Where does the phrase rule of thumb originate from? Why the thumb, of all possible body parts?
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No one knows. The expression has existed in many languages for a long time, which suggests that its origin is pretty old.
There are several theories, some based in the similarities in many languages between the words inch and thumb and how you can measure an inch using the thumb, others based on the general usefulness of the thumb to measure different things.
It's entirely possible that it originally had nothing at all to do with the thumb; that it was a similar word that has become distorted over time, then translated to other languages in its distorted form.
See also: Rule of thumb on Wikipedia.
Perhaps it's because the length of the thumb joint to the end of the thumb is a fairly accurate representation of an inch. So rule of thumb was likely a way to quickly verify the measurement before cutting for construction work rather than search for a yard stick. The meaning probably began to be used in a more abstract sense as a rule to quickly validate something.
The origin is most likely derived from the use of the thumb as a practical way to measure/estimate different things such as distances or temperatures:
From the Phrase Finder :
The earliest instance unearthed by Gary Martin (Phrasefinder) is in a rhyme found in Augmented with Ingenious Conceites for the Wittie and Merrie Medicines for the Melancholic, published in 1640:
According to World Wide Word the origin is more likely to derive from measuring distances rather than temperatures:
and also from here:
The Phrase Finder also considers the possible origin that refers to the "legal" rule of beating with a stick one's wife, but not enough reliable evidence has ever been found to support it:
If you ever do any carpentry you can get pretty close with your thumb as a rule / gauge.
So any measurement not using actual instruments is by "rule of thumb", or "by eye".
Not sure if it helps, but this expression reminds me of basic Physics lessons in secondary school: Fleming's "rule of thumb"/right hand rule (similar Oersted's rule in the wiki article posted by Guffa)
Rule of Thumb is an undocumented, implied rule to abide.
One possible origin, or at least implementation, is found in the 117th New Constitution of Roman Emperor Justinian I, published in 529 C.E., granting a husband freedom to "beat his wife with a whip or rod" for divorcable offenses. The "rule of thumb" was possibly conjured to suppress nefarious abuse of the law. This rule has never been documented, as it is merely a guideline, to help prevent serious injury.
An example rule of thumb is: "Slice a peach along its suture, to remove the pit." There's no harm in bisecting the fruit along any other geodesic. It's simply easiest to remove the pit when bisected in a specific manner. It's also a good rule to not call the suture of the peach its "butt crack" (or worse), as this will likely result in a negative impact to social status among your peers.
The failures of man to abide by rules of thumb resulted in the invention of posting warning signs for the most unlikely and oddly specific circumstances.
As @NathanCTresh highlighted in his comment, the rule of thumb is indeed an oral tradition. Because this is rule passed on in oral tradition, the term is spoken in modern English ("rule of thumb"), and not in Latin ("pollux regula").