Copyright © Karl Dahlke, 2023
Put a marble in a spherical bowl, at the bottom in the center, and it is in stable equilibrium. If the wind blows it out of position just a hair, or if you tap it, it rolls back to the center. Oh it might wobble back and forth for a bit, but it comes to rest at the center. This is a stable equilibrium.
Turn the bowl upside down and balance a marble at the top. This is an unstable equilibrium. In a perfect world, it stays there forever, but the slightest breeze pushes it off center, then gravity pulls it more off center, and then it rolls off the bowl and onto the table.
These are examples of negative and positive feedback loops, respectively. Positive doesn't mean good and negative doesn't mean bad. Positive and negative describe the forces that act on the object, relative to its position. Consider again the marble inside the bowl. If it moves to the right, gravity pulls it back to the left, downhill, back to where it started. This is called a restoring force, and it establishes a negative feedback loop. The force of gravity opposes the marbles motion, and brings it back to start. Now consider the marble balanced atop the upside down bowl. If it moves to the right, gravity makes it move farther to the right. It induces more motion in the same direction. This is a positive feedback loop.
Positive feedback loops are usually bad. Bad in engineering, bad in our society. We'll see why below.
Here's a positive feedback loop we have all experienced. A public address system, or any microphone and speaker forming an amplifier. What happens if you hold the microphone too close to the speaker? You've done it, what happens? It makes a terrible high squeal, as loud as the speaker can generate. You quickly put your hand over the microphone to stop it, or shut it off, or pull the microphone away from the speaker, cause it's awful.
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Let's look at our amplifier example. The microphone is a given distance from the speaker, say 11 feet. If the room is dead silent, nothing happens.This is an unstable equilibrium, like the marble balanced atop the bowl. But say there is a noise, even the slightest whisper. Sound is air pushing back and forth in a pressure wave, vibrations of air, from 20 times a second, the lowest note we can hear, to 20 thousand times a second, the highest note we can hear. A slight breath, maybe the wingbeat of a fly across the room, a sound so quiet we can't even hear it, causes the air to press against the microphone membrane. The membrane moves inward and creates an electrical signal. The electrical signal is amplified by the electronics, that's why it's called an amplifier, and in a faithful representation of the sound, the speaker moves inward as well. The speaker moves inward more, because it is making the sound louder, but it moves inward in response to the microphone membrane moving inward. There's a small delay, the electricity going through the wires and the transistors, and then the speaker responding to the signal, i.e. the paper cone moving inward. It's a fraction of a millisecond, and we can calculate it. Now, the speaker moving inward pulls the air back. A suck so to speak. This low pressure wave moves across the room at the speed of sound, about 760 miles per hour. A fraction of a second later the suck reaches the microphone and pulls the membrane out. This creates an electrical signal, which goes through the amplifier, which pushes the speaker out in obedient response. The cone pushes out and creates a high pressure wave, which moves across the room, which pushes the microphone membrane in. This generates an in signal, which runs through the amplifier, which causes the speaker cone to pull in. This creates a suck, which travels across the room and pulls the microphone membrane out. Round and round and round it goes, getting louder and louder, because that's what an amplifier does. It's a positive feedback loop because any sound will get louder, and louder, and louder, using the energy of the amplifier. Pretty soon it is making sound out of thin air, out of nothing at all. The original source of the sound is long forgotten.
There is a select frequency, a perfect note. It depends on the characteristics of the microphone, and amplifier, and speaker, but mostly, the distance between the speaker and the microphone. The time it takes for an in-push on the microphone membrane to go round and pull the speaker cone in and create a suck that goes across the room and pulls the microphone membrane out. That time is some fraction of a second. Do some math, what number is plausible? We already said the speed of sound is 1100 feet per second. We have them separated by 11 feet, so 0.01 seconds. One one-hundredth of a second. That's half the cycle, a full in and out vibration would be 2 hundredths of a second. The sound is 50 hertz, or 50 times a second. That's a low note, a hum, but well within the range of human hearing.
You may have experienced positive feedback when the speaker and microphone were just a foot apart, 500 hertz, a high note that is loud and piercing.
High feedback squeals happen in concerts, even though speaker and microphone are dozens of meters apart, because of high harmonics. The speaker might go in out in out in out in out in, and the first in reaches the microphone, and pulls its membrane out just in time to go round and push the speaker out. So it's a harmonic of the fundamental frequency, determined by the distance between microphone and speaker. The harmonic that is most efficiently amplified by the system is the note you will hear the loudest.
Engineers always want negative feedback loops. If a rocket goes slightly off course, the navigational control system puts it back on course, like the marble rolling back to the bottom of the bowl. During launch, or a critical maneuver, the engines are making adjustments dozens of times a second, tilting this way and that, to make sure the rocket stays on coarse. They compensate for any deviations.
Consider fiber optic cables, the backbone of our internet. These cables are designed to keep light on course, even if it deviates from its path, which it certainly will, in just a few centimeters.
Take a flexible tube, like the hose from a vacuum cleaner, hold one end up to your eye, and hold the tube straight out. If you can hold it perfectly straight, you'll see a small picture of the world in front of you. It might be hard to hold it straight - if the tube is longer than your arms. Let it hang straight down instead, and look at the floor. Now bend it slightly, a gentle curve anywhere along the tube. Everything goes dark. Why? Because light travels in straight lines. If there is a curve in the tube, the light crashes into the wall of the tube and does not make it to your eye. Your tube has to be perfectly straight, or no dice. How then can we send light through a fiber optic cable, as thin as a hair, and 100 miles long? Does it have to be precision straight, for 100 miles, without a curve or deviation the size of a gnat? If that's how optical fibers worked, we couldn't send a signal more than 6 inches. But that's not how they work.
Light travels in straight lines, but there are exceptions. Light bends when it goes from air to glass, or glass to water, or heavy glass to lighter glass, at an angle. This was described in the chapter on optics. This is how most telescopes work, and microscopes, and your eye glasses. Take off your glasses and look; it's not a flat pane of glass like a window. It's curved, thicker in some places, thinner in others. It causes the light in front of you to bend in certain ways before it reaches your eyes. This distortion is just what you need to correct your vision. Fiber optic cables rely on refraction as well.
The center of a fiber optic cable is ultra-clear glass. This carries the light signal, sometimes for miles. Around this core is another layer of glass, like a sheath, but it is lighter, so to speak. More accurately, it has a lower refractive index. When light strays from the core into this cladding, the change in glass forces the light back into the core. It "bends" the light back. This happens all along the cable. The light stays in the core, even as the cable curves around obstacles and bends (gently) around corners. Finally, a layer of insulation covers the outer glass, to protect it from the weather, or light that might filter in from outside.
In summary, a fiber optic cable is designed to provide negative feedback all along its length. Whenever light strays from the core, an outer layer of glass pushes it back.
There are many positive feedback loops in society, and they are almost all bad! Perhaps the most visible is a run on the bank. A few people are afraid the bank will fail, and they run to get their money before that happens. Others see this, and after the first group gets their money, the bank will have even less, so they get in line to get their money, too. Others see this, and the cycle continues, and amplifies. Of course the bank doesn't have assets in-house for all those people; it has invested some of that money, so that it can make profit, and pay interest on the checking and savings accounts. That's how a bank works. Eventually the bank does run out of money, and it's a crisis. We saw this in the movie It's a Wonderful Life, and we read about it in The Jungle. Read again the words of Upton Sinclair.
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Had something gone wrong with the bank? Nobody was sure, but they thought so. Couldnât she get her money? There was no telling; the people were afraid not, and they were all trying to get it. It was too early yet to tell anythingâthe bank would not open for nearly three hours. So in a frenzy of despair Marija began to claw her way toward the doors of this building, through a throng of men, women, and children, all as excited as herself. It was a scene of wild confusion, women shrieking and wringing their hands and fainting, and men fighting and trampling down everything in their way. In the midst of the mĂȘlĂ©e Marija recollected that she did not have her bankbook, and could not get her money anyway, so she fought her way out and started on a run for home. This was fortunate for her, for a few minutes later the police reserves arrived. In half an hour Marija was back, Teta Elzbieta with her, both of them breathless with running and sick with fear. The crowd was now formed in a line, extending for several blocks, with half a hundred policemen keeping guard, and so there was nothing for them to do but to take their places at the end of it. At nine oâclock the bank opened and began to pay the waiting throng; but then, what good did that do Marija, who saw three thousand people before herâenough to take out the last penny of a dozen banks? To make matters worse a drizzling rain came up, and soaked them to the skin; yet all the morning they stood there, creeping slowly toward the goalâall the afternoon they stood there, heartsick, seeing that the hour of closing was coming, and that they were going to be left out. Marija made up her mind that, come what might, she would stay there and keep her place; but as nearly all did the same, all through the long, cold night, she got very little closer to the bank for that. Toward evening Jurgis came; he had heard the story from the children, and he brought some food and dry wraps, which made it a little easier. The next morning, before daybreak, came a bigger crowd than ever, and more policemen from downtown. Marija held on like grim death, and toward afternoon she got into the bank and got her moneyâall in big silver dollars, a handkerchief full. When she had once got her hands on them her fear vanished, and she wanted to put them back again; but the man at the window was savage, and said that the bank would receive no more deposits from those who had taken part in the run. So Marija was forced to take her dollars home with her, watching to right and left, expecting every instant that some one would try to rob her; and when she got home she was not much better off. Until she could find another bank there was nothing to do but sew them up in her clothes, and so Marija went about for a week or more, loaded down with bullion, and afraid to cross the street in front of the house, because Jurgis told her she would sink out of sight in the mud. Weighted this way she made her way to the yards, again in fear, this time to see if she had lost her place; but fortunately about ten per cent of the working people of Packingtown had been depositors in that bank, and it was not convenient to discharge that many at once. The cause of the panic had been the attempt of a policeman to arrest a drunken man in a saloon next door, which had drawn a crowd at the hour the people were on their way to work, and so started the ârunâ. |
Runs were all too common during the Depression. To combat this, FDR and Congress enacted the FDIC, Federal Deposit Insurance Corporation, to guarantee funds in the bank. Banks might not have cash on hand for you at the moment, but you would not lose your money, the government has guaranteed it. If need be, a Brinks truck from the federal reserve would show up tomorrow with your money. This removes the panic, the force that drives the run on the bank. It turns off the amplifier. Since that law, we have had recessions, and the crash of 2008, but no more runs. The FDIC was a brilliant and far-sighted piece of legislation. Anything that damps down a positive feedback loop is probably a good idea.
In the 70's and 80's,credit unions rose in popularity. In response, the government enacted the FSLIC, Federal Savings and Loan Insurance Corporation, to guarantee those funds. This has the same calming effect, and prevents a run on the credit union. Once again the government is damping down positive feedback loops, one of its most important, though underappreciated, functions.
After Adam Smith published The Wealth of Nations in 1776, people discovered that he was right _ capitalism does indeed create wealth. However, it does not distribute wealth evenly or fairly. In fact, capitalism is rife with positive feedback loops that make the rich richer, while the masses descend into economic slavery. Eventually the rich control the government, even if it claims to be a democracy. They write the laws to their advantage, and enforce those laws preferentially upon the poor. To be fair, other economic systems also have these tragic flaws.
Once again, the government must step in and quell these feedback loops. There is no magic bullet here _ instead, the government should develop a wide array of programs to serve the needs of the public, funded by a progressive tax code. The earned income tax credit, for example, has been shown to assist the working class, and many countries around the world have adopted it, in one form or another. Comprehensive health care, first suggested by Teddy Roosevelt, is such an obvious win for society, it's hard to believe some countries still haven't implemented it. Public education, food assistance, job training, inheritance taxes on extreme wealth, low income housing, and grants for first-time home buyers, all have a role to play. One program isn't going to do the trick, but a suite of laws and regulations, and gentle interventions, can quiet the feedback loops that ran rampant in 19th century England and America. If people get too rich, there are forces that address this, and if people get too poor, there are safety nets. This is how we maintain a stable middle class across time.
The most pernicious feedback loops are driven by, and support, racism. In my country, the most obvious example, like the elephant in the room, is, âBlack people have criminal tendencies.â As long as people believe that, they create forces that make it so.
A cop pulls a black person over for no reason, except that he looks "suspicious". Then he goes fishing, to justify the traffic stop. Perhaps the driver doesn't have a license, or registration, or insurance, or maybe there's an open bottle of alcohol in the trunk. Meantime, a white driver speeds by, sporting all these violations, but he isn't stopped. If the cop can't find an excuse for the pullover, he manufactures a charge out of thin air. Don't tell me that cops don't do this; I've seen it happen, in my own family. The white prosecutor, judge, and jury all believe he is guilty, and thus, by definition, he is! Our black driver is now a criminal, and white people everywhere can cluck their tongues and say, âSee, I told you so. He deserves whatever punishment he receives. Actions have consequences.â
The next day the same thing happens to another black driver, or maybe even the same driver, and the cycle repeats, like an amplifier turning a soft whisper of racism into the loud screech of systemic oppression.
The mechanisms that derive from, and feed, racism, are too complex for this book. I recommend the documentary 13th, or Born a Crime, by Trevor Noah.
There are some changes that would dampen these feedback loops, but nobody is taking them seriously. Here are a few examples.
Districts receive no revenue from tickets, court fines, bonds, probation fees, etc _ thence there is no economic incentive to turn people into criminals. Taking money out of the equation is half the battle. Americans love capitalism, they almost worship it, but they don't understand it. When districts realize profit from tickets and arrests, what do you think the invisible hand is going to do?
If prisoners are employed, they must be paid minimum wage _ thence there is no economic incentive to create a pool of cheap prison labor.
Every pullover is reviewed by an impartial panel, which includes minorities. This is similar to New York reviewing a close play at the plate _ but it happens with every pullover, in real time. It doesn't matter what the cop found later _ if the pullover was not caused by overtly dangerous driving, then the driver is set free, and the cop loses $300 in his next paycheck.
Driving is a right, not a privilege. A license can only be revoked for 12 points, and points are only awarded for egregious driving.
Inmates can vote, and thus have a voice. This is the case in Maine and Vermont, and those states have not descended into lawlessness.
We can't claim we live in a great country, until systemic racism is in our rear view mirror. The government has a role to play, and so do we, for ultimately, it is our Monster from the Id.
Are there any positive feedback loops that are good? There are, but they exist primarily at the individual level.
John has had a string of misfortunes, and is depressed. He has tried to escape from his quagmire for years, to no avail. Now he sits on his couch and watches tv all day, waiting for his world to implode. He doesn't try any more, thus nothing will ever get better. This is a positive feedback loop that pushes him further into failure and despair. However, one day he reads a self-help book, or adopts a new religion, or starts to meditate, or anything that might convince him he will succeed. He goes out and looks for a job, or starts a business, or takes some online courses. If he's lucky, he will see some success before the placebo effect wears off. That starts a positive feedback loop that benefits him, and harms no one else. âI knew I could do it.â he might say. He works harder, and gets a modest raise, or a small promotion. This reaffirms his self-worth, and the upward cycle continues.
If you aren't a student of engineering, you might call this a self-fulfilling prophesy. Fair enough - for that's what it is.
Can an entire nation enjoy a similar self-fulfilling prophesy? Perhaps, but it doesn't happen by accident. It requires a strong leader, to say, âWe can do itâ, as when JFK said we could go to the moon. And it requires a populace who trusts their leader, and says, âYes we can.â
Can we, as a nation, dampen the feedback loops that concentrate wealth in the hands of the few, and oppress and marginalize our minorities? Yes we can. That is a task worthy of our efforts _ far more important than going to the moon.