measure unemployment; “positive” is not the multiplier that we want to see.
That said, the current events are eerily similar to the occurrence that produced and prolonged the Great Depression.
Fred,
Good call. Social Security and Medicare are the world’s largest Ponzi schemes. Carlo “Charles” K. Ponzi. was a minor league player compared to our federal government.
The federal government has known for more than 40 years that these programs could not be funded long term. This knowledge is often referred to as “The dirty little secret that everyone in Washington knows.”
The dirty little secret (or covering their butts because of it) may have something to do with congress funding the construction of compounds (holding facilities, including large quantities of freeze dried foods) along both borders over the past few years, and the authorization (by G.W. Bush, in Oct. 2008) for U.S. military to be employeed as law enforcement of civilans in this country. And of course the latest, the use of drones to be used in this country for non-military survellience of our citizens. These are but a pin prick of the number of little things that are developing at this time. Little things that will become monsters if let go over time. As if we needed more monsters to go with our exponential growth society, huh. -bb
Billyb,
Interesting stuff, would you share your sources?
I saw little camera drones at a concert on Thursday night flying over the crowd taking pictures….and landing just over the tree line. They exist. If I hadn’t of seen them for myself, I wouldn’t have believed it!
“Social Security and Medicare are the world’s largest Ponzi schemes.”
With the scheme being that most of the money earmarked for it gets spent on war and corporate welfare instead.
“The federal government has known for more than 40 years that these programs could not be funded long term.”
That’s right. They knew they wouldn’t be able to keep their hands out of it. Now Republicans and Democrats alike want to do away with the Social Security benefits but not the tax to pay for it. They have other plans for that money. Should they succeed, the ripoff of working people will be complete.
Bobcat,
You are absolutely correct in you assumptions of future government actions. They will simply pull the old, “How could anyone have known? We all need to work together and cut benefits.”
The inflation that is “built-in” to our economic system created a mathematical impasse for any program that was based on a “retire now and let others pay later scenario.” That is why we have a $13 TRILLION National Debt! GEEZ!!
Had the money for Social Security been put away for safe keeping, it would be worth pennies on the dollar today. Had it been invested in REAL REDEEMABLE interest bearing securities, it would have created hyper-inflation to keep our compounding interest monetary system alive.
Those who read my book know that I predicted this enduring recession nearly two years before it occurred. I also stated that the dates for the demise our social programs would come rushing forward from a lack of funding. Don’t look now, but employment income in the U.S. has stalled for YEARS when compared to real buying power.
And to think, Carlo Ponzi was imprisoned and then deported for inventing our current system of government math.
Under the John Warner Defense Authorization Act, signed by President Bush on October 17, 2006, the law was changed to state, “The President may employ the armed forces to restore public order in any State of the United States the President determines hinders the execution of laws or deprives people of a right, privilege, immunity, or protection named in the Constitution and secured by law or opposes or obstructs the execution of the laws of the United States or impedes the course of justice under those laws.”
However, these changes were repealed in their entirety by HR 4986: National Defense Authorization Act for Fiscal Year 2008, reverting back to the original state of the Insurrection Act of 1807. Despite this repeal, President Bush attached a signing statement saying that he did not feel bound by the repeal. The original text of the Insurrection Act severely limits the power of the President to deploy troops within the United States. On October 3rd 2008 President Bush, however elected to establish a military force, made consisting of U.S. Army personnel, to quell any uprising in the upcoming presidential elections.
For troops to be deployed, a condition has to exist that, “(1) So hinders the execution of the laws of that State, and of the United States within the State, that any part or class of its people is deprived of a right, privilege, immunity, or protection named in the Constitution and secured by law, and the constituted authorities of that State are unable, fail, or refuse to protect that right, privilege, or immunity, or to give that protection; or (2) opposes or obstructs the execution of the laws of the United States or impedes the course of justice under those laws. In any situation covered by clause (1), the State shall be considered to have denied the equal protection of the laws secured by the Constitution.”
Of course, one can see the can of worms left open to such policy in practice. -bb