These are good, Admiral, but we need to think about future proofing here.
Well, I see what you mean. However, clearly we must proceed to higher dimensionality and give up some of our favorite concepts... Like associativity. If we have difficulty levels only specified in 10 + 8i + 6j + 4k, that still remains too easy... Clearly we will have to use eight "dimensions," then we could have enjoyable challenges where our fighters kill their cruisers, but their cruisers kill our fighters, after which our fighters can kill their cruisers, and so on.
I mean, let's be honest, just how many real numbers are there? Years from now, having fully explored the depths of the irrational difficulties, we don't want to be weeping for the lack of more AIs to conquer.
This game is hard enough without having to worry about going insane. Invocations of Cantor are no longer permitted here. *twitch*
Besides which, Colonel X already had integer and rational levels, so I decided I would avoid the obvious extension to algebraic difficulty of it and go straight for the transcendental challenge. I was not convinced of the need to take the difficulty to a whole new dimension, but you do have a point. Future proofing is always a good thing.
Hence, I conclusively propose that we no longer have a finite number of dimensions of difficulty. Generalize AI War to an infinite dimensionality for the difficulty "level" (of course, realizing that "level" implies order and so the word is clearly a misnomer here) and be done with it.
Now the question is... Exactly how do you win?
Cheers!
PS: If the difficulty "level" is set "high" enough, do you think the AI could find are a kind of number larger than rationals and smaller than reals? I wonder what kind of nightmares I'm having tonight...