There is an unusual paradox. Science exists to be predictable. The main aim of knowledge is to provide certainty to experience, to allow us to calculate what might happen if we did something, before we did it. On a basic level science exists to help comfort us in our belief that the sun will rise tomorrow at a certain time, but also give us the power to calculate future sunrise times, work out why the sun shines at all, and to control our environment and life as we desire. Yet despite this, there are, in quantum mechanics, areas of science that are fundamentally unpredictable. We might be able to say that a radioactive particle is more likely to emit at this time than another, but not exactly when. We can only measure the outcome. So, although science (and the universe and our lives themselves), seems to be reliably predictable, there is some fundamental level where it isn't. Why?
Prediction itself is a factor of belief and of freewill. Fundamentally, we need to feel free, that we can change things. If we could accurately predict the future, such that it was certain to be, then we would be forced to enact it because our actions would be a calculable part of the prediction. In a universe of perfect prediction we would have no free will at all.
The only options are that we accept that we have no freewill and that the universe is totally predictable (but have no power or ability to change it), or accept that the universe is not predictable but have free will.
Which is true?
First, what is prediction? Prediction is an idea of what might happen at a future time. It's a series of options. If I made the bridge from wood, it would be this strong. If I made the bridge from steel, it would be this strong. This sort of prediction relies on our choices. Are there types of prediction that do not involve human choices? Perhaps a scientist would say; I have an object of mass x and velocity y, so I can predict its energy of momentum absolutely, without involving choice. That equation is a fundamental truth. But is that the case? Can one exactly state the exact mass and velocity of an object without ever using judgement?
There are some measurements in quantum mechanics where the choices made by the experimenter have been shown to affect the outcome on a fundamental level. On a more simple level, in any measurement, the experimenter chooses what to measure. The choice to make the prediction itself is one of free will, to choose what to predict. Because of this reason alone there are no circumstances where a prediction can be made that doesn't involve some freedom of choice.
Freedom of choice is an inherent part of making a prediction because prediction is about control. A prediction is a tool to control the world, and for us feel in control we must have freedom. The two things are fundamentally linked. To make a prediction without any freedom to react to its consequences is pointless.
We want a universe that is fully explainable and predictable, but also want control over it. This is impossible. This is the paradox.
So if we had freedom of thought, then that would be unpredictable, we would demand that, but everything else must be predictable. This idea seems a little crazy. Might it be possible that some areas of the universe are fundamentally unpredictable, and that these areas are responsible for free will? That would solve the question firmly.
In that case, what would define the parts of the universe responsible for free will? And surely, we might also want to make predictions about people and how they think and behave? There are only two options; we have free will that is unpredictable, which would make social science and psychology impossible (and every day life somewhat haphazard), or we are fully predictable and free will is illusory. Is this too simple? Can there be gradations of freeness or predictive power?
Not really. We can't have totally accurate predictions and control over them. We can't see into the future, and control it. Everything works brilliantly when we accept that the limits to our predictive power are self-imposed limits of free will. A quantum measurement is exactly predictable, if we accept that we have no control over the prediction until the experiment has concluded. Yet, even outside of the quantum domain, in all experiments and predictions, this is a necessary trade-off. The reason predictions work so well in the macroscopic domain, the world of sunrise times and bridge constructions, is that we have more options, greater feelings of freedom to react to their outcomes. The less options in the outcome of a prediction, the less freedom we have, until we have no free will at all.