Numeracy, relative risk and public policy

Forget the ‘precautionary principle.’ The amount of risk to which the public should be exposed is greater than zero. Michael Krauss, Financial Post, June 20, 2008.

Almost without exception the critical or contentious issues of our times involve numbers–even “intelligent design” advocates usually try to juggle inconvenient dates or data. Errors with numbers are ubiquitous. Sometimes these are amusing as with:

Ideal Toy Company stated on the package of the original Rubik cube that there were more than three billion possible states the cube could attain. It’s analogous to MacDonald’s proudly announcing that they’ve sold more than 120 hamburgers.

(Recorded by J. A. Paulos in Innumeracy.)

Sometimes they may damage the innocent error-maker:

Dear Sirs: We just bought six packages of your blueberries from our local Costco (in San Ramon, CA). On the label it says that the net weight is “2.75 pounds”, or “0.9 Kg”. Indeed, the 2.75 pounds figure appears to be correct — I weighed one of our packages and it weighs 2.93 pounds, including the plastic case, so 2.75 pounds net weight is entirely credible. But in that case, “0.9 Kg” is not correct. There are 2.2046 pounds in a kilogram, so 2.75 pounds converted to kilos is roughly 1.25 kg (actually 1.247 kg), not 0.9 kg. In other words, your packages have more kilograms of blueberries than your label says they have.

I thought you might appreciate the note. David H Bailey

and the response (which did not include a year’s supply of blueberries) that went:

Dear David,

Thank you for bringing this to our attention. We are making the change on our label now. Hope you are enjoying the blueberries!

Best Regards, [owner of the Hurst’s blueberry farm]

Others numerical errors have resulted in the “pentium bug”, Mars missions crashing, Patriot missiles overshooting their targets, and much more.

That said, the lack of numerical sense is more pervasively damaging to all modern public policy debates. All such debates involve a need to grasp notions of relative risk, be they about: infrastructure renewal, health care costs, exposure to carcinogens, nuclear power and waste, regulating nutritonal supplements and organic products, climate remediation, or … mad cow disease. As described by Simon Jenkins in Boneless Wonders in the Times of London, Dec 6, 1997:

The giant finger whooshes out of the night sky and points at the dumbstruck face in the window. “It could be you,” says a voice. This week the Agriculture Minister Jack Cunningham impersonated the National Lottery advertiser. As the nation’s fork was poised with a T-bone steak on its way to the nation’s mouth, Dr Cunningham screamed: “Don’t touch it.” According to the great god science, new variant Creutzfeldt-Jakob disease (nvCJD) could be lurking in that mouthful. There is a small risk, and where there is risk, a government must ban.

Perhaps only mathematicians are aware of the enormity of what the Government did this week. It took a risk that is statistically negligible and exploited it as an act of insufferable nannying. Beef ribs, T-bones and oxtails present a public health risk publicised as “very small” and “a chance of one case per year” (though none of Britain’s 22 nvCJD cases has been positively linked to beef). Most newspapers cluelessly converted “a chance” into a certainty, and ridiculed the risk as a tiny one in 56 million. But that is not what the scientists said. They suggested the chance was “5 per cent”, so the risk is nearer to one in 1.1 billion, or one in 560 million among the half of the population that eats beef. There can have been no more tenuous basis for an infringement of personal liberty.

But given a populace without the tools to distinguish real solutions to real threats from flavours of the week (e.g., H1N1 most recently, anthrax, exploding shoes and plastic knives for plane meals since 9/11, and obesity) how much choice does a democratically elected government have? Especially given media either too willing to feed such confusion or too unschooled to dispel it.

It is possible with a fairly straight face to blame our genes. As Richard Dawkins and many others have observed, and as Kieran Egan writes in Getting it Wrong from the Beginning:

The bad news is that our evolution equipped us to live in small, stable, hunter-gatherer societies. We are Pleistocene people, but our language and brains have created massive, multicultural, technologically sophisticated and rapidly changing societies for us to live in.

He also notes that “The cement like learning of our early years can accommodate almost anything, then it fixes and becomes almost unmovable” but that “we can, as a result, change our earlier beliefs and commitments. We also know this is difficult for most people.”

In On Deep History and the Brain Daniel Lord Smail notes that “the large human brain evolved over the past 1.7 million years to allow individuals to negotiate the growing complexities posed by human social living.” In consequence we find various modes of argument more palatable than others, and are more prone to make certain kinds of errors than others. We are over impressed by coincidence, poor at dealing with very-large scale or small-scale events (spatial or temporal) , and entirely unprepared for Nassim Nicholas Taleb’s Black Swans or tail events, or lotteries.

In consequence, schools could simultaneously improve the general quality of both mathematics education and public policy debate by focusing less on abstract algebra and elementary calculus, and paying a great deal more attention to topics such as

  • robust mental arithmetic: if one needs a calculator to compute 10% of 12 dollars, how meaningful is any discussion of subprime mortgages?
  • orders of magnitude and scale conversions: as for Hurst’s Berry Farm above.
  • approximate reasoning: Guesstimation or Fermi problem solving included.

Nonetheless, this will be to little avail unless the shared supply of common knowledge is also dramatically enhanced. A modern secular education should include a requirement that everyone know things like:

  • the approximate population of Cairo and of Canberra.
  • the distance to the moon and between Mumbai and Moscow (and where they are).
  • the relative cost of a congressional junket to the annual federal US budget.
  • how Google googles?
  • what is a serotonin re-uptake inhibitor, cellulite, or restless-leg syndrome?
  • whether having asbestos in your ceiling riskier than frequenting a tanning parlor?
  • what is a DNA letter, gene, chromosome, telomere, stem cell, recombinant DNA, or for that matter un-recombinant DNA?
  • what is a nanotube, terabyte, database, or multicore processor?

—rather than who starred in Marley and me, whether Michael Jackson fathered his own children, or how much the transfer of Renaldo from Manchester United cost Real Madrid?

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