“Neglect of mathematics works injury to all knowledge, since one who is ignorant of it cannot know the other sciences, or the things of this world. And what is worst, those who are thus ignorant are unable to perceive their own ignorance, and so do not seek a remedy.” -- Roger Bacon
It's no secret that lots of people hate and fear any kind of math. I certainly spent much of my life fighting a kneejerk inward cringe at the mere sight of an equation, and many of the folks I spoke with while writing The Calculus Diaries had even more extreme reactions. They talked about sweaty palms, cold sweats, and a cold knot of dread in the pit of their stomachs when encountering anything to do with numbers. Per my friend Lee, who initially failed her high school algebra class: “It wrecked my self-confidence in a way nothing else ever did, and still knots my stomach. I’m not totally innumerate, but anything that looks like an equation makes me break out into a cold sweat and run screaming in the other direction.”
Another friend, Allyson, was even more blunt: “My initial reaction to the word ‘calculus’ is not unlike a caveman throwing rocks at the moon in ignorance and fear resulting in blind rage. There is no such thing as ghosts creeping up behind me on the stairs, but there is such a thing as a polynomial monster, and it has hooked teeth and causes chronic yeast infections, I’m sure.”
I can't speak to the yeast infections, but a new psychological study indicates that such reactions do have real, measurable physical effects. Specifically, when it comes to neural responses, math anxiety reads much the same as physical pain. It's not the numbers themselves, but the anticipation of encountering them, that seemed to trigger anxious, painful responses in the test subjects.
There are many complicated reasons why people react this way, but one of them might be the fact that math is just so damned unyielding, the enemy of wishful thinking, dashing our most cherished hopes with its cold hard facts. And is it sorry? It is not! Like the infamous honey badger, math don't care. Math don't give a s$%.
Also like the honey badger, math has shown itself to be quite the badass of late. If ever there was an iron-clad case to be made for math literacy, it's what happened over the last few weeks with the New York Times' star statistician Nate Silver and his 538 blog (named after the 538 votes in the electoral college).
For the 0.1% of you who don't know Silver's name by now, he started out analyzing the statistical probabilities of baseball teams, then turned his attention to the 2008 presidential elections. He devised a fairly sophisticated mathematical model that didn't just rely on a few public opinion polls here and there, but fed all the polls into the model, with additional tweaking to eliminate the inevitable sampling errors. And the results were pretty darned impressive: he correctly called 49 out of the 50 states and many of the Congressional races that year as well.
Fast forward to the 2012 presidential election, when most pundits were describing the race as a veritable toss-up between Mitt Romney and Barack Obama. As partisan tensions rose, Silver's forecast became a handy target, because his models consistently gave Obama much better statistical odds than the general punditry at winning re-election. Even at the low point of the Obama campaign, in the aftermath of that first debate, Silver's model still gave the president around a 66% chance of re-election -- largely based on his rigorous analysis of polling trends in critical battleground swing states. A week before Election Day, those odds increased to around 75%, rising steadily to a final prediction of 90.9%.
This was in stark contrast to the conservative punditry, who seemed to be inhabiting a bizarre alternate reality where Romney held a slight lead and was poised to win many of the battleground states. George Will, Peggy Noonan, Newt Gingrich, Fox News' numbers guy Michael Barone, and GOP strategist Karl Rove all predicted a solid Romney win, breaking 300 electoral votes and winning the popular vote, while Dick Morris hopped on the crazy train and predicted a Romney landslide. (Hey, someone's gotta take the longshot odds!)
How to explain the discrepancy? The conservatives went on the offense, attacking Silver's analysis as hopelessly biased -- everyone knew, they said, that Silver was "in the tank" for Obama -- and overly reliant on polls skewed in favor of Obama. This last accusation even inspired a separate Website, Unskewed Polls, purporting to be an unbiased analysis -- shades of Fox News' laughable "fair and balanced" tagline. (Huh. Conservatives didn't have a problem with Silver's 2010 prediction of major gains for the GOP in the House, which also proved to be highly accurate.)
The attacks got pretty personal, with David Brooks calling Silver "over-rated," MSNBC's Joe Scarborough dismissing him as an ideologue and "a joke," and even Politico's Dylan Byers pondering whether Silver was "a one-term celebrity" -- as if it was his name recognition, rather than the numbers, that mattered. And the Unskewed Polls founder, Dean Chalmers, sneered in The Examiner that Silver was "a man of very small stature, a thin and effeminate man with a soft-sounding voice that sounds almost exactly like the 'Mr. New Castrati' voice used by Rush Limbaugh on his program."
Honestly, what could a scrawny, liberal-intellectual girly-man with a reedy voice really tell us about such a close election, relying on something as magically intangible as numerical wizardry? Silver channeled his inner honey badger and handled the backlash admirably, ably defending his statistical methodology against the charges of wizardry and partisan bias, and cheekily responding to his detractors on Twitter.
(My favorite Silver tweet, after the massive storm, Sandy, devastated New York and New Jersey: ""CAN'T BELIEVE METEOROLOGISTS USED MATH AND SCIENCE TO PREDICT THIS STORM. THEY MUST BE MAGIC WIZARDS."
He kept chugging away at his predictive model, feeding in the daily poll numbers and crunching the data, accounting for confounding factors and potential sources of bias, trusting in teh math over the gut instincts of the punditry. As many others have pointed out, there was a great deal of ignorance of statistical probabilities -- and the nature of uncertainty -- behind much of the Silver criticism (not that there aren't valid things to criticize in his model, but bitching about his reedy voice and slight built aren't among them).
Clearly, that widespread antipathy towards all things numerical plagues some otherwise very smart people. But the outcry was as much part of the rampant anti-intellectualism that dominates certain circles in our society. In a post at Deadspin, David Roher opined, "It was only a matter of time before the war on expertise spilled over into the cells of Nate Silver’s spreadsheets." Stephen Colbert memorably said reality has a well-known liberal bias; apparently that bias extends to math.
(For those keen on knowing more details, Zeynep Tufekci of the University of North Carolina offered one of the best defenses of Silver and statistical modeling methods at Wired: check it out.)
Silver is not an oracle, and has never claimed to be, so the over-reaction was just plain silly. Sure, by late October 538's models favored Obama 79% to 21%, when the national polling averages were indicating a dead heat. But any good poker player will tell you that a 21% favored hand wins quite frequently -- i.e., 21% of the time. In fact, Silver himself used the poker metaphor in his last post before Election Day, estimating Romney's chances of winning the election as being roughly the same odds as drawing in inside straight:
[I]n poker, making an inside straight requires you to catch one of 4 cards out of 48 remaining in the deck, the chances of which are about 8 percent. Those are now about Mr. Romney’s chances of winning the Electoral College, according to the FiveThirtyEight forecast.
As any poker player knows, those 8 percent chances do come up once in a while. If it happens this year, then a lot of polling firms will have to re-examine their assumptions — and we will have to re-examine ours about how trustworthy the polls are. But the odds are that Mr. Obama will win another term.
He later slightly revised those odds to give Romney a 9.1% chance of an upset -- largely to account for just the sort of pro-Obama potential bias in the polls that his critics had been braying about. So how'd Silver do in predicting the actual election? Check it out:
Boo-yah! Behold the data, for it is mighty! Silver correctly predicted 50 states out of 50, and even nailed the popular vote within a few tenths of a percentage point. When the graphic above hit Twitter, Alaska's returns hadn't been recorded, but it went, as predicted, to Romney. The sole genuine toss-up state, Florida -- which Silver had at 50/50 odds -- is still technically not final (as of 5 PM EST on Wednesday, November 7), waiting on votes from Miami-Dade county, which heavily favors Obama, who already holds a slight lead. It's expected Florida will also land in Obama's column, so Silver's controversial last-minute switch of Florida from light pink to light baby blue was justified. (To see how all the others fared, check out this graph.)
Plus his book sales are skyrocketing, he's well poised to negotiate an even more lucrative contract with the Times, and he's inspired his own Chuck Norris style Twitter hastag, #NateSilverfacts. (My favorite so far: "When criticized by pundits, Nate Silver doesn't get angry - he regresses toward the mean.") Oh, and one satirical Website proclaimed Silver a witch. One imagines an elated Silver dancing Gangnam style in his office digs, thoroughly vindicated by the election returns -- although it's more likely that he collapsed in exhaustion, given his feverish frequency of updates over the last few weeks. But he's certainly earned to the right in indulge in a bit of Schadenfreude.
That was just the presidential race, of course. I haven't seen a full assessment of his predictions for other races, but there was at least one major upset in North Dakota, when Heidi Heitkamp (not Heitberg, a typo in the original post) narrowly edged out opponent Rick Berg, despite Silver giving the latter a 92.5% chance of re-election.
And he missed on a Montana race, too, where the Democratic candidate handily won, although Silver gave his Republican opponent a 66% chance of winning (although there were far fewer Montana polls, and hence not as large of a data sample). So, yanno, the guy's not perfect. That's statistical uncertainty for you.
Still, to quote a classic xkcd comic: SCIENCE! It works, bitchez! The math doesn't care what you want to be true: it calls it like it sees it, denialism be damned. The honey badger heartily approves.
Which is why it was so fascinating to watch the election coverage meltdown on Fox News as the numbers came rolling in: denialism crashed head-first into numbers-based reality and popped the conservative punditry bubble. The cognitive dissonance was palpable. (As Steve Mirsky noted on Twitter, "Fox News is having a psychotic break.)
Rove actually objected on-air when Fox's independent election analysts called the race for Obama, insisting Romney still had a fighting chance in Ohio. Anchor Megyn Kelly marched down the hall to the analysts' desk and demanded an explanation.
To their credit, the analysts (who had done the math) didn't back down: “We’re actually quite comfortable with the call.” And of course, the analysts were right, something Rove -- a smart, math-minded guy in his own right, when he's not blinded by partisanship -- grudgingly conceded in the end. (So did Barone, Gingrich, and Morris.)
So is Nate Silver the new God of the Geeks? Should we all bow down to our thin, effeminate Mathematical Wizardry Overlord? Not so fast. As several folks pointed out this morning, Silver certainly wasn't the only poll-savvy statistician with heavy odds favoring an Obama re-election -- most notably, Sam Wang's Princeton Election Consortium gave Obama 98% odds of re-election. He was just the most visible.
Silver's gift is combining rigorous statistical modeling with a savvy populist approach. But he did bear the brunt of the criticism, so it's only fair he reap the requisite rewards. Ironically, Silver also predicted the post-election reaction to his analysis, in an interview with Buzzfeed: "I'm sure that I have a lot riding on the outcome. I'm also sure I'll get too much credit if the prediction is right and too much blame if it is wrong.”
The real winner wasn't Silver, but the math. The 2012 election was a real-time experiment in the accuracy of statistical modeling, and it passed with flying colors. That doesn't mean there still isn't room for improvement, or that such models are infallible, but the fundamental principles are solid. For now. Call it the triumph of the nerds. I doubt we've seen the end of denialism, by a long shot, but it's nice when, once in awhile, scientific rigor gets a big win.