Occupy Math will start by reassuring anyone who needs it that the point of today’s post is that social media and an atomic bomb share a fundamental mathematical property: positive feedback. There is no actual danger of nuclear radiation from social media beyond the small chance it may someday start a war though misuse. The topic of today’s edition of Occupy Math is positive feedback loops which drive everything from annoying squeals when the person with the microphone walks too close to the loudspeaker to the uncontrolled fission reactions that destroyed two Japanese cities at the end of the second world war. The phenomenon of positive feedback is also relevant for the bubbles that form on social media and the success of fake news, a topic of great currency.
Positive feedback is a way of turning a relatively small input into an explosion.
To be quite clear about the topic of today’s post, the type of positive feedback that Occupy Math is talking about is not the motivational sort. This post is about systems that drive themselves out of control or to extreme states. The fundamental principles of positive feedback are simple:
- First, you must have a system where output is proportional to input,
- Second, you must feed (part of) the output into the input.
Not a lot of moving parts, are there? This means this type of system is not too hard to identify.
Consider the microphone-squeal. In this situation a person is using a microphone hooked up to an amplifier that projects his voice. The input is the microphone, the output is from big speakers somewhere. When the person walks too close to one of the speakers, the sound coming out of speakers reaches the microphone and you get a horrible sound as the system drives its input with its output. An idealized, mathematically perfect, positive feedback system acts like this:
This sort of idealized situation isn’t what happens in the real
world. A feedback squeal is constrained by the fact the amplifier has
a maximum output annoying, but not actually a lethal sonic weapon.
Constrained positive feedback looks like this:
What we don’t see, in this abstract example, is how high the limiting value on the output of the system is. Let’s look at the example of an atomic bomb. Here the input to the system are low-speed neutrons. When one of these is absorbed by an unstable atom, the atom breaks up. This releases energy and (here’s the key point) more than one neutron. The result of bringing together enough of the right kind of unstable atoms is a runaway positive feedback loop where neutrons beget neutrons. There is a constraint — you run out of unstable atoms. In fact, you run out of unstable atoms quite quickly. An atomic bomb is a constrained positive feedback system — the place where the signal (energy) levels out is just extremely large.
What on earth does this have to do with social media? In social media, ideas can act like neutrons — but there are lots of different ideas that should interfere with one another and so keep the system from going into explosive positive feedback — except that we have seen, recently, that this is not what happens. The incredible success of fake news and the complete acceptance of obvious falsehoods during the recent American election were driven by a type of positive feedback.
How can a positive feedback system form in a diverse marketplace of ideas?
The answer is: by exterminating the diversity with confirmation bias and news-source filters. Confirmation bias is the tendency to look for news and information that confirms your own beliefs. To put this in terms of a feedback model, this means that the signal from sources you don’t agree with or don’t like has less power as an input to your thinking and beliefs than things you agree with. Making this much worse, Facebook, Google, and other on-line news sources permit you to intentionally filter your news or, worse, automatically amplify your confirmation bias by statistically modeling what you like and showing you additional information of that kind.
Confirmation bias is as old as humanity and news filtering isn’t completely new — which means that there had to be some sort of co-conspirator in the recent orgy of disinformation. A good candidate for this is fake news. Some fake news is motivated by profit. There is some evidence that fake news may be action taken by foreign governments intended to disrupt the American election. To be clear, fake news is different from satire. Occupy Math is not advocating destruction of fine cultural institutions like The Onion. The role of fake news in the recent election suggests that an understanding of the simple mathematical concept of a positive feedback loop has become an invaluable tool, not just for those interested in national security, but for every citizen in a working democracy.
A New York Times editorial discussing the issues of fake news, fact checking, and their impact on our society quotes the inestimable mathematician and philosopher William Kingdon Clifford: Ambivalence about objective evidence is an attitude corrosive of democracy. This phrase is a perfect description of the 2016 election. Clifford speaks sternly about the absolute obligation of a citizen in a democratic society to understand and research the truth behind what they believe and repeat to others. The entirety of Clifford’s essay, The Ethics of Belief, is linked here. It is worth noting that Clifford identified this danger to democracy more than a century ago.
Positive feedback loops are relatively simple mathematical models. Their use as weapons of information war is not even that new — spreading rumors that cause panic is an idea that is centuries old. Social media and super-fast communications act to weaponize positive feedback of information, making it potentially deadly. This leads to some disturbing issues.
Should manipulating a country’s social media systems to change the outcome of an election be considered an act of war?
Not yet, but the potential for steering a nation’s social media to manipulate its behavior does represent a vulnerability that should be addressed. At a minimum, there is a pressing need to teach skepticism, critical thinking, and research skills in high school or even earlier — and to continue teaching it throughout the life of any citizen. At a recent conference, Occupy Math was utterly appalled at the number of colleagues — professors and world class researchers who were willing to believe things without checking them.
What would happen if we got better at listening to one another?
A hypothesis that Occupy Math has seen from many sources — and with which he agrees — is that the 2016 election could be seen as an incredible failure of our ability to listen to one another. To put this back into the context of feedback loops, listening to one another permits different types of ideas to interact and constrain one another. If we simplify the situation to the point where mathematics can deal with it we get Lotka-Volterra equations. If you’re a math geek, follow the link; otherwise, here is what the output of the feedback might look like for two competing types of ideas, shown in green and blue. The vertical scale shows the degree of acceptance of each idea as they interact and evolve.
The big difference we get when we listen is that we don’t get stuck.
Occupy Math is a fantasy game referee. Several years ago he had conversation with his older son about the different ways civilization could end, as the opening scene for a post-apocalypse game. That conversation was the first time Occupy Math heard the term media bubble. Occupy Math’s son proposed the idea that a media bubble could end civilization. The scenario is that people get so bad at understanding reality, because they only hear one point of view, that civilization collapses because pressing crises are ignored. At the time, Occupy Math was skeptical. No more: we could seriously damage our civilization by ignoring climate change, poverty, or threats posed by emerging diseases. These are all examples of problems that are currently being actively ignored in many quarters because of indifference and ignorance aided by media bubbles. It is key to understand that positive feedback loops are the glue that hold media bubbles together.
People used to take arsenic to lose weight — it worked, but there were side effects. Some time ago morphine and heroin were used as (highly effective) children’s sedatives. With a lot of evil help from tobacco companies, it took way too long to realize that cigarettes were really bad for you — Occupy Math’s father died from complications related to smoking three months before retiring to his beloved childhood home in Inverness, California. These are several examples of societal practices, once main-stream, that we now consider insane. Keeping this evolution of our collective thinking in mind, consider the following thought on social media.
There is quite a bit of evidence that social media are addictive. Abuse of social media is implicated in depression. Social media may well be the cigarettes of the 21st century. Occupy Math enjoys his time blogging and participating in Facebook. He tries to maintain contacts across the social spectrum — aided by many former students with a diverse set of beliefs. It seems that all of us who use social media should help dampen the dangerous feedback by listening — especially to viewpoints with which we disagree. It might even reduce the toxicity of social media. Atomic materials can make bombs or medical isotopes to track and cure diseases. Social media also has upside potential and downside potential.
Each of us must find our own ways out of any media bubbles we are trapped in, but other people are a primary resource in this endeavor. Occupy Math hopes this week’s post is a secondary resource in helping to understand that there is a problem and to illuminate a few exits. If you have thoughts on these issues, do not be shy: tweet or comment!
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics