Occasional reflections on Life, the World, and Mathematics

The first statistician

I like to share with beginning statistics students the aphorism of C. R. Rao

Uncertain knowledge + knowledge about the extent of uncertainty in it = Useable knowledge

And it just occurred to me that the extreme limit of this dictum is that if you are infinitely uncertain, if nothing is knowable, the knowledge of that fact in itself is highly useable. The realisation of which would seem to make Socrates the first statistician:

Well, although I do not suppose that either of us knows anything really beautiful and good, I am better off than he is – for he knows nothing, and thinks that he knows. I neither know nor think that I know. In this latter particular, then, I seem to have slightly the advantage of him. (Apology, translated Benjamin Jowett)

From a collection of aperçus by Howard Brubaker in the May 16, 1936 edition of the New Yorker:

The Supreme Court judges are having long, deep thoughts about the Guffey Act. They know it is unconstitutional, but they can’t seem to think of the right reason.

I don’t know anything about Abercrombie & Fitch. I know it’s a chain of stores that sell clothes, I’m sure I’ve seen their stores, but I’ve never been inside them. Everything I know about their brand comes from an 80-year-old satire by James Thurber that begins

 I always try to answer Abercrombie & Fitch’s questions (in their advertisements) the way they obviously want them answered, but usually, if I am to be honest with them and with myself, I must answer them in a way that would not please Abercrombie & Fitch. While that company and I have always nodded and smiled pleasantly enough when we met, we have never really been on intimate terms, mainly because we have so little in common. For one thing, I am inclined to be nervous and impatient, whereas Abercrombie & Fitch are at all times composed and tranquil…

Take the one recently printed in an advertisement in this magazine. Under a picture of a man fishing in a stream were these words: “Can’t you picture yourself in the middle of the stream with the certain knowledge that a wise old trout is hiding under a ledge and defying you to tempt him with your skillfully cast fly?” My answer, of course, is “No.” Especially if I am to be equipped the way the gentleman in the illustration is equipped: with rod, reel, line, net, hip boots, felt hat, and pipe. They might just as well add a banjo and a parachute….

I was reminded of this in reading about a case that is currently being considered by the US Supreme Court, in which Equal Employment Opportunity Commission has charged the company with religious discrimination, after it refused to hire a Muslim woman, because her headscarf would conflict with the Abercrombie dress code. (As the law would require reasonable accommodation to be made for religious observance, the legal case turns on the relatively uninteresting question of whether the district manager who made the decision, and who reportedly said  “if we allow this then someone will paint themselves green and call it a religion”, is really the last man left in America so uncontaminated by media representations of Muslims that he is not even aware that Muslim women often wear headscarfs as part of their religious practice.)

According to court documents,

Abercrombie described its brand as “a classic East Coast collegiate style of clothing.” When Elauf applied for a job in 2008, the Look policy included prohibitions on black clothing and “caps”; these and other rules were designed to protect “the health and vitality of its ‘preppy’ and ‘casual’ brand.” As Justice Alito put it during oral arguments, Abercrombie wants job candidates “who [look] just like this mythical preppy or … somebody who came off the beach in California.”

From fly-fishing in an east-coast stream to a beach in California. You’ve come a long way, baby!

Do all babies look alike?

And if not, why don’t they have any privacy rights with regard to their photographs?

Here is the illustration provided by the BBC on its home page for a report on the decision to approve fertility procedures that take genetic material from three different people:

Not a three-parent baby, but they are expected to look similar to this one.

Not a three-person baby, but manufacturers promise they will look similar to this model.

One wonders what purpose this photograph serves. Are there readers who see the headline and think, “Wait, babies, I’ve heard of them. Can’t quite remember what they look like…” In what sense is this an illustration of the article? It’s not even a newborn infant. They might as well have shown a 90-year-old lady, because making three-person babies inevitably leads to the eventual creation of three-person 90-year-olds. It might be even more relevant to show an elderly person, because that’s the goal: the purpose of the procedure is to improve the health and longevity of the humans so conceived.

They could have used their stock photograph of weirdly lighted lab technicians pipetting something into a test tube instead.

I’m wondering, who is this baby who is standing in for a “three-person baby”? I’m used to seeing children have their features blurred out in news photos. But, of course, this one was presumably a “volunteer” model. One baby can stand in for all babies. (As long as it’s white, of course.)

I was amused by the comments made by right-wing American TV news personality Bill O’Reilly, who referred to his time in the Falklands “war zone” because he reported on an unruly protest in Buenos Aires after the war ended. He supported his position by quoting a NY Times report that referred to a police officer firing five shots, without mentioning that the shots were fired “over the heads of fleeing protestors”.

Rich Meislin, the Times reporter who wrote the article, said on Facebook that as far as he knew no demonstrators were shot or killed by police that night. On Monday, Mr. O’Reilly said he was just reading clips from the piece during the Media Buzz interview and that official reports on casualties there were difficult to obtain.

One could imagine that in a dispute over the exact number of protesters shot or killed you might say that the official reports were “difficult to obtain”. It seems like an odd defence when people are claiming that the exact number was zero, since, of course, in that case there would be no reports on casualties to obtain. “I do remember that there was tension between the authorities and the crowd,” [CBS correspondent Charles Gomez] said, but added that he “did not see any bloodshed.”

Humans have a separate system for unconsciously apprehending the numbers of items under about four, called subitizing, that is distinct from the conscious process of counting. The idea of “counting” one or two items seems ridiculous, and counting zero items exaggerates the comic effect. I was reminded of a scene in the second volume Douglas Adams’s Hitchhiker’s Guide to the Galaxy series, The Restaurant at the end of the Universe. Ford Prefect and his friends have accidentally stowed away on a space ship programmed to crash into the local sun (as part of the light show for a rock concert). Zaphod Beeblebrox yells “Ford, how many escape capsules are there?”

“None,” said Ford.

Zaphod gibbered.

“Did you count them?” he yelled.

“Twice,” said Ford.

 Update: In another interview O’Reilly continued to conflate the Falklands War with the unruly demonstration in Buenos Aires:

“A lot of people died,” said O’Reilly, nodding his head. “You bet.”

“On both sides, both the British and the Argentines,” Browne said, appearing to reference the broader war rather than the protests.

“Nine hundred deaths on the Island,” O’Reilly said. “And we don’t know how many in Buenos Aires.”

We don’t know how many. The number is generally reckoned to be around… zero.

Powerless

The Oxford Mail moans in a recent headline that the Oxford city council is “powerless to prevent the spread of graffiti”.

MORE than 1,000 cases of graffiti scrawled on private property are blighting Oxford…

That sounds pretty bad. What sort of extraordinary, perhaps dictatorial, powers would the council need to be granted in this state of emergency, to enable them to rescue us from this blight? The article continues that the graffiti cannot be removed

 because firms are not paying to have them removed, the city council’s graffiti team has warned.

“But 99 per cent of them don’t pay because of the cost and they think they shouldn’t have to.

“There are more than 1,000 jobs on my database we can’t touch –and we have the equipment and the training to deal with them.”

The council charges £27 an hour on top of £15 per square metre for the removal of graffiti from privately-owned property.

It seems strange to formulate this in terms of “lacking powers”. My guess is that if they considered it to be a sufficient problem for the public welfare that they wanted to use tax money to fund the cleanup, very few property owners would wish to hinder them. They lack the power to force the property owners to pay because most of the public agrees that, having been victimised by the graffiti writers already, the property owners don’t deserve to be punished with the compulsory expense of cleaning it up.

This is the city council acting like a private company, advertising its graffiti-cleaning service. But a private company would never think to formulate its inability to attract customers willing to pay £27 an hour for its property-beautification schemes as “we are powerless to carry out our plans because 99 per cent of our potential customers don’t hire us because of the cost and they think they shouldn’t have to,” and whine about how unreasonable that is, because “we have the equipment and the training”.

I just read a popular book on chemical elements, The Disappearing Spoon by Sam Kean. It was very entertaining, and seemed quite credible and clear, even if slightly fuzzy on the quantum mechanics. There was one claim that I took exception to, though:

The length of a day is slowly increasing because of the sloshing of ocean tides, which drag and slow earth’s rotation. To correct for this, metrologists slip in a “leap second” about every third year, usually when no one’s paying attention, at midnight on December 31.

Is there any time in the year when people are paying more attention to the time exact to a second than precisely at midnight on December 31? Does he think people would notice an extra second if it were interpolated at noon on July 7? I always assumed they did it at the one time of year when people would notice an extra second precisely because they want to be noticed. “Never fear, humble citizens. While you sleep, we are looking after your time.”

Come home to Israel…

Binyamin Netanyahu is back to grandstanding as king of the Jews — just days after announcing that he would be speaking to the US Congress as “a representative of the entire Jewish people” — telling European Jews that they will always be victimised by non-Jews as long as they stay in Europe, so they should move to Israel, where they can be victimised by fellow Jews instead. But at least in Israel Jews can pray in peace without armed police protecting them; because in Israel the armed police will break up their prayer sessions and arrest them (if they’re women and not Orthodox).

Antinomianism — the belief that the intrinsic holiness of believers liberates them from petty concerns with moral, much less humane, behaviour — often seems depressingly prevalent. At least as prevalent as the mirror-image disposition that many believers attribute to atheists, that if there is no God to set rules, all things are permitted.

I was just reading The Wonderful Wizard of Oz for the first time, and I was struck by the morality of the Tin Woodman, who hopes that the Wizard will bestow upon him a heart. Of course, the running joke is that the everyone is going to the Wizard to get something that they already have. The Scarecrow wants brains, even though he repeatedly proves himself the cleverest of the company; the Cowardly Lion wants courage despite the fact that he repeatedly performs heroic and self-sacrificing deads. The Tin Woodman, although he is made of metal and lacks a heart, is the most tenderhearted of all. At one point he rusts himself through crying over a beetle that he steps on accidentally.

“This will serve me a lesson,” said he, “to look where I step. For if I should kill another bug or beetle I should surely cry again, and crying rusts my jaws so that I cannot speak.”

Thereafter he walked very carefully, with his eyes on the road, and when he saw a tiny ant toiling by he would step over it, so as not to harm it. The Tin Woodman knew very well he had no heart, and therefore he took great care never to be cruel or unkind to anything.

“You people with hearts,” he said, “have something to guide you, and need never do wrong; but I have no heart, and so I must be very careful. When Oz gives me a heart of course I needn’t mind so much.”

Replace “heart” by “grace”, and you see that far too many of the devout believe they have been to Oz.

Are you “cultural”?

A while back I remarked on a tic shared by politicians and political journalists, of designating certain people and their voting choices as “demographic”. Now the RCMP have disrupted a planned mass shooting at a Halifax mall.

wouldn’t characterize it as a terrorist event. I would classify it as a group of individuals that had some beliefs and were willing to carry out violent acts against citizens,” Royal Canadian Mounted Police Commanding Officer Brian Brennan said.

Now, you may be wondering, how do “violent acts against citizens” carried out by “individuals that had some beliefs” — I’m guessing he means to imply that the acts were supposed to be promoting those beliefs somehow — differ from what you or I would call “terrorism”?

He would not specify what those beliefs were, saying simply that “they were not culturally based.”

Got that? “Terrorists” carry out their violent acts in furtherance of beliefs that are “culturally based”. Wanton violence to promote non-culturally-based beliefs are lamentable, but not terrorism.

I wonder if he has any particular cultures in mind?

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