Paradoxes on Cracked.com

Cracked.com asked its readers to send in posters with their favourite paradoxes, which it then published a month ago. I'd meant to post this earlier, but it doesn't matter. Some of these paradoxes have been around for a few millennia. Here's the link:
http://www.cracked.com/photoplasty_2112_20-insane-thought-experiments-thatll-blow-your-mind/

I like entry number 8.

Finding paradoxes where they aren't

"Ik probeer zelfs paradoxen te vinden waar ze er niet staan." (I'm even trying to find paradoxes where they aren't)

Probably unintentional paradox (?) by rector Rik Torfs of K.U.Leuven on a T.V. programme, where he talks about reading the Gospel texts afresh. If the paradoxes aren't in a particular place, you cannot possibly find them in that place. But maybe you can try to find them there.

Audi commercial defeats its own message

This is the first blog post after a long period of radio silence. Sorry about that. I have lots more paradoxes in store, in fact. Speaking of radio, for instance, on the Flemish radio station Radio 1, one can hear a commercial these days for Audi, which says that Audi's commercials needn't mention the brand name at least six times, as commercials for other brands typically do. Only, guess how many times the brand name Audi is mentioned during that commercial? That's right, six times:

Onderzoek heeft aangetoond dat een doeltreffende spot minstens zes keer het merk vermeldt en dat de voice-over roepend boven de muziek moet uitkomen. Behalve bij Audi[1]. Want volgens onderzoek volstaat het om tijdens de Audi[2] Days één keer te zeggen dat er uitzonderlijke voordelen zijn op het hele Audi[3]-gamma. Op de Audi[4] Q5 met Packs Prestige en Design krijgt u bijvoorbeeld 9315 euro voordeel.
De Audi[5] Days. Nu en nog tot 30 mei. Info en voorwaarden op Audi[6].be.

Did no-one at Audi Import Belgium HQ check the commercial for false information?

Strange kind of support for multiple regression analysis

Perhaps I've completely misunderstood the point made by Richard Nesbitt, professor of psychology at Michigan University, but the arguments he adduces against multiple regression analysis are in fact, it seems to me, arguments for it, paradoxically so. I will let you read a stretch from the transcript of the conversation with him on Edge:

"The thing I’m most interested in right now has become a kind of crusade against correlational statistical analysis—in particular, what’s called multiple regression analysis. Say you want to find out whether taking Vitamin E is associated with lower prostate cancer risk. You look at the correlational evidence and indeed it turns out that men who take Vitamin E have lower risk for prostate cancer. Then someone says, "Well, let’s see if we do the actual experiment, what happens." And what happens when you do the experiment is that Vitamin E contributes to the likelihood of prostate cancer. How could there be differences? These happen a lot. The correlational—the observational—evidence tells you one thing, the experimental evidence tells you something completely different. 

In the case of health data, the big problem is something that’s come to be called the healthy user bias, because the guy who’s taking Vitamin E is also doing everything else right. A doctor or an article has told him to take Vitamin E, so he does that, but he’s also the guy who’s watching his weight and his cholesterol, gets plenty of exercise, drinks alcohol in moderation, doesn’t smoke, has a high level of education, and a high income. All of these things are likely to make you live longer, to make you less subject to morbidity and mortality risks of all kinds. You pull one thing out of that correlate and it’s going to look like Vitamin E is terrific because it’s dragging all these other good things along with it. 

This is not, by any means, limited to health issues. A while back, I read a government report in The New York Times on the safety of automobiles. The measure that they used was the deaths per million drivers of each of these autos. It turns out that, for example, there are enormously more deaths per million drivers who drive Ford F150 pickups than for people who drive Volvo station wagons. Most people’s reaction, and certainly my initial reaction to it was, "Well, it sort of figures—everybody knows that Volvos are safe." 

Let’s describe two people and you tell me who you think is more likely to be driving the Volvo and who is more likely to be driving the pickup: a suburban matron in the New York area and a twenty-five-year-old cowboy in Oklahoma. It’s obvious that people are not assigned their cars. We don’t say, "Billy, you’ll be driving a powder blue Volvo station wagon." Because of this self-selection problem, you simply can’t interpret data like that. You know virtually nothing about the relative safety of cars based on that study.
I saw in The New York Times recently an article by a respected writer reporting that people who have elaborate weddings tend to have marriages that last longer. How would that be? Maybe it’s just all the darned expense and bother—you don’t want to get divorced. It’s a cognitive dissonance thing. 

Let’s think about who makes elaborate plans for expensive weddings: people who are better off financially, which is by itself a good prognosis for marriage; people who are more educated, also a better prognosis; people who are richer; people who are older—the later you get married, the more likelihood that the marriage will last, and so on.
The truth is you’ve learned nothing. It’s like saying men who are a somebody III or IV have longer-lasting marriages. Is it because of the suffix there? No, it’s because those people are the types who have a good prognosis for a lengthy marriage.
A huge range of science projects are done with multiple regression analysis. The results are often somewhere between meaningless and quite damaging."

Multiple regression analysis, as I understand it, is precisely a technique which the researcher can use to find out whether a factor shown to correlate with an observed outcome really makes an independent contribution to that outcome or, rather, whether it is 'parasitic' on other more important factors. The technique lets you see what happens when you keep these other factors constant: for instance, will, everything else being equal, make spending more money on your wedding still make your marriage last longer? The examples Nesbitt gives to discredit multiple regression analysis (people's Vitamin E consumption, the type of car people drive, the amount of money people spend on their weddings, etc.) in fact perfectly showcase the technique's merits.

The mindfulness paradox

My son has been taught at school how to eat things mindfully: instead of wolfing your food down in front of the tele, you should concentrate on the food's smell, taste, texture, you should chew consciously, etc. etc. Mindfulness has been a bit of a hype for some time now, but it's also prone to paradox.

I've noticed at the lunch or dinner table that when I instruct my son to eat something mindfully, he is so concentrating on being mindful ("okay, I need to slow down, chew ostentatiously, close my eyes, oh, and make some of those 'mmm...' noises, ...") that he is mindfully being mindful but not mindfully enjoying his food. 

I wonder if it is ever possible to tell yourself to do something mindfully and thereby actually be doing that thing mindfully. In other words, it may be that you can only perform an action mindfully if you're not concerned with mindfulness in the first place.

Self-referential first aid kit

Yesterday's xkcd cartoon was a brilliantly simple case of absurd self-reference.

Is the notion of smashing glass in order to retrieve a 'glass repair kit' also paradoxical? I don't know.

Variant of the Liar Paradox

Each day, except on Wednesdays, when children have the afternoon off, my son's teacher checks in class which kids stay on school for lunch and whether they signed up for a hot meal or not. By now, he pretty much knows the lunch habits of his pupils and so this morning, when arriving at Maitée on his list, he said, "Okay, I know Maitée is going to say now she's going to eat sandwiches", at which point Maitée simply replied with "Yes." My son was quick to point out to his teacher that this was a paradox. Reporting this to me at lunchtime today, he also said the teacher looked in his direction right after his exchange with Maitée, since the teacher also knows by now that my son is a paradox enthusiast.

The paradox can probably be resolved
A. with the help of simple pragmatic theory, which makes a distinction between (i) what is said (literally) and (ii) what is meant by an utterance,
B. and by pointing out that the verb say can be used vaguely to refer either to verbatim statements or to what one means by a linguistic utterance. (That's why, if I ask you whether you'll come over to my place tonight and you just say "Yes", I can say to you tomorrow, in case you didn't show up, "But you said you'd come over," even if you didn't really say "I'll come over.")

Update (29/06/2018):
My son was perhaps a bit too eager to think there was a paradox involved. Maybe the reply "yes" is just ambiguous, i.e., between "Yes, Sir, you're right to assume that I'm going to say I'll have a sandwich lunch" and "Yes, Sir, I'll have a sandwich lunch". Still, what's vaguely (or, who knows, truly) paradoxical here is that when the "yes" is taken to mean the former, the reply actually defeats itself, in the sense that agreeing with the teacher that he has just made a correct prediction is not the same thing as explicitly agreeing with the implicit question "Are you going to eat sandwiches?". So, Maitée's reply should have been: "Yes (you're right), yes (I'm going to eat sandwiches)". With just a single "yes", agreeing with the teacher's full claim corresponding to the entire sentence, the teacher's prediction is both correct and false.

The Game of Set Paradox

I often play a game of Set with my children and invariably lose to my 12-old daughter, whose brain seems to be working like a super computer. In the game, sets are triplets of cards which, all three of them, have to either match or be different for each parameter (number, filling in, colour and shape). In the picture above, I can see at least four sets:

1. the three full red diamonds, the two full green 'sausages', and the single full purple squiggle
2. the three full green squiggles, the two empty red 'sausages', and the single striped purple diamond
3. the three empty red 'sausages', the two full green 'sausages', and the single striped purple 'sausage'
4. the single full purple squiggle, the single empty purple 'sausage', and the single purple striped diamond

The aim of the game is to find sets faster than your opponent(s) can. Now here's the paradox: it seems to me you have to concentrate to find sets, but it is precisely by concentrating that you fail to find sets 'accidentally'. Maybe it's not a true paradox. It's just that you have to focus, but not too hard.

Update: there are two more sets among the cards. Can you find them? (Hint: for one of them, look at the box!)

   

You're rare!

My son said to me yesterday he may have an example of a truism which at the same time is a paradox. He didn't use the word 'truism' -- he spoke of "een waarheid als een koe", which is Dutch for, literally, 'a truth like a cow', that is, an obvious truth. But he did use the word 'paradox'. He's an avid paradox spotter and collector. The example in question is this:

Someone in class saying to someone else in class: "you're rare." (Dutch: jij bent zeldzaam)

As my son pointed out, this is obviously true, since everyone is unique, hence by necessity also rare. (This is a simple matter of scalar reasoning.) But 'rare' doesn't quite hit the mark in describing a person, as this qualification implies that there is more than one similar specimen (although there aren't many). So here's the paradox: since everyone is unique, they're obviously rare, but because they are truly unique, they can't be said to be rare!