In an entry entitled “Negatives” in his Modern English Usage, Henry Fowler gave an amusing collection of examples of blunders that had been made with them. (If you follow this link, you have to scroll down a page to find the article I’m talking about.) Unaware of this, though not surprised to see it, I have been making a little collection myself. Since this is supposed to be a maths blog, let me feebly justify posting it by saying that it is a reflection on the fact that (and at one point on the corollary that ).
1. The first example is something I was once told about a landmark I had asked the way to. I was told that it was large, so that at a certain point on the route, “You can’t fail to miss it.” Fortunately, I did fail.
2. On February 25th 2009, David Thompson, a political correspondent from BBC News, wrote: “No-one would deny that David and Samantha Cameron come from anything other than extremely privileged backgrounds.” I find this a very hard example to understand directly. The easiest way to deal with it is to substitute “claim” for “deny” and see what you get. But I could just go ahead and be a counterexample to Thompson’s assertion: I hereby deny that David and Samantha Cameron came from anything other than extremely privileged backgrounds.
3. On May 2nd 2009, at the weigh-in before his fight with Manny Pacquiao, Ricky Hatton declared to his fans, “You will not go undisappointed.” This defeatist attitude is unusual in a boxer, but it was justified: he was knocked down twice in the first round and knocked out completely in the second.
4. In July 2009, Nathan Hauritz, part of the Australian cricket team, was talking about Australia’s prospects for the last two days of the Test match at Lord’s. He said: “None of the boys don’t think we can’t do the job.” As an Englishman, I am delighted to say that his team’s collective pessimism was again justified.
5. When it came to the one-day series a couple of months later, the tables were turned. An English supporter, reflecting on the situation, wrote in to the BBC website and included the sentence, “Doesn’t mean we shouldn’t overlook the weaknesses in this team though.” He gets a prize for a quadruple negative, but I cannot agree with him: moaning about the weaknesses of our national sports teams is one of life’s pleasures if you are English.
6. Finally, I come to a deeply sinister example. I recently learned that there is a website called Conservapedia, which describes itself as “An encyclopaedia with articles written from a conservative viewpoint.” I look forward to their mathematics section when they get round to it, which so far they haven’t: Grigory Perelman, a noted communist, claims to have solved the Poincaré conjecture, but he has REFUSED to publish his results in a conventional journal, in case they are scrutinized objectively and not just by a team of hand-picked liberal academics; the heat equation and the wave equation are examples of the now-discredited category of evolution equations; using a notion of creation and annihilation operators, quantum field theorists are starting to understand what the Bible could have told them all along; etc. etc. Unfortunately, it seems that Conservapedia is not a Wiki-style site — I can’t think why not — so we mathematicians cannot help them build up a decent mathematics section.
Just for fun I thought I’d have a look at what they have to say about Richard Dawkins. Some of their criticisms were only to be expected: he supports evolution, is a noted atheist, and so on. But I was taken aback by one of them: he is insufficiently solid in his support for Hitler. Here is the passage that shows this (at least as the article was on October 13th 2009 — I hope this blog’s portion of cyberspace is sufficiently disconnected from Conservapedia’s that it will remain that way, but if not, it will be interesting to see whether it can still be found in the history of the revisions of the article):
Dawkins’ Comment Regarding Adolf Hitler
When asked in an interview, “If we do not acknowledge some sort of external [standard], what is to prevent us from saying that the Muslim [extremists] aren’t right?”, Dawkins replied, “What’s to prevent us from saying Hitler wasn’t right? I mean, that is a genuinely difficult question. But whatever [defines morality], it’s not the Bible. If it was, we’d be stoning people for breaking the Sabbath.”
The interviewer wrote, regarding the Hitler comment, “I was stupefied. He had readily conceded that his own philosophical position did not offer a rational basis for moral judgments. His intellectual honesty was refreshing, if somewhat disturbing on this point.”
Well, in one sense it is a genuinely difficult question I suppose. HITLER WASN’T RIGHT. HITLER WASN’T RIGHT. HITLER WASN’T RIGHT!! Hmm, nothing seems to be preventing me from saying that, and I say it without apology. But why was Dawkins not offended by the suggestion that something should be preventing him from saying that Muslim extremists aren’t right**? Perhaps, being a somewhat literal-minded scientist, he was having thoughts such as this: “Well, it does at first seem as though there is nothing to prevent my saying that Muslim extremists aren’t right, but I can imagine circumstances under which I would be so prevented. For example, if I was kidnapped by al-Qaeda and held at knifepoint, then it would be reasonable to say that I was effectively prevented from drawing attention to the lack of rightness of their views. Or for a less artificial example, if I was in the middle of a dinner party with some of my super-bright liberal atheist friends, then I might be prevented by embarrassment from saying that Muslim extremists weren’t right: after all, the statement is normally held to be too obvious to be worth saying, so I might be thought to be protesting too much. Yes, on reflection, this is a genuinely difficult question. And similar difficulties apply if I substitute Hitler for Muslim extremists.”
So much for Dawkins. The motives of his interviewer, and of Conservapedia for gleefully reporting the interview, cannot be explained so innocently. The only reasonable explanation for the interviewer being “stupefied” is that he regarded it as manifestly and shockingly wrong to say that Hitler wasn’t right. In other words, the interviewer was not just a neo-Nazi, but so convinced of his/her neo-Nazism that a contrary view was stupefying. And Conservapedia wholeheartedly agrees with this. We live in worrying times.
As a postscript, let me deal with a small technical point concerning the last example. It might seem as though “What is to prevent us from saying that Hitler wasn’t right?” has just the two negatives “prevent” and “not”. So why do I call it a triple negative? The answer is that I am talking morality rather than semantics in this example. Hitler is the embodiment of evil, so we can build up as follows:
(i) Hitler — bad.
(ii) Saying that Hitler was right — bad.
(iii) Saying that Hitler wasn’t right — good.
(iv) Preventing someone from saying that Hitler wasn’t right — bad.
(v) Implying that one ought to be prevented from saying that Hitler wasn’t right — bad.
(v) Conservapedia — bad.
Needless to say, if anyone else has some good examples of triple negatives, I’d be delighted to hear them.
**Most embarrassingly, when I posted this, I wrote “are right” instead of “aren’t right” here. My only consolation is that I noticed before it was pointed out to me.