The Value of Uncertainty

I once tried to explain the argument behind Schrodinger’s cat to my mother. She was trying to write a poem and hoped that the metaphor would work, but disliked the idea that something could be both true and untrue. I flipped a coin and as it spun through the air I asked if it was heads or tails. Sadly, even that careful exhibition of probabilities failed to hit the mark; my mother believes that things are or are not. The coin is not heads till it hits the ground.

I found this interesting because (though she claims to hate it) in another life she could have been a mathematician. There are more similarities between mathematics and theology than mathematics and science; we have all learned that nothing is ever true in science. Today a virus is airborne, tomorrow passed only by touch. Yesterday immunity lasted three months, tomorrow it might last six. In a world of p-values there cannot be truth, only things that are acceptably possible, and one day the apple that has fallen from its tree, time and time again, will float up into the sky, or explode into a thousand cherry blossoms. The fact that these things almost certainly will not happen means that there is the smallest of possibilities that they could.

But math— math will offer a level of certainty (provided various assumed things actually are true). If \(x = 4 - 1\), then in that situation \(x\) always was three. It was three the moment the equation was written. It will be three when you die. It will be three when the sun falls into itself. Sadly this is not usually as satisfying as theology. Socrates may have considered death the next intellectual horizon, but I am afraid the rest of us might gain some comfort from knowing, if not what the destination is, at least that there is one.

But this is why mathematics and science are in bed together (despite their differences), not mathematics and theology. Imagine, for only a moment, that there was an ultimate formula for everything: want to know the position and velocity of a particle (use the formula), want to know if the patient has cancer (use the formula), want to know if your mother-in-law would prefer that your wife had married the boy down the street (use the formula).

What a dull world. Certainty would become an everyday phenomenon. We would all know the ideal path to work, the exact number of minutes to cook a steak, how many drinks you should have to be charming. No one would ever fall off a bar stool, tell their crush the truth, or play a video game. Not unless the formula told them to.

But you go to a bar because it is funny when your friends fall off bar stools and you blurt out the truth because it is worth saying. Just like mathematicians thrive on the undiscovered portions of their fields and scientists live on a need to understand a fundamentally unknowable universe, it is not worth getting out of bed for a preordained day. Somewhere, there is a woman staring at a chalkboard filled with symbols trying to build some new form of topology. She does not know if it is even possible, just like the man in an observatory trying, once again, to see something that cannot be seen. They have failed a thousand times, but still look.

Which is to say, it is not that the coin can not work that way, it has too. It must be heads, and tails, and every one of an uncountable supply of supposedly impossible options, because otherwise there would be no reason to flip it.