Occasional reflections on Life, the World, and Mathematics

I was talking recently with an Australian, who expressed outrage that the Australian government allows mining companies to extract valuable resources from state-owned land, almost for free. Now, I have expressed similar sentiments in the past about the comparable US practice. But on reflection, it occurred to me that I couldn’t agree with the claim of another lunch participant that it is a “no-brainer” that the public should be taking a significant portion of the value realised from the resources extracted from public land.

If you think back to the time when US mining laws were first laid out — I think the main US law dates back to 1871 or so — the general view must have been, there are vast territories out there, where valuable minerals are buried, that would be of great use to the general economy, if only we could get them out of the earth. Rather than pay people to go search for them systematically, we offer that anyone who finds some and figures out how to get them to market, can keep the profits from their sale. Read the rest of this entry »

An example that is frequently cited in elementary statistics courses for the unreliability of survey data, is that when people are surveyed about their sexual history, men report more lifetime female partners on average than women report male partners. (A high-quality example is this UK survey from 1992, where men reported 9.9 female partners on average, while women averaged 3.4 male partners. It’s possible to tinker around the edges with effects of changes over time, and age differences between men and women in sexual relationships, but the contradiction is really inescapable. One thing that is quite striking in this survey is the difference between the cross-sectional and longitudinal pictures, which I’ve discussed before. For example, men’s lifetime numbers of sexual partners increase with age — as they must, longitudinally — but among the women the smallest average number of lifetime sex partners is in the oldest group.)

In any case, I was reminded of this when reading Stephen Greenblatt’s popular book on the rediscovery of De rerum naturae in the early 15th century by the apostolic secretary Poggio Bracciolini, and the return of Epicurean philosophy more generally into European thought. He cites a story from Poggio’s Liber Facetiarum a sort of jokebook based on his experiences in the papal court:

dumb priests, who baffled by the fact that nearly all the women in confession say that they have been faithful in matrimony, and nearly all the men confess to extramarital affairs, cannot for the life of them figure out who the women are with whom the men have sinned.

Last week I mocked the Spanish health authorities who refused to treat an Ebola-exposed nurse as a probable Ebola case until her fever had crossed the screening threshold of 38 degrees Celsius (or, in the absurdly precise American translation, 100.4 degrees Fahrenheit). Well, apparently the Centers for Disease Control in the US aren’t any better:

Before flying from Cleveland to Dallas on Monday, Vinson called the CDC to report an elevated temperature of 99.5 Fahrenheit. She informed the agency that she was getting on a plane, the official said, and she wasn’t told not to board the aircraft.

The CDC is now considering putting 76 health care workers at Texas Health Presbyterian Dallas hospital on the TSA’s no-fly list, an official familiar with the situation said.

The official also said the CDC is considering lowering the fever threshold that would be considered a possible sign of Ebola. The current threshold is 100.4 degrees Fahrenheit.

Most disturbing is the fact that they don’t seem capable of combining factors. Would it be so hard to have a rule like, For most people, let’s hold off on the hazmat suits until your fever goes above 38. But if you’ve been cleaning up the vomit of an Ebola patient for the past week, and you have any elevated temperature at all — let’s say 37.2 — it would be a good idea to get you under observation.

The tyranny of the 95%

The president of the National Academy of Science is being quoted spouting dangerous nonsense. Well, maybe not so dangerous, but really nonsense.

I found this by way of Jonathan Chait, a generally insightful and well-informed political journalist, who weighed in recently on the political response to the IPCC report on climate change. US Republican Party big shot Paul Ryan, asked whether he believes that human activity has contributed to global warming, replied recently “I don’t know the answer to that question. I don’t think science does, either.” Chait rightly takes him to task for this ridiculous dodge (though he ignores the fact that Ryan was asked about his beliefs, so that his skepticism may reflect a commendable awareness of the cognitive theories of Stephen Stich, and his need to reflect upon the impossibility of speaking scientifically, or introspecting coherently, about the contents of beliefs), but the form of his criticism left me troubled:

In fact, science does know the answer. Climate scientists believe with a 95 percent level of certainty (the same level of certainty as their belief in the dangers of cigarette smoking) that human activity is contributing to climate change.

Tracking through his links, I found that he’d copied this comparison between climate change and the hazards of smoking pretty much verbatim from another blog, and that it ultimately derived from this “explanation” from the AP:

Some climate-change deniers have looked at 95 percent and scoffed. After all, most people wouldn’t get on a plane that had only a 95 percent certainty of landing safely, risk experts say.

But in science, 95 percent certainty is often considered the gold standard for certainty.

[...]

The president of the prestigious National Academy of Sciences, Ralph Cicerone, and more than a dozen other scientists contacted by the AP said the 95 percent certainty regarding climate change is most similar to the confidence scientists have in the decades’ worth of evidence that cigarettes are deadly.

Far be it from me to challenge the president of the National Academy of Sciences, particularly if it’s the “prestigious” National Academy of Sciences, or more than a dozen other scientists, but the technical term for this is “bollocks”. Read the rest of this entry »

One-fifth of a teaspoon

I was brought up short by this odd sentence in a NY Times article on attempts to protect health-care workers treating Ebola patients:

At the peak of illness, an Ebola patient can have 10 billion viral particles in one-fifth of a teaspoon of blood. That compares with 50,000 to 100,000 particles in an untreated H.I.V. patient, and five million to 20 million in someone with untreated hepatitis C.

“One-fifth of a teaspoon” is an odd reference unit. I had to think a moment to realise that the reporter had presumably translated into American from Scientific the sentence

At the peak of illness, an Ebola patient can have 10 billion viral particles in one milliliter of blood.

As I discussed before, the partial conversion to the metric system has left fault lines between and within nations. And the attempt to cover over those cracks mechanically creates odd dissonances. Thus, the 19th century estimate of average human body temperature of 37 degrees Celsius (plus or minus about half a degree) gets turned into the incredibly precise sounding 98.6 degrees Fahrenheit. It makes as much sense as saying “28 grams of prevention are worth 454 grams of cure”.

If the reporter had thought about it, she might have translated less mechanically, writing “an Ebola patient can have 50 billion viral particles in a teaspoon of blood”. But that still leaves the weird resonance of “teaspoon of blood”. A millilitre can be water or blood or Martian atmosphere, but when I hear “teaspoon” I subliminally feel like it’s supposed to go in my tea, or cake, or soup. The thing that people like so much about these traditional units is their historical and narrative specificity, their attachment to human-scale measuring activities, but that also makes them awkward for transferring measurements between domains. I could state my height in furlongs, and my weight in grains, but I’ll just confuse people.

Before posting, I just wanted to check that I was right about the size of a teaspoon in grams. I asked Google, and received the information “1 Imperial teaspoon =5.91939047 millilitres”. So, first of all, I was surprised to learn — if indeed it is true — that the teaspoon has been standardised to the hundred-billionth of a litre. Second, I found the thought of “the imperial teaspoon” hilarious.

Can’t beat duct tape

I remember hearing a comedian — perhaps Garrison Keillor? — saying everything could be fixed with duct tape and WD40. “If it moves and it shouldn’t, duct tape it. If it doesn’t move and it should, use WD40.

I was reminded of this in reading today’s article in the NY Times about the Nebraska Biocontainment Patient Care Unit, a hospital unit specialised for treating the most contagious diseases, that has stood empty, with the staff conducting only drills, since its founding ten years ago, until the current Ebola outbreak. Ot the front line of the high-tech, state-of-the-art defence against contagion,

Nurses on the biocontainment team… take turns spending four straight hours in Mr. Mukpo’s room in full protective gear, including full face shields and three pairs of surgical gloves duct-taped to water-resistant surgical gowns.

For the last millimetre of sealing the boundary, you still can’t beat duct tape. I can’t see this making it into the advertising copy, though.

Political talk therapy

Two apparently unrelated items from Nick Clegg’s speech at the Liberal Democrats’ party congress: First the BBC quoted his exhortation to the party soldiers, that they should

go to the next election with their “heads held high”.

Then came his announcement of

the first national waiting time targets for people with mental health problems.

People with depression should begin “talking therapy” treatments within 18 weeks, from April.

Let’s see: If the depressed Liberal Democrats can get their talk therapy started in April, maybe they’ll hold their heads a bit higher by the 7 May election.

Designing a screening test is hard. You have a large population, almost all of whom do not have whichever condition you’re searching for. Thus, even with a tiny probability of error, most of the cases you pick up will be incorrect — false positives, in the jargon. So you try to set the bar reasonably high; but set it too high and you’ll miss most of the real cases — false negatives.

On the other hand, if you have a suspicion of the condition in a particular case, it’s much easier. You can set the threshold much lower without being swamped by false positives. What would be really dumb is to use the same threshold from the screening test to judge a case where there are individual grounds for suspicion. But that’s apparently what doctors in Spain did with the nurse who was infected with Ebola. From the Daily Beast:

When Teresa Romero Ramos, the Spanish nurse now afflicted with the deadly Ebola virus first felt feverish on September 30, she reportedly called her family doctor and told him she had been working with Ebola patients just like Thomas Eric Duncan who died today in Dallas. Her fever was low-grade, just 38 degrees Celsius (100 degrees Fahrenheit), far enough below the 38.6-degree Ebola red alert temperature to not cause alarm. Her doctor told her to take two aspirin, keep an eye on her fever and keep in touch.

She was caring for Ebola patients, she developed a fever, but they decided not to treat it like a possible case of Ebola because her fever was 0.6 degrees below the screening threshold for Ebola.

A failure of elementary statistical understanding, and who knows how many lives it will cost.

By way of Andrew Sullivan we have this attempt by Philip N. Cohen to apply statistics to answer the question: does texting while driving cause accidents? Or rather, he marshals data to ridicule the new book by Matt Richtel on a supposed epidemic of traffic fatalities, particularly among teens, caused by texting while driving. He has some good points about the complexity of the evidence, and a good general point that people like to fixate on some supposed problem with current cars or driving practices, to distract their attention from the fact that automobiles are inherently dangerous, so that the main thing that causes more fatalities is more driving. But then he has this weird scatterplot, that is supposed to be a visual knock-down argument:

We need about two phones per person to eliminate traffic fatalities...

We need about two phones per person to eliminate traffic fatalities…

So, basically no correlation between the number of of phone subscriptions in a state and the number of traffic fatalities. So, what does that prove? Pretty much nothing, I would say. It’s notable that there is really very little variation in the number of mobile phones among the states, and at the lowest level there’s still almost one per person. (Furthermore, I would guess that most of the adults with no mobile phone are poor, and likely don’t have an automobile either.) Once you have one mobile phone, there’s no reason to think that a second one will substantially

Whether X causes Y is a separate question from whether variation in X is linked to variation in Y. You’d like to think that a sociologist like Cohen would know this. A well-known example: No one would doubt that human intelligence is a product of the human brain (most directly). But variations in intelligence are uncorrelated with variations in brain size. (Which doesn’t rule out the possibility that more subtle measurements could find a physical correlate.) This is particularly true with causes that are saturated, as with the one phone per person level.

You might imagine a Cohen-like war-crimes investigator deciding that the victims were not killed by bullets, because we find no correlation between the number of bullets in a gun and the fate of the corresponding victim.

Just to be clear: I’m not claiming that evidence like this could never be relevant. But when you’re clearly in the saturation region, with a covariate that is only loosely connected to the factor in question, it’s obviously just misleading.

The BBC reports today on the most recent THE global university rankings. The article is illustrated with a grinning, texting stock-photo student (I’m genuinely baffled as to what value these atmospheric photos are thought to add to news article) above the caption

The rankings rate universities worldwide on 13 measures, including teaching.

Wow! These rankings of higher education institutions were pretty thorough, if they even went so far as to include the quality of TEACHING among their 13 factors! If they’d had sufficient bandwidth for 14 factors they might have ranked them on the quality of their wine collections. Then Oxford would have come out tops for sure.

Devices like this one are sometimes still used to watch the BBC!

Devices like this one are sometimes still used to watch the BBC!

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