March 7, 2010 -- As usual, simple arithmetic is crucial to understanding many of the biggest, most important news stories (as well as those, like the Tiger Woods saga, that are of no public significance). What follows is a collage of some of these stories.
One problem is that people often view numbers as providing decoration rather than information. Over the last couple of weeks, for example, I performed a little experiment with people I randomly met.
If our idle conversation turned to current events, I mentioned a headline I claimed to have just read proclaiming, "Experts Fear Annual Housing Costs in the U.S. (Rent, Mortgage Payments) May Top $2 Billion." I followed up with, "Imagine that -- more than 2 billion dollars per year."
People usually responded by bemoaning the mortgage crisis, foreclosures, Wall Street, and a host of other issues. Only one noticed that $2 billion is an absurdly low number. A population of 300 million translates to about 100 million households. Dividing 100 million into $2 billion results in about $20 in rent or mortgage paid annually by the average household. Just $20!
Health Care Bills
This anecdote is not without relevance for bigger issues such as the various health care proposals. There are different bills under consideration, but each of them has an approximate cost of $1 trillion over 10 years.
Most people realize that a trillion is much, much bigger than a billion, and so assume $1 trillion is an overwhelming fiscal burden. But the price tag for the Iraq war was also about $1 trillion in direct costs and double that in associated collateral costs, not to mention the dead and badly wounded U.S. soldiers and Iraqi civilians. One needn't be a pacifist or "leftist" to believe that health care coverage would be a more beneficial expenditure than the Iraq war was.
Climate change is another issue where fundamental numerical misunderstandings are rife. One of the most amazing is the reaction of some politicians, specifically Senators Jim DeMint of South Carolina and James Inhofe of Oklahoma, who said that the big snowstorms in the east this winter are evidence that global warming is bunk.
I hope this was just their lame attempts at humor, but Inhofe suggested that an igloo home be built for Al Gore, and DeMint tweeted that the snow would keep falling "until Al Gore cries uncle."
Here again, one needn't be able to graph y=x+sin(x) to realize that a generally upward movement of average temperatures doesn't preclude occasional local dips. Likewise, someone with terminal cancer will feel pretty good on some days without doctors revising their prognosis.
Stimulus and Jobs
The stimulus bill and its impact on job creation has also been badly misunderstood, and in a somewhat similar way. Newly-elected Sen. Scott Brown of Massachusetts said, "In fact, we haven't created one new job."
But, whatever your attitude toward the stimulus (I think it should have been bigger), a considerable, albeit debatable, number of jobs have been created by it. A monthly net loss of jobs, smaller than it's been but still a net loss, is quite compatible with the creation of many jobs, just as a medicine that makes one better, although not completely so, is still a valuable intervention.
Incidentally, the recent addendum to the stimulus, the jobs bill, costs a measly (in this context) sum of $15 billion, so most job creation over the last year is a result of a weak natural recovery and the much bigger stimulus package, ARRA (the American Recovery and Reinvestment Act of 2009).
Twitter, Small World
Let me twist a bit and turn to Twitter and other social media and the notion of six degrees of separation, the idea that any two people are linked, on average, by a chain of intermediates that numbers six. The number of intermediates varies considerably depending on the assumptions made.
One general point that's been established is that including a few random connections between people greatly reduces the average number of links between people. Related to this is the fact that if you're linked to some well-connected person (President Obama) by a chain of, let's say, four intermediates, then you're connected to everyone he knows (for example, Vladimir Putin) by a chain of, at most, five. Social media from Facebook to Twitter to Chatroulette certainly knit us closer together and have gone some way to shrinking our world to that of a global village.
One downside to living in a village is that everyone tends to know your business, a condition that most people are only slowly coming to realize.
Facebook and Netflix have had privacy lawsuits filed against them; the Italian authorities have also sued Google over its Google Earth street scenes. And, of course, Google was recently criticized when, in an effort to compete with Facebook, it released Google Buzz.
In the first incarnation, Gmail users were automatically "followed" by those people with whom they were in most frequent contact. Many Gmail users worried that their followers could see each other. It's not hard to imagine situations in which a person who corresponds with both X and Y may not want X or Y or others to know this. Google later changed some settings and eliminated the auto-follow model.
(Irrelevant to privacy, but perhaps interesting is the number of possible tweets. As I tweeted recently at twitter.com/johnallenpaulos, the number is staggeringly humongous: Each tweet can be 140 characters long, each character one of about 100 possibilities on most keyboards, so there are 100^140 or approximately googol^2.8 possible tweets, where a googol, from which Google derives its name, is 10^100th power, one followed by 100 zeroes. Of course, almost all tweets are nonsensical.)
The Winter Olympics are over, and the medals have been bestowed. Watching them was alternately pleasurable and perplexing, and, in the case of curling, both simultaneously.
Too focused an emphasis on which country was the "winner" was disturbing to me, since it seems inconsistent with the ethos of the games. It also ignores the myriad ways the national rankings can be achieved.
If total medals won is the criterion, the U.S. was the winner. If total number of gold medals won is the criterion, Canada was the winner. If we take account of a country's population, some much less populous countries, among them Canada, Germany, Norway, and a few others, beat out the U.S. (Although the maximum size of every country's team is the same, the best athletes from bigger groups will, in general, be better than the best from smaller groups.)
If we factor in the fraction of the population devoted to the sport, or the money invested in the training programs, or the climate (not many lugers in Thailand or India), or any number of other factors, we can probably make a case for any of 10 different countries being the winner.
But, happily, it is individual athletes who get and deserve the medals, not countries.
John Allen Paulos, a professor of mathematics at Temple University in Philadelphia, is the author of the best-sellers, "Innumeracy" and "A Mathematician Reads the Newspaper," as well as (just out in paperback) "Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.