Literally: love – separate – detach – suffering
Alternately: The pain of being separated from your loved ones. This is one of the “eight sufferings” of 四苦八苦.
Notes: The separation in question is most often due to the loved one’s death, but may also be a result of mere distance and circumstances. In either case the separation is relatively stark; you don’t properly feel 愛別離苦 from a playmate going to use the restroom, for example.
This compound is somewhat unusual in that instead of its parts being grouped 2 and 2, it forms a 1-2-1 pattern: it names the suffering (苦) that comes of being parted (離別) from those you love (愛).
This phrase comes to us from the Mahāyāna Mahāparinirvāṇa Sūtra, a.k.a. the Nirvana Sutra, in Japanese 『大般涅槃経』= Daihatsunehangyou.
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