All Hail Numeracy

John Allen Paulos, who writes about numbers as well as anyone around, has just published another excellent piece in the Times Magazine, this one about the strengths and limitations of relying on data to make decisions in the modern world. The underlying message: provenance matters, more than just about anything. And, furthermore: “No method of measuring a societal phenomenon satisfying certain minimal conditions exists that can’t be second-guessed, deconstructed, cheated, rejected or replaced.”

As he did here, Paulos provides an excellent example of tricky statistics from the medical realm:

Medical researchers face similar problems when it comes to measuring effectiveness. Consider the temptation to use the five-year survival rate as the primary measure of a treatment for a particular disease. This seems quite reasonable, and yet it’s possible for the five-year survival rate for a disease in one region to be 100 percent and in a second region to be 0 percent, even if the latter region has an equally effective and cheaper approach.

This is an extreme and hypothetical situation, but it has real-world analogues. Suppose that whenever people contract the disease, they always get it in their mid-60s and live to the age of 75. In the first region, an early screening program detects such people in their 60s. Because these people live to age 75, the five-year survival rate is 100 percent. People in the second region are not screened and thus do not receive their diagnoses until symptoms develop in their early 70s, but they, too, die at 75, so their five-year survival rate is 0 percent. The laissez-faire approach thus yields the same results as the universal screening program, yet if five-year survival were the criterion for effectiveness, universal screening would be deemed the best practice.

What are the weapons best deployed to fight data smog?

Footnotes, I guess, and transparency, and a generally higher level of numeracy among the populace. That’s been Paulos’s mission for some time now. He is of course the kind of service provider who could put himself out of business if he does his job too well. But given the current level of, say, simple financial literacy, I doubt that is much of a threat.

Tom C

I've always wondered how we can fight "data smog" ( I haven't read Shenk's book linked in your blog). It seems that people will live-and-die by whatever stats suit them best. In a perfect world, we would have a simple test to apply to any stat that would reveal its worthiness or credibility. In the meantime, I guess the best approach would be to tackle flagging numeracy and urge people to think twice about (or at least dig into) stats.

Tom C.
Baltimore Estate Planning

Eric M. Jones

(Some report here) The CFO of a company I worked for was befuddled when I mentioned that the national debt was (then) a shocking three trillion dollars. "Trillion? You mean three billion...?" the MBA-CFO-Executive said. His incapacity still bothers me...I wonder where he works now?

Billion, trillion, zillion, million, what's in a name? I read and hear that cognitive consonant confusion of those terms on the news and in the media on a daily basis. No one corrects them. The TV listings said that a 60 Minutes segment examined the state of California being $40 million in debt. I would have watched the show to see how this was possible, since $40 million comes less than $1.10 per Californian. Amazing if true, but of course, they meant billions not millions.

Often, I've wondered if I heard the person right. The words rhyme after all-and the really significant amounts differ by only a single phonic. It would be an improvement if the words for increasingly-large sums of money would be increasingly longer and more difficult. .

It is hard to think about big numbers-and it is fascinating that most people seem to have no clear understanding of large sums. If they did, reasonable persons would strike, riot in the streets and take sniper positions when an executive gets a couple billion dollars. Why? Well, the town I live in, and all its 17,000 citizens, has a combined net worth of maybe a couple billion dollars. See-

There are many ways to calculate this, but the point I am trying to make is that big money has only the faintest connection to reality, or at least is totally incomprehensible to most people-even the people who are getting the really big bucks.

When the Wall Street bailout sailed through the Congress I was mortified that few really took any notice of what had been done. That $800 billion (or so) is the approximate amount it would take to build every single structure (and its infrastructure) in the entire state -Every private home, public building, road, bridge, courthouse, street, waterline, electrical line, sewer, power generating plant, gas station, highway, overpass, playground, airport, dam, farmhouse, cell tower, prison, library, school, museum, dock, hotel, firehouse, store, sidewalk, tunnel, waste treatment facility, railroad, light pole, traffic signal, police station, restaurant, warehouse, lumber yard, grocery store, hair salon, bar, manufacturing plant, parking lot....all of it. And you could throw in the most expensive public works project in the history of the US...the Big Dig, which costs as much as 2.25 Panama Canals.

The Panama Canal- the largest construction project in history at the time- cost $375 million in 1913 dollars. The CPI from that time to today has grown 21.2X, making the cost in 2008 dollars about 7.95 billion dollars. So $800 billion today would buy from scratch, 100 Panama Canals.

The only way of understanding really big numbers of dollars is "Opportunity Cost"; that is, what you could buy with the money.

Just five percent of a billion dollars (That's $50-million) would buy you: A lifetime lease on a Gulfstream G450 at your beck and call. A home, condo or apartment in ten major exotic destimations, with an ultra-luxury fleet of cars at each. A servant staff of 20. Then you could sit around imaging ways to spend the other $950-million dollars.



If "data smog" implies being given hazy figures, the 'real world' actually provides the opposite, which is a lack of explanation or context. Your posting does provide context in the medical example provided; however, when one reads a newspaper, such context is never given, but only makes a "factual assertion" that the public and other media types go crazy over when hearing it.

Rudiger in Jersey

I went to college and went as high as Integral Calculus in Math. After a decade in my career, I am left wondering, what was that all about? Though I am in a science field, Calculus has NO value. Basic geometric approximations are adequate 99% of the time.

Statistics by comparison, is more valuable than algebra, trigonometry and calculus combined.

Why are we still teaching L'Hospital's Rule? Why do Americans FREAK OUT with a mathematical problem that involves two trains at different speeds? Why did the lumberyard guy when asked to cut a 2x4 by 8 feet wood into thirds, hand me three unequal pieces? Why do kids spend more time watching television, playing video games and surfing the net in one day than in study academics for a whole week?

Michael Perkins

Oscar Wilde said: "The mark of the truly educated is to be deeply moved by statistics"


Is it really still newsworthy to remind the world that you can come up with statistics to support virtually any opinion? Manipulating data is an age old practice, utilized time and again to provide an uneducated public with the reassurance necessary to push through decisions, legislation, etc., that suits the manipulator.

You can find me at Life: Forward ( talking about women, the wage gender gap, and body image.


"What are the weapons best deployed to fight data smog?"

Base rate information.


The best way to limit data smog is to stop it at the source, perhaps with a tax on data emissions.

sick of calc

@Rudiger in Jersey

You make an excellent point in terms of your implication the ratio of calculus to statistics being taught in school is wrong. However, for some reason I can't stop laughing when I see your reference to "L'Hospital's" rule. I'm sure I was taught "L'Hopital's" rule", but having said that it did often make me feel sick :D


I once read of a plan to sell 600,000,000 litres of water per year from Lake Superior to a Japanese company for bottled water. It was cancelled since it would cause significant lowering of the water level. As far as I could tell, 600 million litres would take [600,000 m^3 ÷ 82,100,000,000 m^2] off the top of the lake, or about .007 mm. Maybe the disappearance of 1/140th of a mm is significant in some way I don't know of, but it seemed like it was actually a lack of numeracy killed that project.



I wish was more emphasis on statistics and probability as well as "time value of money" in education.

But, I think to be an engineer or scientist and not get the concepts of calculus very well would be a bad thing.

Maybe, just maybe, one fewer calc semester and one more statistics/ probability.

But, in grad school (MBA with ECON major) those with an understanding of calculus got it a lot better than the rest - when it came to marginal cost concepts.


Ah, lead-time bias. A tricky issue for sure in the medical world.