Counting sheep

Counting sheep is a mental exercise used in some Anglophone cultures as a means of lulling oneself to sleep. It most likely arose from Yan Tan Tethera, a traditional numbering system used by some British shepherds to count their flocks.
In most depictions of the activity, the practitioner envisions an endless series of identical white sheep jumping over a fence, while counting the number that do so. The idea, presumably, is to induce boredom while occupying the mind with something simple, repetitive, and rhythmic, all of which are known to help humans sleep.
Although the practice is largely a stereotype, and rarely used as a solution for insomnia, it has been so commonly referenced by cartoons, comic strips, and other mass media, that it has become deeply engrained into popular culture's notion of sleep. The term 'counting sheep' has entered the English language as an idiomatic term for insomnia. Sheep themselves have become associated with sleep, or lack thereof. For example, an ad campaign of the Serta mattress company features the Serta Counting Sheep, a flock of animated sheep who resent said company's mattresses for supposedly rendering their services unnecessary.
According to an experiment conducted by researchers at Oxford University, counting sheep is actually an inferior means of inducing sleep. Subjects who instead imagined 'a beach or a waterfall' were forced to expend more mental energy, and fell asleep faster than those asked to simply count sheep. Sleep, by this logic, could be achieved by any number of complex activities that expend mental energy.
It has also been whimsically suggested that the phrase originates from a Hebrew pun on a Latin phrase 'sopor sond' (supposedly sleep deeply/soundly). The Hebrew pun is ספור צאן (sopwor tsoan), an imperative that means "count sheep!". However, this is likely a folk etymology; for one thing, "sopor sond" is not actually meaningful Latin (although "sopor" does in fact mean "a deep sleep").

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