Let us have some fun. I desperately need some after being two months into a strict lockdown, and counting.
Let us see if we can pair an exact science – where the indisputable is fact – with free speech – where the disputable is often presented as fact. A story of lies meeting linear algebra, and how degrees of freedom define our ability to discover truths.
Free speech has been in the news lately because of Elon Musk’s pending purchase of Twitter. Twitter has come to personify the good, the bad, and the ugly of free speech. But those cut across all social media platforms as they all provide a ready and supportive audience for whatever anyone wants to say (or shout).
Math is my passion and my training. The discipline definitely falls in the category of exact sciences. We can all recall episodes in primary school when we were convinced – and tried to convince our math teacher – that 3 plus 3 made 7. For the record, 3 plus 3 makes 6 and there is no room for argument. If you think otherwise, I can point you to a few institutions where you will find likeminded people.
It is a fact that 3 plus 3 makes 6. You cannot argue with facts, even when they are inconvenient. I found that out early in Grade one. That got me on the path I took and the passion I developed for math, the language of the sciences. When venturing into the quicksand of free speech, math is a good guardrail to hold on to.
How do we pair free speech with math? Why would we even want to do that? Remember, I want to have some fun. Let me tackle the why question first. It turns out that linear algebra can give us some insight into the dangers of free speech. In fact, I will show you that the truth can become elusive when we let free speech take over. Let me first say a few words about free speech.
What is free speech? Basically, it is your right to say whatever you want, whether it is true or not. Social media has given all of us a bullhorn and – as you might have noticed – an audience that will readily agree with whatever it is that you say. If you shout out that the world is flat, you will find plenty of likeminded believers to join in. Just to keep the record straight, the world is not flat. It is not quite a perfect sphere but definitely not a flat pancake. When the pizza guy is spinning the dough around his finger, he is not showing you conclusive evidence that a spinning earth has to be flat!
The problem is that whatever you say has consequences. If you send a tweet that the bank on the corner is giving away money because it ran out of space to store it, more people will show up than there are characters in your tweet. Guaranteed!
Furthermore, sensational lies trump – for lack of a better word – boring facts. Just think of the posts you share. These tend to be clever truths or hilarious nonsense packaged as truth. Not that we believe in the latter but we appreciate its entertainment value. Unfortunately, what is entertainment for some is truth for others.
In a world of political correctness, comedians are about the only ones left who can still say the truth no matter how inconvenient that truth might be for some. And even that is under threat. These days, it takes courage to say what needs to be said (and say nothing when it is better not to). Indeed, and the motivation for this blog, facts and truth are under attack. But that is nothing new.
As Albert Camus wrote in The Plague (La Peste), “.. there always comes a time in history when a person who dares to say that two and two make four is punished by death.” He wrote this more than 75 years ago, and his words are as true today as they were then. Is our courage and resolve waning?
It appears that facts cannot stand on their own feet anymore. The sciences are all based on facts but that is a world most of us do not live in and are not familiar with. If we all had an understanding of the scientific process and its rigor, we would all see free speech for what it is : Swiss cheese with more holes than cheese. A sad reality, but one I want to poke some fun at. As the Dalaï Lama used to say, when people laugh, they can change their minds. Let’s follow that line of wisdom. Let me first dust off your linear algebra a bit.
Assume that we have a brother and a sister, and we are trying the figure out how old they are. As we are not in South Korea, we will use the yardstick that birth is ground zero. Let us assume that we know that the sum of their ages is 27. Hence, we have a linear equation that establishes a truth but one that by itself is not enough to determine the exact ages of the siblings.
I put the truth in the form of an equation because that is how the laws of nature often reveal themselves. Just consider Einstein’s fundamental equation of E=m c2 (just move the 2 a notch up so it looks like c squared, which it is supposed to be). In the sciences, fundamental truths often reveal themselves in the form of relationships which we can express in equations. For the siblings, a fundamental truth is that age(brother) + age(sister)=27. Not as dramatic as Einstein’s equation, but then we are not in pursuit of a Nobel prize but merely want to have some fun.
If all we know is that the sum of their ages is 27, we can’t really figure out their respective ages. They could be 1 and 26, but 13 and 14 are equally likely. The equation narrows down the range of possibilities (e.g., we know that the siblings are not octogenarians!), but we still have a degree of freedom on what their exact ages might be. In the language of linear algebra, we have one equation in two unknowns and, hence, plenty of possible answers. Unless we know something more about their ages, they will remain a mystery.
What additional linear equation would we need? One that is relevant and consistent with the unknown facts. Relevant means that it contributes to solving the puzzle of their ages. Knowing, for example, that the brother has freckles might be a fact but that fact is irrelevant to establishing his age (and that of his sister). Consistent means that it reveals another truth about the ages we are trying to uncover.
One example could be that when the sister will be 18, her brother will be the age she is today. This equation together with the known sum establishes the fact that the brother is 12 and the sister is 15.
If, however, the second linear equation were one that states that the sister is twice as old as her brother, then the brother is 9 and the sister is 18.
Obviously, both examples of the additional equation we need cannot hold at the same time because they are inconsistent. Only one can hold. If, for the sake of our discussion, we assume that the first one is true, then the second one becomes – what Kellyanne Conway coined – an “alternative fact”. Not exactly a scientific term, but certainly one that has gotten her famous. In any science, we would call such a “fact” by its real name: utter nonsense. But this gets us into the messy backyard of free speech.
Free speech means that we can say anything we want and state it as a fact. If Kellyanne came along and threw her alternative fact into the puzzle, we would have three linear equations in 2 unknowns. This leads to an overdetermined system of equations; i.e., more equations than unknowns. I doubt you remember, but such a system has no solution. Hence, the mere fact that Kellyanne shows up with her “fact” implies that we can no longer recover the ages of the siblings! Thanks Kellyanne. She is certainly entitled to free speech but adding her non-sense as fact has made the truth elusive.
That is the long and dark shadow of free speech. If we consider a tweet as factual when it is not, linear algebra tells us that this will make our puzzle insolvable. That is the algebra of free speech: adding facts that are not facts perpetuates the mystery. Doing so will only open the floodgates for more twitter nonsense. Elon, we’ve got bigger problems on our hands than fake accounts. Just do the math.