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I'm looking for a game that one can play solely within one's own mind. Most people, when given this task, say things like "count how many [objects] there are in the room", or "make up a story about the people around you", or maybe "make up an entirely new story in a made up world", but the problem with these is that they depend on there actually being something around you to give you external input. Even the latter two, where you make up a world, don't necessarily count as games, and they require external input anyway, because to know how to create something, you have to have influences of some sort. What I'm searching for is a game one could hypothetically play if one forgot everything about the world, the universe, and one's life. All memories gone, except for the game and how to play it.
So there's the hypothetical. Can you think of a game you could play within your own head that does not require any external input? Keep in mind the definition of a game. "Game" is one of those words that's hard to define exactly, but let's say "a goal-oriented task that requires reasoning, strategy, and/ or skill to overcome various obstacles".
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You can play mentally "rock scissors stone" in your head against yourself without any exernal input but the game and the objects it uses are referenced externally from memories of earlier usage of visuals of words.
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1: create four or more (rely depends on you) entities in your mind that have a set way that they interact with each other or themselves. The point is also to have them as simple as possible I.e one entity brings 2 others closer together, one keeps them a slight distance apart, one adds to the effect of another (Increasing or decreasing it) and one recreates the affect of two other non contradicting pair.
2: simulate how they would interact with one-another and see how complex of a system you can create with the pre-set entities.
3: You can set a certain effect as the endpoint or just continue on creating effects
4:(extra) try and create a mathematical system that dictates how larger and larger systems would function in relation to each other.