Illusory or impossible to achieve; existing only in imagination. Chimerical hopes or plans are unrealistic fantasies that cannot be realized in practice.
From the Chimera, a fire-breathing monster in Greek mythology with a lion's head, goat's body, and serpent's tail - a creature that was literally impossible because it combined incompatible parts. The word came to mean anything that seems real but is actually impossible.
The mythical Chimera was a biological impossibility - part lion, part goat, part snake. Chimerical dreams are like that monster: they might look impressive, but they're made of incompatible parts that could never actually work together in reality.
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