tv. to “drink” in a concept or knowledge and assimilate it; to understand something; to appreciate someone or something; to relate to someone or something. : I don't quite grok that. Run it by again, would you?
Dictionary of American Slang and Colloquial Expressions by Richard A. Spears.Fourth Edition. Copyright 2007. Published by McGraw Hill.
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"to understand empathically," 1961, arbitrary formation by U.S. science fiction writer Robert Heinlein, in his book "Stranger in a Strange Land." In use 1960s, perhaps obsolete now.