Why do we say "At wit's end"?

Background:

(Note: We'll also accept "A white elephant" as a correct answer for this Wordplay.) "At wit's end" means to be out of ideas about how to solve a problem (e.g., “I’ve tried everything to get Johnny to study but he just won’t; I’m at wit’s end!")

First, a note about how the phase is printed. Writing an apostrophe either before or after the “s” is correct—so "wit’s end" and "wits’ end" are both acceptable—but it’s never okay to use “wits end” in this context.

Some credit the origin of this idiom to the Bible. In the King James Version (KJV), Psalm 107:27-30 is written:

"They mounted up to heaven; they went down to the depths;
their courage melted away in their evil plight;
they reeled and staggered like drunken men
and were at their wits’ end.
Then they cried to the LORD in their trouble,
and he delivered them from their distress.
He made the storm be still,
and the waves of the sea were hushed. "

The books of the Bible’s Old Testament were composed over the course of a thousand years, from about 1400 BCE to 400 BCE, and Psalm 107 likely dates from around the latter end of that range, about 536 BCE. Originally written in Hebrew, the psalms have been translated many times over the centuries, with greater or lesser degrees of accuracy, and the King James Bible, published in 1611, was the first to translate the phrase in this psalm to “wits’ end.” (Subsequent versions of the Bible, like the Revised Standard Version and the New International Version, which are viewed by some as more accurate than the KJV, also insert the saying here as written.)

However…

Most scholars feel the phrase “at wit’s end” predates its use in the KJV, so most don’t cite the Bible as the origin for the idiom. Instead, sources point out that the first use of it in print is by poet William Langland (c.?1330 – c.?1386), author of the Middle English alliterative poem Piers Plowman (c.?1377). In it, Langland describes a situation that is so perplexing that no one knows how to solve it, and “Astronomyens also aren at hir wittes ende” (“Astronomers are also at their wit’s end”). Linguists feel the phrase must already have been in wide circulation at the time Langland included it in his work. And because Piers Plowman is from the 14th century and the KJV the 17th, scholars surmise the Bible’s translators relied on the commonly understood phrase “at wit’s end” to get their meaning across.

“At wit’s end” is widely used today and understood by most. The idiom is ubiquitous in modern culture.

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