You can’t have your pocket money and save it too

My 13-year old child received the following maths problem in school:

Paul saves 4/15 of his pocket money and spends 5/12 on topping up his mobile phone. What fraction of his pocket money does he have left?

(The question was part of a sheet from Cambridge Essentials.) With a PhD in mathematics, I usually feel myself adequately qualified to deal with school maths questions, but this one stymied me. I have decided to stop blaming myself, though. This question is

  1. misleadingly formulated;
  2. ambiguous;
  3. exceptionally dependent on hidden cultural assumptions.

Let’s start with number 1. Who counts fractions of pocket money? This makes about as much sense as asking

Paul and Paulina order a pizza together. Paul eats 0.375 pizza. Paulina eats 0.5 pizza. How much pizza do they take home?

It’s like you were trying to teach children about toothbrushes, and showing them how useful they are by having them use the toothbrush to clean the floor. Sure, you can do it, but it’s really not the tool anyone would choose to use, and it doesn’t give them a fair impression of what it could really be good for.

Okay, maybe Paul lives in a socialist country, where “from each according to his ability”, so that prices are stated as fractions of your income. But it gets worse. Point 2: My first thought was that Paul had spent 11/15 of his money on other things — probably drugs — and now had to top up his phone, which cost 5/12 of his pocket money. But he only has 4/15, which is smaller, so he needs to go into debt by 5/12-4/15=3/20. Okay, that didn’t seem likely. So then I figured that the 5/12 was intended to be a proportion of the 4/15 that he has remaining. Then it would at least make a little bit of sense to express it as a fraction. (Extreme socialism: Prices are all formulated as a fraction of the money you have in your pocket. Customer: How much? Merchant: How much you got?) So the amount remaining is 4/15*7/12=7/45.

But on further discussion with my partner I recognized that neither of these versions was what was intended by the people who set the question. I was thinking in terms of a model of sequential spending: The money you “save” is the money you have available to spend the next time an expense arises. The question, though, presumes that money that is “saved” is being saved from yourself. Whereas I would think that the money you “save” is part of — or possibly identical with — the money you “have left”, you were supposed to think of spending and saving as just two different ways of losing money. You add the two together to get a total loss of 4/15+5/12=17/30, leaving Paul with 13/30 pocket money units to spend on non-mobile-phone and non-banking expenses. (Probably drugs.)

Of course, I’m overthinking this. The point is that you’re not supposed to think. You’re just supposed to see two fractions and add them, because that’s what you’ve been learning to do. It’s a kind of pseudo-applied maths problem that is quite common — even at university level — where any actual thought about the issues involved will only penalise you. It’s a puzzle, where you’re supposed to read through the irrelevant verbiage to get to the maths problem that has been concealed there.

I call this “adding up the temperatures”, after the story by Richard Feynman (in Surely You’re Joking, Mr Feynman) about his time evaluating textbooks for the state of California. He describes a problem from one elementary school textbook:

Red stars have a temperature of four thousand degrees, yellow stars have a temperature of five thousand degrees, Green stars have a temperature of seven thousand degrees, blue stars have a temperature of ten thousand degrees, and violet stars have a temperature of … (some big number).

John and his father go out to look at the stars. John sees two blue stars and a red star. His father sees a green star, a violet star, and two yellow stars. What is the total temperature of the stars seen by John and his father?

Feynman points out that the temperatures aren’t really right, and that there is no such thing as green and violet stars, which he is willing to tolerate, but then blows up at the sheer pointlessness of adding up temperatures. Like the above, it only looks like an application of the mathematical tool being presented (in this case addition).

But I’m even more amazed at the absurdity of the story. How is it possible that John sees only 3 stars, his father sees 4, and they see completely different stars? But the point is, in school mathematics you’re supposed to do, not think.

Foreigners in Britain and Germany

Many years ago, when I was hitchhiking through the US, I met a guy at a highway rest stop who, for no particular reason that I could discern, was agitated about foreigners. (My accent in English strikes some Americans as vaguely foreign, even though it is unmistakably American to any non-American native English speaker.) But I was surprised about why he was angry. I had always assumed that animus toward immigrants was directed at transients who have no roots or attachment, don’t speak English, are really oriented toward their home country. But this guy thought it was great to have people come and do unpleasant work for low pay for a few years, as long as they move on. What he didn’t like were immigrants who come and remain permanently.

Apparently the current UK government agrees. People like me are a failure of the system. Soon after they came into power the government announced the goal of “breaking the link between temporary and permanent migration.” Now, as net immigration ignores the government’s arbitrary goals and continues to rise, they are growing desperate, even forcing out highly skilled and expensively recruited foreigners who thought they had immigrated. They have introduced draconian fines and even prison sentences for landlords who rent to illegal immigrants; since landlords are hardly equipped to judge people’s immigration status, the effect (possibly unintentional) will be to make life difficult for everyone who looks or sounds foreign.

Most of Europe decided that “temporary workers” isn’t a category that you can reasonably force people into. As Max Frisch famously commented on the European experience of the 1950s through 1970s, “Wir haben Arbeitskräfte gerufen, und es sind Menschen gekommen.” (“We called for workers, but human beings came.”)

The contrast to Germany is stark. Universities are switching much of their lecturing to English, in an effort to attract bright students from around the world to study in Germany. UK universities scrabble for foreign students, too, but the justification is primarily mercenary: non-EU student fees are uncapped — typically they pay around £20,000 a year, whereas EU nationals pay £9,000. German universities, on the other hand, don’t charge fees. 

We could call it plutocratic tolerance: Germans are, by and large, willing to live with foreigners as long as they can profit from them. Britons are willing to exploit foreigners economically, but only if they don’t have to live with them. (The Home Secretary has particularly identified students as people whose otherwise welcome money is tainted by their propensity to continue existing after they have spent it, and to impose their existence on the long-suffering British. “Universities should now develop sustainable funding models that are not so dependent on international students” she said.) Next year’s EU referendum will force the population to decide which of the famous “British values” — greed or xenophobia — has priority.

This issue is not identical with, but obviously not entirely distinct from, the disgusting British government response to the refugee crisis in southern Europe — a combination of “it’s not my problem” and pompous moralising about the moral hazard of encouraging desperate people to make perilous journeys. Angela Merkel has resolutely refused to pander to anti-foreigner sentiment, and has even managed to pressure the UK into taking some small measure of responsibility for taking in some refugees — even if they’ll never accept that they, of all Europeans, bear the most direct responsibility for the Syrian disaster, which is part of the long-term aftermath of Tony Blair’s splendid little war in Iraq.

National typography

jekyllandhyde

I noticed this sign the other day in the Ruhr city of Hagen. It’s an Irish pub whose sign uses a sort of Gothic script that otherwise is used in Germany as a marker of conservative German gastronomy (as on this restaurant in Munich, since 1800), and that is used on pubs and restaurants elsewhere simply to signify “German”, particularly beer. Here, it’s Irish for some reason.

And on top of that, this Irish pub is named for a quintessentially London character (or is it two characters?) in a novel by a Scottish author. At least they got the shamrock right.

The man with the Kalashnikov

Having been on a Thalys to Paris yesterday I took particular interest in the aborted attack the previous day. We hadn’t heard anything about it, but a conductor told us a bullshit story about how the news media got the story all wrong: the attacker was actually being followed by police, the capture was planned, and he didn’t have firearms.

But here’s what I’m wondering. According to the NY Times,

Less than an hour away from Paris, a French passenger got up from his seat to use the toilets at the back of the carriage. Suddenly, in front of him rose a slightly built man. Across the man’s chest, in a sling, was an automatic rifle of the kind favored by jihadists the world over: an AK-47.

The passenger threw himself on the man. The gun went off, once, twice, several times. Glass shattered. A bullet hit a passenger.

The man with the gun kept going down the carriage, holding his AK-47 and a Luger pistol. In a pocket was a sharp blade capable of inflicting grievous harm. He had at least nine cartridges of ammunition, enough for serious carnage.

So, they’re heroes. But if this had happened in the US, would they be the ones in prison? After all, up until the point where they attacked him, he was just another open-carry enthusiast celebrating his constitutional right to keep and bear arms. Once he was attacked, of course, by rowdy foreigners, it is perfectly understandable that he started firing. And even if he did fire a single shot first (the news reports disagree on this point), well, how could they have known that it wasn’t self defence. They should have waited until he’d shot at least two people before infringing on his civil rights.

Maybe that’s why they don’t have trains in Texas… (Actually, that’s not entirely true.)

“Serving the purposes of the Israeli apartheid and colonial regime”

The American Jewish reggae singer Matisyahu has been expelled from a Spanish music festival, for refusing to issue a statement in support of a Palestinian state. Apparently such loyalty oaths are required of suspect persons, such as Jews. His silence, they said, serves “the purposes of the Israeli colonial and apartheid regime”.

This buttresses the view that BDS has a significant dollop of antisemitism in its ideological matrix, even if not every BDS supporter is antisemitic (and not everyone motivated partly by antisemitism is entirely or even consciously motivated by antisemitism).

This takes me back to 2007, when one UK academic union, the National Association of Teachers in Further and Higher Education (since melded into the University and Colleges Union (UCU)) couldn’t find any more relevant challenge to higher education in the UK than a boycott of Israeli academics who do not “publicly dissociate themselves” from Israeli “apartheid policies”.

I immediately recognised a problem: What is the appropriate form for expressing such dissociation? And how would we test whether the self-criticism was sincere, or merely careerist dissimulation. After all, we wouldn’t want crypto-Zionists sneaking in to British universities and scientific conferences, infecting them with the taint of racism and colonialism. Leaping into the breach, I composed a form to enable the aspiring good Israeli to have his anti-Zionist bona fides tested and confirmed by the proper authorities.

Primary sex ratio, the short version

Five months after our article with Orzack et al. appeared in PNAS, showing that the primary sex ratio (the fraction of boys conceived) is close to 50%, contradicting centuries of supposition that it was substantially higher (more male-biased), Bill Stubblefield, Jim Zuckerman and I have published a popular account of the research in Nautilus. It was an interesting experience, the back and forth with an editor to make something comprehensible and gripping for a general audience.

I didn’t end up exactly as we would have liked, but it was probably better — as an effort to explain the science and the background to a general audience — than what we would have produced entirely on our own. The layout and graphics are also very well done.

It’s now been condensed down to three paragraphs on Gizmodo. They even condensed the illustration.

“I wish that I was a film comedian”

I’ve just been reading David C. Cassidy’s updated version of his Heisenberg biography, titled Beyond Uncertainty. He reports that in May 1925 Wolfgang Pauli, who was struggling together with Heisenberg to apply the new quantum theory to calculate the spectral lines of hydrogen, wrote in a letter

Physics is at the moment once again very wrong. For me, in any case, it is much too difficult, and I wish that I was a film comedian or something similar and had never heard of physics.

Here is a challenge for a young postmodernist film-maker: Produce the silent-film comedies that Wolfgang Pauli would have made, had he never heard of physics (or abandoned physics? Presumably they would have been different…)

Alternatively, a science fiction author could write about a universe governed by Charlie Chaplin’s quantum mechanics.

Gender asymmetry…

… and the “pussification of America”. This term came up in an article in Slate about the decision by the American retailer Target to remove the gender attributions from its toys. Since I had children I’ve been amazed at the extent to which children’s clothes and toys have become gender-specific since I was a child in the 1970s. And it amazes me as well how closely identified the colours pink and blue have come to be with girls and boys, despite the fact that it’s an obviously artificial (and quite recent) tradition. (Jo B. Paoletti has written a book on the subject, Pink and Blue: Telling the Boys from the Girls in America.) I have also long been intrigued by the way people seize upon even the most tenuous evidence that “science has proved” the validity of this or that gender stereotype.

Anyway, someone set up a honeytrap fake Target customer service Facebook account to collect the outrage that some people (men and women) were spewing over this issue. As chronicled in AdWeek, there are some biblical arguments, like

God made a difference between male and female as there should be. I would never give a boy a barbie doll. It’s not chauvinistic but the BIBLE says women are the weaker vessel I Peter 3:7 so many people are making their boys the weakest link and making their daughters manly.

(Interesting that “as there should be”. Not that she’s simply going to accept on faith that God got this one right. But she approves.) And many rants against PC

You guys should listen to the people who spend money in your stores, not the liberal, PC Complaint people that don’t have two cents to rub together.

I thought the PC Complaint people were wealthy elitists…

Anyway, I thought this comment was particularly telling:target-troll-12a

This is classic Simone de Beauvoir stuff. This is an American woman, outraged at a refusal to emphasise gender distinctions, because it will feminise America. Because America is a man, and if America can’t get a steady diet of trucks and toy soldiers when he’s a boy, he’ll be “pussified”. She’s not concerned that America will be toughened, or dickified, or whatever the corresponding word for “pussified” would be.

By their scandals you shall know them

I’ve always been impressed by German political scandals. More generally, I think that the quality of political scandals is an excellent indicator of the general health of a country’s political culture. More than 20 years ago I was in Germany during the Briefbogenaffäre, the “letterhead affair”, when the business minister and deputy chancellor Jürgen Mölleman was forced to resign after having used his department’s letterhead to tout a really banal business idea of his cousin (selling plastic chips to be used instead of one-mark coins to stick into supermarket trolleys as deposit), calling it a “pfiffige Idee” (clever idea). At the time I thought the whole thing seemed ridiculous, and simultaneously I was impressed at a political culture capable of being genuinely shocked by minor corruption. You couldn’t imagine an Italian minister being forced to resign over something like that.

Now there’s a new scandal, and Germany has again showed itself to be a country that takes democratic values seriously. About a week ago the blog netzpolitik.org, a major organ for German journalism about issues of internet freedom and privacy, received notification that the Generalbundesanwalt (GBA — basically, attorney general) that they were officially being investigated under suspicion of treason, for having published secret documents of the Bundesamt für Verfassungsschutz (BfV — the “Federal Agency for Defense of the Constitution”, the somewhat Orwellian name that Germany has bestowed on its internal secret police) relating to its new plans for mass internet surveillance with a special secret budget. The letter says that the investigation was provoked by a criminal complaint issued by the Verfassungsschutz.

What happened next was surprising. The Verfassungsschutz and the GBA were both strongly criticised in the press, with accusations that they were trying to stifle public criticism. Comparisons were drawn to the 1962 Spiegel Affair, a crucial event in postwar German history, where the government imprisoned journalists who had revealed secret documents showing weaknesses in German military preparedness, but was then forced to back down. Then the circular firing squad began. The justice minister criticised the decision as improper. The GBA office said they were obliged to act on the complaint from the BfV. The BfV said they only reported the facts to the GBA, they had no responsibility for the criminal investigation. Then the GBA fired back at the justice minister, saying his comments were an “intolerable interference” in the independence of the judicial system. Whereupon the justice minister fired him and had the investigation stopped.

It’s hard to imagine any important political or judicial figure in the UK or US losing his job because he was seen as being too aggressive in protecting state secrets against press freedom.

More uncertainty confusion

After commenting on the confusion between different clichés about physics and physicists in reporting about Angela Merkel, I feel obliged to note this sentence, from an article in the New Statesman about the fake traveller-tourist dichotomy:

The rush to witness the “authentic” ultimately alters the reality, in a kind of behaviourist butterfly effect.

Once again, physics clichés are being confounded. When you’re looking for an educated-sounding way to make the banal observation that it’s hard to observe things without getting mixed up in them, and so changing them, the cliché you want is “uncertainty”. The “butterfly effect” is what you cite when you’re bloviating about how small actions can have large long-term effects.

It’s slightly depressing for anyone who has hopes for general science education. It suggests that even if you come up with compelling ordinary-language metaphors for scientific concepts, the result will just be a salad of interchangeable expressions gesturing vaguely at an undifferentiated mass of physics woo-woo concepts.