In praise of negative feedback

Operational amplifier noninverting

Feedback is a funny thing. I'm not talking about the social feedback you give to another person after an interaction (or am I?). I'm talking about the physical principle of feedback where you take the output from a process and feed parts of it back into the input of the same process.

There are two kinds of feedback: positive feedback, where you just feed parts of the output back without changing it, and negative feedback where you reverse the signal before feeding it back.

Positive feedback is often accidental and undesirable. It is the bane of sound engineers for example. When a microphone picks up the sound from amplifiers in addition to the voice of the singer, the feedback loop will end up creating the screeching noise we're all familiar with. Basically, positive feedback reinforces the signal exponentially and ends up saturating or breaking the system.

This is not to say it's totally useless and bad: there are situations where saturation is precisely what you're trying to create. In fact, digital electronics are built on positive feedback and saturation, as the binary zeroes and ones are simply the extreme saturated states of otherwise perfectly analog devices.

Take the modest flip-flop, one of the basic building blocks in digital electronics.

Flip-flop

The way this works is that each transistor's output feeds into the other's input, creating a bi-stable system, where there are two stable states and a way to flip from one to the other. In other words, a bit of memory.

If you're interested in the details, check out footnote[1]

The entire tech industry is built on positive feedback, a useful but blunt device that wipes out all subtlety and details, by design, and only remembers zeros and ones. Again, no connection to any social issues here…

Negative feedback on the other hand is a wonderful and subtle tool. By subtracting when the signal is raised, and adding when the signal is lowered, you get natural regulation and stabilization. Positive feedback destabilizes and brings a system to saturation or collapse, whereas negative feedback stabilizes.

A simple negative feedback example is this analog amplifier using an operational amplifier:

Operational amplifier noninverting

Glossing over the details, the way this works is that the output of the amplifier is fed back through Rf back to the negative input. Equilibrium is reached when the positive and negative inputs are at the same tension. Any deviation from that will cause the feedback loop to pull the system back into the equilibrium state.

At equilibrium, Vout = (1 + Rf/Rg)Vin, so it's easy to choose resistors to obtain any stable gain you want. Note that there are hidden power sources in the above amplifier: stability doesn't come for free.

Similarly, when you ride a bike, your body makes all kinds of unconscious movements that are stabilizing your position and preventing you from falling. Learning to ride a bike is largely learning how to apply negative feedback. Self-balancing machine such as a Segway or a hoverboard also work by applying negative feedback to stabilize an otherwise out of equilibrium state.

And… it's time to break the promise I made at the beginning of this post not to talk about social issues…

Capitalism. You knew we were getting there, didn't you?

Capitalism thrives on positive feedback loops and exponential, infinite growth (a thing that is even more impossible than pulling yourself by your own bootstraps). That seems to work for a very limited time, but if the physics above taught us anything, it's that there are only two possible outcomes from positive feedback loops: saturation and destruction.

Saturation could manifest as two forms of stability: one that capitalism abhors, zero growth, and one it seems to love, monopoly.

Destruction would be the catastrophic collapse of the entire system, one after which only ruins remain.

It should be very obvious by now that our modern industrialized capitalistic societies are speeding up towards the second option.

Some countries are doing better than others of course. For example, Europe's social democracies, by regulating the excesses of capitalism, exert some negative feedback and achieve some social stability as a result. The USA, on the other hand, are currently doubling down on positively reinforcing short-term profit mechanisms, and are visibly on the verge of violent collapse if not right in the middle of it.

What will come out of the rubble and ashes when all is said and done is anyone's guess, but let me mention another fundamental physics principle: all systems have a state of minimum energy, called the ground state, that they naturally tend towards under the pressure of growing entropy. To prevent a system from decaying and keep it in a higher energy state, it is necessary to bring energy into it. For human society, history shows this ground state probably looks like local fascist feudal lords keeping serfs under control and barely surviving.

So what do we do? Can we prevent the world from falling into some fascistic chaotic ground state? I don't know. What I know is that it will take all of us, vigorous negative feedback, and certainly a redesign of society towards a model that observes its own outputs and uses them to tame itself.

If advocating for regulating a system for stability sounds a little conservative, remember that conservatism really advocates for maintaining the system, not its state. Negative feedback loops make it possible to reach the state you desire and intend, and then maintain that state. Change is facilitated, not avoided: just modify the characteristics of the feedback loop.

So a strong democracy with strong counter powers? Maybe that old idea didn't suck. Protests help if they are allowed to feed back into the system, which is why modern constitutions and the Universal Declaration of Human Rights enshrine the rights to protest and to speech free of state repression. Fascist states by contrast, by severely repressing protests, by subjucating the press and by concentrating powers, make an attempt at removing that feedback. Don't let them, don't comply.

Negative feedback is necessary and healthy.

Footnotes

[1] If you close the first switch, you're setting the base of Q1 to ground. A transistor will let current through if the base voltage is high enough. In this case, it won't, so A will take 5V from the power rail through R1. That will propagate to the base of Q2, which is now high enough that it will let current through, which will bring B down to ground, again setting the base of Q1 to ground. The interesting thing though is that you can now release the switch and the loop I just described is still maintained. In other words, you've set the system in the state where A is 5V and B is 0V, and that state will persist after you've released the switch.

Now if you close the second switch, you're setting the base of Q2 to ground, so it becomes blocking and B takes 5V through R2, which propagates to the base of Q1, which is thus letting current through, which brings A down to 0, which propagates to the base of Q2, reinforcing that it's grounded. The second switch can then be released and the A 0V and B 5V states persists through the mutual feedback loop.

The switches are the inputs and the circuit will keep the data that was entered through them long after they've been released.