Often when we are watching science fiction shows or movies, they imagine fantastic devices that are just at the edge of possibility according to modern physics. Ideas like death stars, faster-than-light travel, or teleportation are all things we are unlikely to see for many years, but can’t totally dismiss as potential inventions of the far future. But every once in a while, science fiction posits something so totally absurd that I can’t help but laugh. The other day, while watching an episode of Star Trek: Deep Space Nine, I saw an idea in this category: a small device that would alter the laws of probability.
The plot of this episode, titled “Rivals”, involved a series of strange events on a space station. Gamblers would win against impossible odds, the infirmary suddenly filled with victims of freak accidents, a computer search of an unsorted file list would instantly discover just the right data, and a crew member who stunk at racquetball suddenly started making impossible trick shots. As expected for a Star Trek episode, this all boiled down to an alien technological device, in this case one that could alter the laws of probability. Once the captain found and destroyed the device, everything could go back to normal.
Now at first you might just label this as another piece of random technobabble used to advance a sci-fi plot. But I think this hits at a popular misconception about probability. Many people think then when the odds of some event are low, it’s some kind of conspiracy of the universe against them. So if you have a one-in-a-million chance of making a trick racquetball shot, why shouldn’t some gizmo be able to alter that probability and help your game? But actually, the low probability just reflects the fact that there are a million different ways you can hit the ball, all of which are equally valid executions of the laws of physics. The universe doesn’t really care about the one shot that we abstractly label the great trick shot: it’s just another in a huge sea of possibilities. Tiny variations in the angle of your aim and the force of your swing can make a major difference in where the ball goes. You can imagine a million parallel universes in which you hit the ball, and only one of them involves you making the shot successfully. Which one is it? You might care, but it’s none of the universe’s business. All are roughly equally likely, depending on your exact position and momentum when you hit the ball.
So what would it mean for an alien device to change the laws of probability? It is theoretically possible for some specific technical gizmo attached to your arm to bias it towards the successful racquetball shot. But a generalized probability gizmo that could enhance your shot, improve computer data searches, enable victories at roulette, and cause freak accidents? How would this device know how to bias the universe precisely in ways that we label as “unlikely” results, in all these diverse domains? In the racquetball shot example, we’re estimating that there are a million possibilities, so *every* shot you take will be a one-in-a-million result: no matter what ends up happening, there was only that same tiny chance of that specific shot occurring. So a machine that caused an “unlikely” result for events would be useless at choosing the victory shot for you— every non-victory shot is equally as likely, and there are 999,999 of them. On the outer fringe of possibility, perhaps if the machine had full artificial intelligence capability, there might be possibilities here. But then it would be a techno-gremlin notable mainly for its intentional meddling in other’s lives, and nobody would describe this strange robot’s actions as a change in the laws of probability.
We can see similar laws at work in many parts of our daily lives. Is my daughter engaged in a specific effort to make her room messy? If I don’t enter my daughter’s room for a few weeks, books, toys, and clothes are strewn about everywhere, with barely a path available to the bed. But is she deliberately trying to make the room messy? Though there is some doubt about her intentions here, I think it’s really a result of the fact that there are many more configurations of the room that are messy than non-messy. You can put a sock in 1000 locations that are not the sock drawer, but need to spend some energy to intentionally put it in the sock drawer if that’s what you want. Combine all the objects in the room, and it seems there are uncountably more ways for the room to be messy than clean. Thus, without intentional action to drive it towards one of these clean configurations, small continuous changes will probabilistically lead to complete messiness. So she doesn’t need to be trying, the messy room is just something that will happen with high probability unless someone invests energy to prevent it. This is similar to the basic principles that the thermodynamic laws of entropy are built upon, though I won’t say much more about that right now, due to the large number of websites that seem to admonish us against the messy-room metaphor for this concept.
So, in short, when some event we want has a low probability of occurring, it is usually just a measure of the fact that there are many possibilities of what can occur, and only a small number have property that is significant to our human interpretations. The universe doesn’t know which one we want, so it has no particular reason to deliver the desired outcome. Imagining a technical device that can alter the laws of probability is like imagining a device that can make 2+2=5, or can cause triangles in a Euclidean plane to have angles totaling 190 degrees: it simply violates the fundamental mathematics of the situation. Over the next few millennia, humanity may see miraculous inventions such as laser pistols, teleportation, starships, or halfway decent William Shatner albums, but I think we can safely bet that no machine will ever alter the laws of probability. If you’re frustrated sometimes by things not going your way, you should take comfort in the fact that there are many ways things can go, and figure out what you can do to reduce the number of possible bad outcomes. The universe is not engaged in some kind of conspiracy against you that needs to be fixed with a magical gadget.
And this has been your math mutation for today.