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Why can't you play Call of Duty with an arcade light gun?

In the mainstream shooting games, the Reticle is fixed in the center of the screen and never moves.
In order to shoot a target, the player must move the muzzle of the gaming gun. But Moving the muzzle, inevitably deflects the Reticle on the screen. That doesn't match the experience of a gun. So the proposition itself is a contradiction, a paradox. If analyzed by modern control theory, this is an "uncontrollable system".

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