How could prediction be used in the game?
An idea for a level that requires observation and prediction: Imagine a platform game like Mario. There is a box that hero must hit with their head, and a bonus item flies from the box. Hero must catch the item, because when it falls on the floor, it breaks... then another box comes (there is an infinite supply of boxes) and hero can try again.
The difficult part is this: The item flies to one direction (left or right) so quickly that it is impossible to catch it, unless player predicts the direction and is already running there while hitting the box. Also player must catch 10 items in a row to complete the level.
The direction of the item somehow depends on the shape / color / symbol of the box. So the right way to win this level is to just hit the first few boxes, observe the direction and make a model; and then apply this model to the following boxes. The rules could be selected randomly, for example "if the box is red OR the symbol is a fish, the item flies left, otherwise it flies right".
This article relates to a game, being developed by Shiny Ogre Games, based on "The Twelves Virtues of Rationality" by Eliezer Yudkowsky.
We can write whole books about empiricism, describing what it is, why it's useful, and how it works. We can use an innumerable amount of words to describe the nuanced techniques involved in thinking empirically about a problem. Words are certainly valuable for describing things, but can gameplay describe a thing more effectively?
Our brains are pattern-seeking machines. We like figuring things out, it's a survival mechanism. Our brains release endorphins when we decode the noise of our environment.
Games more or less consist of a series of interesting challenges (or patterns), with mechanics that allow the player to figure out the challenges (or decode the noise). Decoding noise is what our brains do all the time, when we find patterns in the noise, we cache those for later reference. We do this because it is fun.
As Raph Koster famously said in his book, A Theory of Fun: "Fun is just another word for learning", because of this, gameplay can be expressive. By designing the challenges so that they evoke your various modes of thinking, and then setting those challenges into a narrative where the player assumes a role and is allowed to explore the system within the constraints of that role, a game can allow the player to experience the application of a concept.
In the Empiricism level, we are trying to create a puzzle that requires empirical thinking to solve. That is, the player can only solve the puzzle if they are able to draw on their experiences and observations both within the game and without to make accurate predictions about how the puzzle elements should behave. In this puzzle, we do not try to trick or mislead the player, we do not require the player to react quickly, there is no violence, and the player cannot die. We give the player the freedom to experiment with the puzzle, and all we ask is that the player think empirically about the world presented by the puzzle.
If all goes as planned, the player will solve the puzzle not through logical-deduction, process of elimination, or wild guessing, but by empiricism. They will do this without a single word of instruction or narrative, and they will grasp the concept on a deeper level because of it. Hopefully.
Here's some art: