Curcumin does not usually cause drowsiness, and it is safe to drive or operate machinery after taking curcumin with one possible exception:
In laboratory experiments with animals, curcumin restores normal rhythms of day and night waking and sleeping after alcohol consumption.
This means if you drink heavily (say, more than 3-4 drinks a day) and you've been staying up late, or if you are an alcoholic recently (in the last 3-4 weeks) beginning recovery, curcumin might will help you return to a normal sleep pattern. Whether that's good or bad is really up to the person taking the supplement.
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Jagota A, Reddy MY. The Effect of Curcumin on Ethanol Induced Changes in Suprachiasmatic Nucleus (SCN) and Pineal. Cell Mol Neurobiol. 2007 Dec;27(8):997-1006. Epub 2007 Sep 11.