The old medical practice of removing blood from sick people because doctors wrongly thought it would cure diseases, or metaphorically, any reduction in size or cost.
From 'blood' (Old English 'blod') plus 'letting' (allowing to flow). The practice comes from ancient Greek medicine's theory of balancing four humors.
Doctors once believed four bodily 'humors' controlled health—bloodletting was supposed to balance them, but it actually killed many people who needed fluids. It's a haunting reminder that confident doctors can be completely wrong about medicine.
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