The Math of Free Speech

(Be careful what you wish for...)

I am not making this up.

The San Diego County Board of Supervisors wants to control speech. In a recent actual resolution we find this proclamation, targeting those (who else?) who do not agree with them:

“NOW, THEREFORE, IT IS HEREBY RESOLVED that it is the sense of the Board of Supervisors that health misinformation is declared a public health crisis and the County of San Diego should commit to combating health misinformation and curb the spread of falsehoods that threaten the health and safety of our residents.”

So, let’s consider this carefully through the lens of our position that, in order to manage something, you must be able to measure it. Let’s appeal to our reliable font of rationality, mathematics, to better understand.

I admit that free speech is not absolute. The classic example is that you are not free to yell “Fire!!” in a crowded theater when there is none. The implication is that you can cry “Fire!!” any time you wish if you are alone on a raft in the middle of the ocean. To examine this idea, here is a graphic of part of the real number line (the entire line stretches from negative infinity on the left to positive infinity on the right, covering pretty much everything).

Notice this concept allows for an infinite number of points. No matter how dense and crowded the line becomes there is always a tiny space between any two points where another number, apart from its neighbors on either side by an ever-smaller distance, may be placed. This is important. For lots of fun with number lines go to this link.

By analogy, think of the continuum of permissible speech as being the real number line. Our two examples of when it is permissible to yell “Fire!!” or not might be thought of as existing at the extreme ends with “No!” on the negative end. 

What about alternatives in the middle? Can you cry “Fire!!” in a theater with just two people in it? How about on a raft alone but with another person on a different raft ten feet from you? Sound silly? Hang in there.

Now let’s enrich the analogy by broadening the scope from speech to ideas. What one says is a fraction of what one thinks. Why? Because, if your spouse is lucky, you do not say everything you think. So, if we include thoughts as points on the real number line, the number of points increases. Society’s question: Is this something we want more of or less of?

Suppose we imagine a society located on water. Sound nuts? (Sometimes it can be - see hilarious example at this link.) Just go with me for a minute. People or creatures who live on or in the ocean are connected by water, a common resource all have an interest in protecting. One could claim that land-based, air breathing, creatures are similarly connected since there are minute particles of water in the air we breathe. As those particles circulate through, among other things, people’s lungs, they collect various things. Some of these are beneficial (there is oxygen in all water). Some of these are harmful pathogens. Everyone agrees the latter is a bad thing (it is also in the minority or we would all be dead). Our question: Can this be prevented? More importantly, can it be prevented by passing laws? Most important, what are the consequences of trying? A huge part of the Societal Dilemma is assessing the costs and benefits of granting or restricting freedom to particular segments of the population to perform various acts.

The County of San Diego wants to “…commit to combating health misinformation and curb the spread of falsehoods that threaten the health and safety of our residents.” OK, how do we do that? First, we have to define what “health misinformation” is precisely. It is, presumably the opposite of health information. Second, we need to define a “falsehood.” Once we know EXACTLY what health information is, and for every human soul on the planet, then we need to determine when and under what conditions it is altered, wrong, misguided, mistaken, poorly contextualized, fabricated, twisted, otherwise untrue or fake, making it misinformation. Then we need to agree on who gets to decide those things, what penalties are to be imposed for spreading misinformation and by whom violations are to be enforced. Since we have defunded the police who once enforced laws against physical violence, the new arbiters of right and wrong must be – you guessed it – the Thought Police. This is because on the real number line the things you think are very close to the things you say. So enforcing one, as a practical matter, means enforcing the other.

Let’s put a positive spin on this story. Like droplets of water, information travels through the air. Some of it carries unpleasant, ill-conceived, poorly reasoned, rude, useless or harmless information or misinformation (much of it having to do with the Kardashians). Like air-borne pathogens, it is in the minority. Far more of it is beneficial.

The concept of a society based on freedom of speech involves the recognition that the free travel of information is, on balance, better than the alternative. Whatever it is you know at this moment, it is a good thing to be able to learn constantly. There is always room for another snippet of information squeezed in between two closely related but still different other ideas (some would call this “diversity”). So, we start with some arbitrary number of ideas. Let’s populate part of the real number line with, say, ten ideas.

Time passes. Through the free exchange of information a new generation of ideas emerge, say, twice as many, fitting into the sequence tightly in between the others…

…and so forth to the next stage. (It is hard to see but there is no overlap of the points below if they were all on one line.) A few of the tiny little green dots below might be trigger words for the hyper-sensitive but some might be a cure for Cancer or even COVID.

Suppose you are afraid to speak out loud what you are thinking?

This, like many other things, is an optimization problem. Do we achieve the best outcome for the most people by allowing freedom of thought and speech even if we know some of that speech will be wrong, bad form, impolite, hurtful or politically incorrect? Are we willing to restrict our knowledge by making the insertion of a new concept on the real number line of thought illegal? Do we want a government that claims to know how to do that by “…combating health misinformation and curb[ing] the spread of falsehoods that threaten...” If we do, we need to be ready for a government to decide what you are reading at this moment is bad for you and I should be jailed, shot or disappeared for writing it. When that happens you need to be very careful about what you think, say or write.

I do not want my lungs invaded by harmful droplets. Nor do I want my mind invaded by something worse or shielded from something beneficial. Even less do I want all of my fellow citizens to be restricted in what they say or think. That is far more dangerous than the flu.

No good comes of a government allowed to yell “COVID!!” in a crowded world.

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