Innumeracy: Today's Illiteracy

Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.
-- Robert Heinlein, Time Enough for Love

Twenty years ago, the all-around scientific genius Douglas Hofstadter coined the term "innumeracy" to describe an ignorance of mathematics. To emphasize the personal and social consequences of innumeracy, he labeled it "the mathematical counterpart of illiteracy."

A failure to understand simple statistics may cause us to draw crazy conclusions from firm facts. For example: In the 1927 season, Babe Ruth hit an astonishing 60 home runs -- far outstripping any other Major League Baseball player in history. The next year, he hit a merely spectacular 54 round-trippers -- a 10 percent decline. Compare the Babe's performance with that of Washington Senator (the team, not the elected rep from the Evergreen State) Samuel Filmore West (the outfielder, not the famous Frisco concert hall). In 1931, West hit six four-baggers, 100 percent more than the three he'd managed the year before.

It would be absurd to claim that West's 100 percent increase made him a better home run hitter than Ruth with his 10 percent decrease. Yet this sort of irrational thinking can wreak havoc in our everyday lives.

Take the stock market, which lost around 50 percent of its value between October, 2007 and March, 2009. It has since posted a 50 percent gain, which is a fine thing. But if you think that evens things up -- and are ready to buy or sell on that basis -- check your 401K first. You're probably still 25 percent down.

A lack of a modicum of math savvy can be dangerous at all levels of financial decision-making. Too many consumers don't calculate the huge late fees on top of usurious interest penalties for credit card payments that are even one day late. Business owners leveraged to the hilt often pay little attention to their long term debt until revenues crumble and they can't make their interest payments, let alone operating expenses. And as for the immensity of our budget deficit -- a surplus when "W" took office but currently weighing in at over a trillion dollars -- and national debt -- now around twelve trillion -- how many are more than dimly aware of the meaning of these numbers, let alone the potential consequences of letting them get so out of hand?

Innumeracy also threatens to distort the way we perceive this phase of our economic crisis, with observers trumpeting statistics that, at best, indicate slight improvement from last year's debacle.

A recent Newsweek cover blared, "The Recession Is Over." But all that would mean -- even if it were true -- is that the economy has stopped contracting. According to the New York Times, "The Commerce Department reported that home sales rose 11 percent in June, an increase that dwarfed economists' expectations." But, the story went on, "it's also true that despite this monthly increase, sales of new homes were still down 21 percent from June 2008." And June 2008 sucked!

A bit more economic optimism is constructive, but you needn't be a math whiz to see that this is no time for celebration. Those less-horrendous stats are slippery little devils subject to revision. In the sobering blog entry "Deeper Than We Thought," New York Times chief financial correspondent Floyd Norris concluded on Friday -- on the basis of recently revised government reports -- that, "In general, the things we thought were bad turn out to have been worse."

Compulsive gamblers will tell you -- and neuroscience has shown -- that no matter how low their fortunes sink, the slightest uptick gets those endorphins flowing and sends rationality packing. A couple of tiny wins and it's time to double down because -- even though they're still almost broke -- they're "on a roll" and can win back what's been lost, and more. The inexorable mathematical truth, though, is that there's only one gambling guarantee: do it long enough and you'll lose every dime.

Most people don't care about probabilities and statistics, or feel intimidated by percentages. Some even wear their innumeracy as a badge of pride, contrasting their own language skills or artistic talent with a dismissive, "I don't do math."

If your math gene is recessive, check out http://www.wolframalpha.com/ a new search engine that provides computational help on everything from mortgage rates to molecular weights.

If the idea of looking at a mortgage statement or credit card bill still makes you want to gag, don't despair. Albert Einstein had this advice for troubled innumerates: "Do not worry about your difficulties in mathematics; I assure you that mine are greater."

Follow Michael Sigman on Twitter: www.twitter.com/majorsongs

Comments

[Nutcase]

For your amusement and consideration.

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. - Albert Einstein

In theory, there is no difference between theory and practice. But, in practice, there is. - Jan L.A. van de Snepscheut

[KillTheMessenger]

The difference between theory and practice is what keeps scientists employed.

:-)

[Chris Weigant - Huffpost Blogger]

Nice article, and nice quote. I thought I was the only one here who quoted Heinlein, glad to see I have company!

:-)

"If it can't be expressed in figures, it is not science; it is opinion."
(ibid)

-CW

[Nutcase]

You can be really different and quote me, Chris.

[KillTheMessenger]

Yep. And I love the Heinlein quote, even though I usually don't like the writings of the man.

However, I am afraid, wolframalpha is of no help to those who have failed to listen in math in high school. It is a great tool for those, who have listened to math in university, though.

[LaurenJill]

Are some cultures more gifted in math than others?
http://tasteslikechicken2me.wordpress.com/2009/03/06/are-some-cultures-more-gifted-than-others/

[KillTheMessenger]

Err... I taught myself calculus by watching similar tv classes... and I am not highly gifted. Not even close. I am merely proficient in trivial mathematics (like single variable calculus). The problem this parent has is that she does not know the difference between high school math and real mathematics.

The SAT test will tell you nothing about how gifted a student is in math, either. If you want to know, let a professional mathematician talk to them for a couple of hours. They have the right "test problems", fun things you have never heard of unless you are mathematicians yourselves. A child which enjoys that conversation and comes out of it with a huge smile has a chance to become a mathematician. Chances are most children will not enjoy it, at all, and the mathematician will tell you that the kid is smart (or not)... but not gifted.

Asian students are being forced by their parents to learn more. And they do. That does not make the vast majority of them more gifted. It merely makes the vast majority of their parents driven (and driving). Asian cultures (and Europeans, too) are a environment that force students to make the best of the time when they can learn the most the easiest. That does not make for geniuses and it does not make for happy students. It does, however, make for well prepared adults who have access to more information than their peers in the US.

[nudger]

Great article - though I would suggest that the problem is less one of manipulating numbers (the definition of innumeracy) but more of not understanding probability. And that incapacity is something that's genetically hard-wired into human beings. All our decision tools developed in an environment where the choices were simple (fight or flee) and the consequences very asymmetric (eat or be eaten). But now we live in a complex world where the probabilities, consequences and outcomes are manifold.
The best example of our probabilistic limitations is the famous case of the Monty Hall problem ( http://en.wikipedia.org/wiki/Monty_Hall_problem ) as explained by Marilyn vos Savant. A thousand Ph.Ds wrote in that she was wrong when she explained that the chance of winning increased if you changed your choice of doors. The famous mathematician Paul Erdos was unconvinced even after being shown a proof - it took a numerical simulation of the solution to get him to accept the counterintuitive result.
Our difficulties with probability are long standing. We reason by anecdote, and decision-making under pressure is still governed by the part of our brain that controls emotion. It's a wonder we've made it this far...

[Michael Sigman - Huffpost Blogger]

Great point.

[steppenwolfsayshi]

That's why people should be taught stats in school. I took it in highschool and its sooo useful but I don't know hardly anyone who did. If I need to make a decision, I reason it out mathmatically. Everyone has that capability if they are taught. There is no excuse for our horrible school system.

[sonofsamphm1c]

Almost all of the educated people who disagreed with Monty Hall had taken mathematics and statistics. That is why they were so angry. They thought they had been taught 50/50.

Now, did Monty Hall study math? If I remember his interview correctly from the time the "problem" hit the press, he said he was not much of a math student.

[Mark Mack]

I don't think we should be blaming self indulgence on innumeracy. The issue is that people incorporate new statistics or hold on to outdated ones, to modify their beliefs. The people making the decisions are not uneducated in numbers, they are willfully ignorant to serve their means.

.

[jeanrenoir]

You're both right. The American masses are both innumerate and illiterate, and they like it that way, until, DUH?, they find themselves Madoffed by Wall St. and the Republicans, jobless, homeless, and savingsless. Of course, in their hapless lack of self-knowledge, they still blame everyone but themselves for their ignorance, stupidity, and gullibility. So self-indulgent rationalizing, and victim thinking, still trumps reality, self-knowledge, and responsibility as much as ever.

[WindySailor]

You are all correct, but I feel part of the problem is that people in large quantities basically do not think. They accept whatever they are told by whomever they assume to have the correct information. That saves one a lot of effort that can instead be spent remembering Dale Earnhardt Jr.'s or Tiger Woods' career win total or the names of the contestants on "American Idol".

It goes far beyond numbers and statistics.

[twisted-european]

In Asia, they still use abacuses and run circles around our calculators. Bring on the abacus and let the people THINK!

[KillTheMessenger]

I was one of the last generations of German students who were taught how to use a slide rule... that's a way better tool to get a grip on math than the Abacus.

[FearlessFreep]

This reminds me of a CALVIN & HOBBES episode.

Calvin's Dad: "How's your math coming?"

Calvin: "I don't do math. I'm more of a visual person."

Dad: "Good. Visualize yourself as the only 45-year-old in the first grade."

[TheLastWallStreeter]

Couldn't agree more - the meme that math is for geeks is probably one of the worst cultural icons of the Baby Boomers.