In a way that shows deep sadness and hopelessness, without any comfort or relief.
From disconsolate (14th c.), combining dis- (not) + consolate (from Latin consolari: to comfort). The -ly ending converts the adjective to an adverb. The meaning evolved to describe someone who cannot be comforted.
The word 'console' appears in both 'disconsolate' and 'console' (the gaming device), but gaming consoles actually distract us from feeling disconsolate—they're named after the idea of comforting or consoling during lonely moments!
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