I used to be of the belief that the field of statistics only exists because of the inherent nature of the universe. Put another way, I believed that everything in the known universe was ultimately deterministic, but because we do not have a direct blueprint outlining how the world works, we have to infer the rules based on what we can observe. Given that everything we observe is the result of (literally) atomic-scale interactions, we simply have to do the best we can and accept that, given certain data under certain conditions, we’re going to be wrong some fraction of the time. Hence, statistics.
However, recently I’ve begun rethinking this belief. But more on that later.
Quantum physics states that true randomness underlies everything in the known universe. Now I want to emphasize this point here: randomness is a subtle concept in terms of what it actually means, and the word has become so colloquial that no one really considers what it actually implies anymore. Computers have generated “random” numbers for awhile, but they go by a different flavor: pseudorandom. The fact is, we humans are awful when it comes to recognizing and creating true randomness.
(I highly recommend this book if you want to learn more about the randomness we overlook in our daily lives, or flat-out confuse for some sort of pattern)
Here’s a personal anecdote from just last night: in celebration of having finished our machine learning midterm, the other first-year PhDs and myself got together for a board game night, and one of the games we played was the (in?)famous Settlers of Catan.
Don’t let its innocent veneer fool you: while the mechanics of the game itself call for a great deal of strategy, the whole premise is built on a foundation of pure randomness: the roll of dice. However, even dice rolling is predictable in the statistical sense: there are very few ways of rolling a 2 or a 12 (in fact, exactly 1 way for each), but loads of ways of rolling 6s, 7s, and 8s, so over an infinite number of dice rolls you would expect to see a lot more 6s, 7s, and 8s than 2s and 12s. And, believe it or not, you base your entire strategy off this premise.
Which may or may not hold for the duration of a single game. Like last night. I won the privilege of choosing my starting position before any other player, so I set up camp adjacent to two 6s, statistically hedging my bets on the likelihood of this number being rolled.
Over the course of the entire game, 6s were rolled a grand total of 3 times. How’s that for statistical improbability?
Still, there’s no way for me to prove one way or another whether true determinism underlies every particle in the known universe, or if everything follows the full definition of random. Quantum physics says that by simply observing a system, we change it, thereby making objective observation impossible. Thus, we’ll never be able to extrapolate all the individual variables that make up a given system.
Anyway. Any debate beyond this point without a degree in quantum physics is purely speculative and philosophical, and I have Ph.D. research to get back to (which is why I’ve been so terrible at updating this thing lately). I’m hoping to update a bit more often, but we’ll see what kind of coherent thoughts I manage to isolate first 🙂