Tired, confused, and unsteady, especially just after waking up or recovering from sleep.
From 'grog' (diluted alcohol), the drink of sailors, implying the sluggish state of someone who has consumed alcohol; 'grog' itself comes from Admiral Vernon's nickname 'Old Grog' (from his grogram cloak).
Sleep inertia—that groggy feeling when you first wake up—happens because your brain's prefrontal cortex (responsible for clear thinking) takes 10-30 minutes to fully activate, which is why waking someone mid-REM sleep makes them extra groggy.
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