When we predict that something or other will happen, we are “saying before” what we think the outcome will be. This implies that we have some internal model of the process in question, and that we can evaluate the outcome of our model faster than the real-world process unfolds. We know that our model has fidelity to reality, and is fast, when our prediction matches reality’s outcome.
When we are able to make a prediction that comes true, we also know something else: that the thing we are predicting is based on a law of some kind; otherwise we wouldn’t be able to make a useful model. Only when we can make true predictions do we know for sure that we know something true about reality.
But aren’t there some things that are random? Like tossing a coin or dice? If I could reliably predict the outcome of dice, I would be planning some quality time in Vegas. There is a difference, it turns out, between whether a prediction is possible, in principle, and whether I can make such a prediction. With enough data about the dice throw, and enough computational horsepower to crunch that data in accordance with the laws about how they move and roll, it is possible to know how they will fall. But that data is hard to get, and hard to get into a device that can make the calculations fast enough to get a prediction.
Most of what we call “random” is not random in the impossible-to-predict sense, but functionally random in the too-hard-to-predict-to-be-useful sense. As our computational cojones have increased, so too have the outcomes we can predict. Consider predicting just which thrusters to fire, for how long and how strong, to achieve a desired Shuttle reentry.
Are there any truly random processes? In the impossible-to-predict sense? Richard Feynman discusses the fundamental un-predictableness of whether photons will pass through, or be reflected by, a sheet of glass in his popular book, QED and through which opening an electron will pass in the double-slit experiment in his 1964 Cornell lecture. We observe that there is no possible way to predict the outcome in these experiments. With the first, we can predict the proportion of photons that will be reflected vs. pass through, but not which outcome will apply to any given photon. Also in 1964, John Bell demonstrated (oringal paper here) that not only can we not, in principle, predict the outcome for a given photon, but that there aren’t any “hidden variables” that determine the outcome, knowable or not.
So, it appears that true, impossible-to-predict randomness exists in a limited sense: though we can predict the probability of an outcome, for example the portion of photons that will be reflected, we can not, in principle, predict the outcome of the individual photons.