Follow the clearly defined rules to find the next box. That is determinism. That is all it is.
Now notice what we are not saying here. We are not saying that all deterministic systems are fully predictable. The vast majority of them are not. Let me repeat that, in case it wasn't clear: we cannot predict the future values for the vast majority of deterministic systems that we could create. Why? Well, just think about a VERY BIG flow chart. We might know that we're in box C, and we might be looking for box D on this chart, but the chart is so big that box D is somewhere near the center of the Milky Way galaxy. We cannot yet get to that box to read what will happen in box D.
We can tell that this is a deterministic system. We can see box C, and we can see the clear deterministic rule from saying that the next box is thattaway, in that direction. But the flow chart is so big that we simply can't follow where that line goes. In computational terms, what this means is that if we set up a computer to approximate this deterministic system, our beautiful sun will burn out before the computer could finish its calculations. We wrote a computer program to run this deterministic system. Sure. We can do that. And we know it's deterministic, because [i]the system is well defined[/i] as it's being programmed into the computer. Determinism is about well defined causal chains. Everything in the system runs according to fixed rules. Nevertheless! We still cannot predict where this system will go because we simply don't have the computational power to "follow the flow chart". The math problem is too hard for the computer to run it in less than 10 billion years. The flow chart is, so to speak, too large for us to read the entire thing.
This is why computer metaphors are so common in these discussions. It's the power of computation that, finally, gave us the key to unlock our understanding of the limits of predicting deterministic systems. Physicists used to believe that if they had the equations to describe the world, then they'd be able to predict... well, pretty much anything.
It was only after the computer era that it fully sank in, on a gut level for the people who work with these kinds of deterministic systems, that the vast majority of these systems are not computable within the human lifetime. Or even within the earth's lifetime. If we had the processing power, we could predict the future. But we don't. And then the even more staggering realization: our processing power comes from computers that exist inside this universe. They are, thus, necessarily smaller than the universe as a whole. It's a necessary result, that even if our universe happens to be deterministic, that any computer inside of the universe cannot run a simulation of the universe that it is in. A computer that is smaller than the world cannot simulate the entire world. Can't be done. Agents within a deterministic universe must necessarily remain mired in ignorance of what will happen next.
The question is, then, what kinds of deterministic systems can we simulate? Well, only very simple ones right now. But nevertheless, we can learn quite a bit from those simple deterministic systems if we try.
One thing we can do is, for example, create miniature civilizations. Like computer games, but without any player input. It's a simulation that repeats the same outcome over and over again, every time it's played. That is a deterministic system.
And an interesting thought experiment is to have multiple programmers. There might be World-Programmers who create the simulated game world, and Agent-Programmers who create the best little robot they can to navigate the game world. The Agent-Programmers might not even know the full details of the world that their poor little agent will be dropped into. So they have to create an agent which has some small chance of survival in a variety of different worlds. They have to create an agent that will react to what it sees in different kinds of worlds.
World+Agent is a deterministic system. Every time the system is run, the same outcome will happen. The agent will make the same choices every time. But nevertheless, we are free to call the agent's "decisions" by that very name. No other word is appropriate. We know that if the agent were dropped in World2, after all, their decisions would be different.
World+Agent is a deterministic system. It plays out the same way every time it is run. World2+Agent is also a deterministic system. It plays out the same way every time the simulation is run. Yet the agent makes different choices in the different worlds, as a result of experiencing different input. The deterministic system is not the World by itself, and not the Agent by itself, but the combination of the two together. The chain of cause-and-effect can work out very differently, even with an identical "person".
Yet if you listen to conversations on this topic, you will often hear the claim that in a deterministic world, there are no "actual" decisions. That just makes no sense. Of course there are decisions. How could there not be decisions? As has been very well said:
Choices do not fall from the sky.
There can be a (deterministic agent) trying to to optimize their experience based on limited information, embedded inside a (deterministic) world that follows a strict chain of cause and effect based on fixed rules, but that agent will be clearly making decisions. Given a slightly different (deterministic) world, the agent will make different decisions.
That fits any definition of decision I've ever seen... at least when "decision" is also defined in a clear way, as determinism is so defined.
It's my belief that working through these sorts of hypotheticals can clear up a lot of previously fuzzy thinking about the nature of our definitions. We seem to have as many definitions of free will as we do posters. We seem, also, to have plenty of misconceptions about extremely well defined concepts like causal determinism.
If just one person reads through these sorts of ideas -- except written better than in my post here -- and has that light-bulb moment, then yeah. I think that person has a chance to reflect more carefully on definitions in other topics, and maybe -- on rare occasions -- to make better choices based on a clearer understanding of what a choice actually represents in a deterministic world. Our choices matter because our choices are part of the causal chain. We know that we would make very different choices if suddenly embedded in a different causal chain, because we can see the same thing happening on a much smaller scale.