It alludes to "breaking on the wheel", a form of torture in which victims had their long bones broken by an iron bar while tied to a Catherine wheel. The quotation is used to suggest someone is "[employing] superabundant effort in the accomplishment of a small matter".
The quotation is sometimes misquoted with "on" in place of "upon".
The line "Who breaks a butterfly upon a wheel?" forms line 308 of the "Epistle to Dr Arbuthnot" in which Alexander Pope responded to his physician's word of caution about making satirical attacks on powerful people by sending him a selection of such attacks. It appears in a section on the courtier John Hervey, 2nd Baron Hervey, who was close to Queen Caroline and was one of Pope's bitterest enemies. The section opens as follows:
Let Sporus tremble –"What? that thing of silk,
Sporus, that mere white curd of ass's milk?
Satire or sense, alas! can Sporus feel?
Who breaks a butterfly upon a wheel?
Yet let me flap this bug with gilded wings,
This painted child of dirt that stinks and stings;
Whose buzz the witty and the fair annoys,
Yet wit ne'er tastes, and beauty ne'er enjoys,
"Sporus", a male slave favoured by Emperor Nero, was, according to Suetonius, castrated by the emperor, and subsequently married. Pope here refers to accusations made in Pulteney's Proper reply to a late scurrilous libel of 1731 which led to Hervey challenging Pulteney to a duel. Hervey's decade-long clandestine affair with Stephen Fox would eventually contribute to his downfall. As first published the verse referred to Paris, but was changed to Sporus when republished a few months later.
"What? that thing of silk" uses a metaphor of a silkworm spinning that Pope had already used in The Dunciad to refer to bad poets. "Ass's milk" was at that time a common tonic, and was part of a diet adopted by Hervey. "This painted child" comments on make-up such as rouge used by the handsome Hervey.
Another graphic instance of the usage can be found in An Introduction to Harmony by William Shield (1800), wherein he writes: "Having brought this Introduction to Harmony before that awful Tribunal, the Public, without first submitting it to the inspection of a judicious friend, I shall doubtless merit severe correction from the Critic; but as my attempt has been rather to write a useful Book, than a learned Work, I trust that he will not break a Butterfly upon the wheel for not being able to soar with the wings of an Eagle."
William Rees-Mogg, as editor of The Times newspaper, used the "on a wheel" version of the quotation as the heading (set in capital letters) for an editorial on 1 July 1967 about the "Redlands" court case, which had resulted in prison sentences for Rolling Stones members Keith Richards and Mick Jagger.
The philosopher Mary Midgley used a variation on the phrase in an article in the journal Philosophy written to counter a review praising The Selfish Gene by Richard Dawkins, where she cuttingly said that she had "not attended to Dawkins, thinking it unnecessary to break a butterfly upon a wheel."
The British rock band, The Mission, enjoyed a no. 12 hit in the UK Top 40 (no. 1 in South Africa) in January 1990 with a song entitled 'Butterfly On A Wheel'.
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