Inverting inversely
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Paul Kay wrote to point to a sexist joke that inverts a scalar predicate, in a way that's similar to what happens in the "No head injury is too trivial to be ignored" / "No wug is too dax to be zonged" type of misnegation:
The speed in which a woman says "nothing" when asked "What's wrong?" is inversely proportional to the severity of the shit storm that's coming.
For the line to correctly invoke the stereotype, it needs to be "The speed with which … is directly proportional …", or else "The delay before … is inversely proportional …"
But the incoherent version, as quoted, is a perfect example of what Wason and Reich ("A Verbal Illusion", The Quarterly Journal of Experimental Psychology 31(4):591-97, 1979) called "sentences which expressed pragmatic information". In other words, the joke expresses an easy-to-understand commonplace idea, like "you shouldn't ignore a head injury even if it seems trivial", or "you shouldn't believe someone who says 'nothing' quickly when asked what's wrong", so that listeners quickly jump to the intended meaning despite the fact that what was said or written actually means the opposite.
There's still something to be explained here. Google finds 27 versions of the joke with the incoherent wording quoted above, compared with 14 replications of a semantically correct version:
The speed at which a woman says "I'm fine" is directly proportional to the severity of the shit storm that's about to follow.
Similarly, "we cannot underestimate" is about four times as common as "we cannot overestimate". Wason and Reich explain why people sometimes get confused — but not why they sometimes prefer to be confused.
Elonkareon said,
September 26, 2015 @ 6:58 pm
It seems to me it could be read to stereotype as is. That is, don't believe someone who answers "nothing" too slowly. Then again I'm not really familiar with the stereotype, just the behaviour of the women (and some men, including myself) I've known. Of course when you combine the two sayings they cancel out to "Don't believe someone who answers "nothing" when asked what's wrong."
phspaelti said,
September 26, 2015 @ 7:24 pm
I'd argue that the inverted version stems from thinking of "speed" not to mean the actual speed, but rather as "time till response", as in how quickly the answer comes. So the shorter the response time, the greater the 'shit storm'.
Jerry Friedman said,
September 26, 2015 @ 8:38 pm
phspaelti: I often hear that kind of mistake from my students.
JS said,
September 26, 2015 @ 9:40 pm
The specific wordings "we cannot underestimate" and "we cannot overestimate" seem like they'll frequently appear in the context of exhortations and thus will be (propositional logic-ally) correct more often than not. If so, the frequency difference might be down to the fact that claiming xyz has been overlooked packs more rhetorical punch than claiming xyz is attracting too much attention.
D.O. said,
September 26, 2015 @ 10:15 pm
Is one's sense of dread inversely or directly proportional to the distance from the dentist's chair?
Finn said,
September 26, 2015 @ 11:09 pm
Yes, "cannot underestimate" can be correct in a variety of situations. For example, a politician might say (40 years ago), "We cannot underestimate the threat posed by the Soviet Union," meaning, "If we underestimate the threat posed by the Soviet Union, we will be putting ourselves in danger, so we must not do that."
Rose Eneri said,
September 27, 2015 @ 7:34 am
I agree with Finn. So to avoid ambiguity, it might be better to say "We SHOULD not underestimate the threat…"
Eric P Smith said,
September 27, 2015 @ 3:50 pm
It seems to me that a very naive person – one who has no understanding of human nature – might suppose that the more quickly and confidently someone says that there is nothing wrong, the more likely it is that, indeed, nothing is wrong. Perhaps to some people “inversely proportional” suggests “the correlation here is the opposite of what you might naively suppose”. So, “The speed in which a woman says ‘nothing’ when asked ‘What's wrong?’ is inversely proportional to the severity of the shit storm that's coming" is read by such people as meaning “Contrary to what you might naively suppose, when a woman is asked what's wrong and quickly says ‘Nothing’, there is very likely a whole lot wrong."
J. Goard said,
September 29, 2015 @ 11:08 pm
Part of the confusion, I suspect, is that "speed" of response is almost certainly gonna cash out as a measure of time in people's minds, because for a single, immediate event there's nothing convenient to attach speed to (it's not mph or wpm or rps, it's "how long she took").