In a way that captures and holds someone's complete interest and attention in a compelling manner.
From fascinate + -ing (present participle) + -ly (adverb). The root fascinare (Latin: to bewitch) evolved semantically to mean 'grip attention' rather than literal spell-casting.
Interestingly, 'fascinating' became a social convention word—Victorians used it constantly to describe things they found intellectually stimulating, and it developed into the bland politeness word we still overuse today.
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