What isn't so

Irrationality at large

“It ain't ignorance causes so much trouble; it's folks knowing so much that ain't so.” —Josh Billings

The local affiliate of Salem Communications broadcasts a short news break just before the hour. Sometimes I tune it in just before punching the button for a more mainstream station's top-of-the-hour newscast. These occasional doses of right-wing media keep me informed on what the nut-case fringe is saying, and it can be enlightening. Recently, while driving to school in the early morning, I tuned in the Salem station and heard its newscaster's report, “The nonpartisan Congressional Budget Office reports that the Obama administration's healthcare act will cost the nation's economy two-point-three million jobs in the next dozen years.”

It was startling news. My first thought: That's a lie. I was considering the source. By the end of the day, I had discovered the truth. The full implementation of ObamaCare would pick the so-called “job-lock” and free people who had been forced to stay in jobs they hated simply to preserve their health benefits. The CBO estimated that over two million people would be able to give up their second (or third!) jobs, scaling back to something less burdensome without running the risk of losing health insurance. In many cases, it would presumably enable parents to spend more time at home with children, which is something Republicans also support as long as it's merely theoretical.

And, as we have already seen, the GOP will repeat the “job-killing” claim at the top of their lungs all during the 2014 election campaign. Will this be the year that it doesn't work because they've cried “wolf” much too often already? If so, I look forward to their being devoured.

Ignorance is not a mysterious thing. All of us have it in abundance, even as we whittle away at it during our lives. What we have been seeing, however, to a greater degree in recent years than I can recall in previous decades of politician-watching, is the deliberate nurturing of ignorance, the creation of fake knowledge (like an inoculation?) to keep people from absorbing genuine knowledge. The right-wing propagandists have raised this to a high art.

It was just a few years ago that I was in Texas during the summer to visit some friends who had moved from California. The matriarch of the clan was concerned about the state of the national economy and confided her worries to me. Knowing that I had been a legislative staffer in Sacramento and assuming I still had some insight into such matters, she wanted to know if there was any chance that the U.S. Congress would “fix” matters by repealing ObamaCare. “If only they could get rid of it, the national debt problem would be solved!” She really believed that (and had never heard about the CBO analysis that determined ObamaCare would reduce the nation's annual deficits).

She also had Fox News playing in the den during every waking hour. She wasn't uninformed. She was massively misinformed.

Quite recently one of my nieces became one of the president's hapless victims. She wasn't quiet about it. ObamaCare had forced her to change doctors (which, you know, never happened when insurance companies ran the world) and “Becky” was furious:

Becky feeling annoyed

So... I am so disgusted in Obama!!!! My insurance plan disappeared because it was not OBAMA approved. So instead of having basic insurance and paying cash for my dental and vision and paying $300 for my family. So now I am being forced to go to Covered California and pay $250 with the state paying $250 and putting my kids on medical. How does make any sense!!!!!!

After reading her plaintive post on Facebook, I pointed out a little bit of reality (cribbed from my blog post on same):

Your insurance company did not have to cancel your policy. It decided that it wanted to do it despite language in the healthcare act that permits individuals to maintain existing policies. It's in Section 1251 of the Affordable Healthcare Act:

SEC. 1251. PRESERVATION OF RIGHT TO MAINTAIN EXISTING COVERAGE. (a) NO CHANGES TO EXISTING COVERAGE.(1) IN GENERAL.—Nothing in this Act (or an amendment made by this Act) shall be construed to require that an individual terminate coverage under a group health plan or health insurance coverage in which such individual was enrolled on the date of enactment of this Act.

What the act did not do, however, was mandate that the insurance companies keep offering the plans people wanted to keep, and many companies have grabbed the chance to cancel lots of policies. They didn't have to. They wanted to. The administration should have anticipated this and blocked it, which would have given some teeth to the president's you-can-keep-it pledge.

I might as well been hollering into a dry well. Some of Becky's Tea Party buddies chimed in. Here’s a couple:

Sadie: I hated him before this - but we had all sorts of trouble getting coverage because of Joeys pre existing condition - even though that wasnt ment to be taken into consideration. Its a joke and a very bad one.

Sadie refused to recognize that the ACA is what made her husband’s pre-existing condition irrelevant. It was all the fault of the hated president, who was daring to occupy the White House while black.

Gertrude: All the people that voted for him owe the rest of us working people an apology !!!

Don't hold your breath, Gertie!

And here’s my niece again, for the big finish!

Becky: To privately cover my family would now cost me $800-$1000 per month with a $4000 deductible. That is ridiculous.

So Becky points out that private health insurance is damned expensive. As much as a thousand per month, with a high deductible. Wow! Instead of like before, when her bare-bones insurance plan cost her $300 (as mentioned above). Now, of course, under Covered California, she’ll pay $250 for a $500 policy. Hurray? No! That's only because she's also getting a $250 subsidy, and that’s (apparently) awful and humiliating! Like welfare!

Sounds like ObamaCare worked to her advantage, although there is the aggravation of having to choose a new primary care physician, since her old doctor was tied to the old plan and (I guess) is not available under the new. But saving $50 each month is sort of good, no? No! It’s communism! (Or something.)

Perhaps I'll get some sympathy when I tell my niece that I had to change health plans in order to keep the doctor I've had for several years as my primary care physician. When she gloats that I, too, am a victim of the Affordable Care Act, I'll mention it occurred before the measure was enacted. I was, instead, a victim of my college district's health insurance providers—back in those days when the insurance companies ran everything and the president had yet to drive us from health-insurance paradise.

Cheerfully innumerate

Happily ignorant

I'm sure we all remember in Season 17 when Marge Simpson expressed to Lisa her regrets about blowing off the calculus final in order to party with her boyfriend Homer: “Since then, I haven't been able to do any of the calculus I've encountered in my daily life.” Ah, yes. Thus do our mistakes return to haunt us, and—as we all know, a working knowledge of calculus is crucial for success as a homemaker.

The obvious basis for the humor is the effective disjunction between calculus and housekeeping. The more subtle reason is perhaps more significant: a sense of relief in the viewer. “Ha, ha! Thank goodness it doesn't really matter that I didn't learn any of that useless stuff!” It salves their guilty consciences over their collegiate screw-ups and omissions. “Math! Who needs it? Only nerds! (And I'm not one. Hurray!)”

 Brian O'Neill seized the opportunity to write a semi-humorous article for the Pittsburgh Post-Gazette after discovering that Google's Laszlo Bock found no significant connection between college grades and job qualifications. He cites Bock as saying in a New York Times interview that “G.P.A.’s are worthless as a criteria for hiring, and test scores are worthless.”

What? Algebra grades don't predict job performance? Grades in English composition don't correlate with corporate success? Shocking!

And why should they? I concede that the classroom is an artificial environment that does not in general (and is not intended to) emulate future work experience. The integration of the knowledge you acquire in the classroom is a separate skill, as is the selection of the right tools for doing a particular job. Why are heads exploding (or pretending to explode) over these “revelations”? People don't begin entry-level jobs with all of their skills and knowledge pre-melded into a unitary capability. Who knew?

A degree really signifies that you are able to achieve a goal, which is why many companies care more about your persistence in achievement than they are in the grade point average you attained. This, however, is the point at which people bewail the math classes that prevent attainment of a degree: “I can't do the math required for a college degree, so math shouldn't be required.” But college degrees are a sign of a range of qualitative and quantitative skills, so this argument suggests a watered-down college degree is okay. Should it have an asterisk on it? Should it be labeled “college degree lite”. Does everyone deserve a college degree even if he or she is illiterate or innumerate? Note how readily the argument generalizes:

“I can't do the _____ required for a college degree, so _____ shouldn't be required.”

Student success would soar! And student job options would correspondingly shrink.

Oh, but Google says academic success doesn't correlate with occupational success. Please pause to consider that Bock was describing what they discovered in the people they hired. Go ahead and visit Google's job opportunity site. They need account managers and executives more than anything else (at least during this summer of 2013). Minimum qualifications? Looking at today's listings in order, I see BA/BS (MBA preferred), BA/BS, Bachelor's (MBA preferred), BA/BS, BA/BS, BA/BS, BA/BS, BA/BS, BA/BS, BA/BS (and that's just page one). You get the idea.

Shall we do what Google says and ignore college attainments, or as Google does? While Google may not ask for GPAs and specific college majors, it still wants to know you can complete a certain level of education. If you can't, they're less interested in you (although they will in some instances accept “4 years relevant work experience” in lieu of the bachelor's).

Students without math skills may nevertheless thrive in the many occupations that minimize the need for numeracy, but those students dramatically constrict their options and straiten the path to success. And it's too late to have Euclid himself as an instructor: “Give him a coin, since he must profit from what he learns.”

Freeper math madness

Innumerate significance

One of the symptoms of the derangement of today's right wing is innumeracy. I'll grant that this is a broad-based problem not confined to the ranks of teabaggers and other exponents of troglodytic conservatism, but these people have a peculiar talent for making a hash of math and then solemnly assuring each other of the significance of their screwed-up calculations. Today I ran across a characteristic pair of examples from Free Republic, the Fresno-based sink of deranged teabagging. They occurred in comments in a thread devoted to bemoaning the ratification of the New Start treaty, which apparently entails the unilateral disarmament of the United States and its immediate surrender to Soviet Russian conquest.

By an amazing coincidence, the 71-26 vote in the Senate is almost exactly the same percentage as the Parliament’s vote in support of Chamberlain’s Munich Agreement (369-150).

28 posted on Wednesday, December 22, 2010 1:24:45 PM by StanFran

Let's check StanFran's math, shall we?

A total of 97 senators cast votes on the New Start treaty. The ayes were 71/97 = 73.2% and the nays were 26/97 = 26.8%. (Amazingly, these add up to 100%!) Now let's consider the British parliament's vote on the Munich agreement. The ayes were 369/519 = 71.1%, while the nays were 150/519 = 28.9%.

Do you believe that 73.2% is “almost exactly the same” as 71.1%? If you don't, then you don't qualify as a Freeper. Furthermore, you must seek dark significance in the purported (but actually nonexistent) equality.

It would actually be more accurate to point out that Ronald Reagan was almost exactly 71.1 years old when he delivered his Indianapolis speech in 1982 on the New Federalism, thus proving (proving!) that he was secretly inspired by Neville Chamberlain and actually intended the New Federalism to serve as a disguise for the New World Order ushered in by his successor, George Herbert Walker Bush. Subtle! And scary!

The second example of bad counting was provided in an angry observation about ratification having been accomplished in a lame-duck session of the Senate:

Why are FIRED employees still making decisions that affect the health and well being of the company (country)?

They should be shown the door with a swift boot to help them along the way.

26 posted on Wednesday, December 22, 2010 1:23:45 PM by SunTzuWu (Political correctness does not legislate tolerance; it only organizes hatred. - Barzun)

“Fired” employees? Let's check the roster of New Start supporters. Recall that there were 71 of them. How many were actually rejected by the voters last November (as opposed to retiring of their own volition)? The first senator who fits the bill is Bennett of Utah, a Republican who was denied renomination by his own party. Next is Feingold, the Wisconsin Democrat who will be sorely missed. Continuing down the list, we find Lincoln of Arkansas, the hapless Democrat who unfortunately survived a primary challenge and flopped spectacularly on election day. Finally, there's Specter of Pennsylvania, the long-time Republican who switched to the Democratic Party in a futile attempt to survive.

Count them up. That's it. Four. New Start would have gotten 67 votes even without the support of the “fired” senators. For the benefit of Freepers and other ignorant types, that's the two-thirds majority required for ratification of treaties. New Start was not nudged over the finish line by supposedly discredited legislators.

So there.

Não conta

Innumeracy abroad

My faithful reader and commenter João Paulo has shared with me the results of a 2008 hearing in the 8th District of Lisbon's Civil Court. (How else would you translate 8.^o Juízo Cível da Comarca?) My ability to read Portuguese is limited and not enhanced by the legal terminology in the report on the court's proceedings, but I think I've puzzled out the key points.

Here is the summary of the court's decision:

8.^o Juízo Cível da Comarca de Lisboa

A fls. 189 vem o executado apresentar um requerimento intitulado de "oposição a penhora", em que alega ter sido ordenada à penhora de 1/6 do vencimento que aufere, sendo que atentas as despesas correntes que apresenta ter, o deixa numa situação de grave carência económica.

Conclui, pedindo a isenção de penhora.

Notificado o exequente, vem este requerer a manutenção da penhora.

For ordenado a elaboração de um relatorio sócio económico do executado, o qual se mostra junto a fls. 213.

Apreciando.

O Tribunal deve ponderar entre o interesse do exequente em ver o seu direito assegurado, e o do executado em cumprir o pagamento da quantia a que se encontra vinculado, interesse esse que tem de ser proporcional.

Pese embora os factos relatados pelo executado, e sendo certo que não competindo ao Tribunal restringi-lo de refazer a sua vida como entender, também não pode o Tribunal prejudicar os compromissos anterioremente por aquele assumidos.

Assim, determina o Tribunal proceder à redução da penhor dò vencimento do executado para 1/5 do vencimento.

You see, some hapless guy got slammed with a “penhora,” which translates into English as “distrainment”—the seizure of personal property to enforce the payment or discharge of an obligation. In this particular case, the subject of the distrainment had suffered the seizure of 1/6 of his assets (garnishment of his wages). He petitioned the court for relief, claiming that he was suffering grave economic hardship.

The court solemnly pondered the petitioner's request, noting the necessity of proportionately balancing the petitioner's well-being against his responsibility to discharge his legal obligations. Upon consideration, the court ruled that the distrainment of 1/6 of the petitioner's assets had been too severe and ordered a relaxation of the order. The new order instead stipulated a seizure of 1/5 of his assets.

And thus is justice done by those with limited skill in matemática.

Muito obrigado, João Paulo!

The world ends again

Just as I was getting the hang of it

In 1994 I was teaching an evening math class at my college in addition to my usual day schedule. By some divinely inspired coincidence, this put me on the road at just the right time to catch Harold Camping holding forth on the radio with his Open Forum question-and-answer program. Camping's dry-as-dust mode of declamation is probably dangerous to listen to while driving, for fear of falling asleep and causing a traffic accident.

Nevertheless, I faithfully tuned in for several days in a row because of Camping's fascinating topic. He had, you see, figured out the day the world would end. As a clever Bible scholar, he had apparently figured out a way around Matthew 24:36 (“But of that day and hour knoweth no man”) and had computed that Jesus was getting ready to return on September 6, 1994.

Camping was giddy during the September 6 broadcast, knowing, as he did, that he might not even manage to finish the program. The blast of God's last trumpet could preempt him at any moment. But finish it he did. September 6 passed without a redeeming revisit.

Camping refused to be crushed by his experience of rapture interruptus. He did some more mystical math and announced he had found an error in his calculations. The second coming of Christ would actually occur between September 15 and 17.

Again, Jesus was a no-show.

It was only fair, of course, that Harold Camping suffered the fate of all false prophets. In brief, he just kept plugging along in his ministry, still leading his flock of credulous sheep.

It's a tradition! History gives us the example of Charles Taze Russell, who promoted the idea that the end of the world would occur in April 1878. When the great disappointment occurred instead, despite some defections, the Russellites soldiered on. The loony door-knockers known today as the Jehovah's Witnesses are their direct descendants.

They never learn. Their failures merely demonstrate the need for stronger faith.

In token of their invincible ignorance, believers are now being presented with Harold Camping's brand-new prognostication of the end of the world. This time it's going to be May 21, 2011. (Perhaps I should hold off on grading the final exams for the spring 2011 semester, just in case.)

Camping's new prediction was featured in an article by Justin Berton in today's San Francisco Chronicle. It appeared on the front page of the newspaper's C section (“Bay Area”).

Camping patiently explained how he reached his conclusion for May 21, 2011.

“Christ hung on the cross April 1, 33 A.D.,” he began. “Now go to April 1 of 2011 A.D., and that's 1,978 years.”

Camping then multiplied 1,978 by 365.2422 days—the number of days in each solar year, not to be confused with a calendar year.

Next, Camping noted that April 1 to May 21 encompasses 51 days. Add 51 to the sum of previous multiplication total, and it equals 722,500.

Camping realized that (5 × 10 × 17) × (5 × 10 × 17) = 722,500.

Or put into words: (Atonement × Completeness × Heaven), squared.

“Five times 10 times 17 is telling you a story,” Camping said. “It's the story from the time Christ made payment for your sins until you're completely saved.

“I tell ya, I just about fell off my chair when I realized that,” Camping said.

And I just about fell of my chair when I read that in the morning paper. Camping thinks this is some kind of proof. It's both amusing and sad.

Berton does a good job in his article in conveying the pseudoscientific environment in which Camping's mumbo jumbo flourishes. Unfortunately, the journalist makes one significant mistake in his reflexive application of the balanced treatment approach to reporting:

Camping is not the only man to see truths in the Bible hidden in the numbers. In the late 1990s, a code-breaking phenomenon took off, led by The Bible Code, written by former Washington Post journalist Michael Drosnin.

Drosnin developed a technique that revealed prophecies within the Bible's text. A handful of biblical scholars have supported Drosnin's theory, lending it an air of legitimacy, and just as many scholars have decried it as farce.

Hold on just a second there, Justin. Did you really mean to equate the detractors of the Bible code with the “handful of biblical scholars” who accept it? It's demonstrably false to say “just as many scholars” denounce it. Very few embrace it. Many disbelieve it. There is no parity. (Only parody.)

Apart from that one faux pas, however, the Chronicle's report on Camping's apocalyptic prediction gives us a clear perspective on religion's ability to erode a man's thinking processes. Until a stupid pill is developed, religion can serve that purpose.

Those of us who are not befuddled by a religion can make plans to get together to celebrate the post-apocalypse on May 22, 2011. See you there!

When liars figure

Although the figures don't lie

Misleading numbers are everywhere. Is it innumeracy or mendacity that spawns them? Sometimes I think it's both. Remember the bogus argument that autoworkers were making $70 an hour? That grotesque exaggeration was spread by right-wingers who embraced its propaganda value. Some of them probably knew it was false but didn't care.

Does Bill Saracino care when he peddles bad numbers? Does he even know that he's doing so? He uses simple arithmetic to calculate his misleading results, so it's possible he has great confidence in their accuracy. It's difficult to say. It's not, however, difficult to discern their bogosity. Check this out, from the February 5, 2009, installment of the Sacramento Union:

The stimulus bill gives the Coast Guard $572 million for “acquisition, construction and improvements.” It is claimed that these funds will create 1,235 new jobs. Grab your abacus and do the math. The cost of “creating” each of these occupations comes to $460,000 per new job.

---

We see that Bill cared enough to put “acquisition, construction and improvements” in quotation marks but not enough to read the words. “Acquisition” suggests buying property or matériel; that doesn't go into the pockets of the workers. “Construction” says that things are going to be built. Labor is by no means the only cost of construction projects. The results will be new Coast Guard facilities with a useful lifetime of decades. “Improvements” are in this same vein.

But Bill isn't done:

The Department of Defense gets $200 million to install plug-in car stations for its plug-in cars, of which it has 53,526. We taxpayers get each plug-in station for the bargain price of $3,700 per car serviced.

---

He evidently has a key on his calculator that permits him to do division. Good for him! But once again he neglects the minor consideration that the plug-in stations will create jobs for construction workers and electricians, that the stations will used for decades, and that the DoD's need for such stations will undoubtedly grow in the future. It's a long-term investment with immediate job-creation aspects.

One more:

The bill proposes $600 million for the federal government to buy new cars. The feds already spend $3 billion a year on a fleet of 600,000 vehicles. America’s Big Three automakers got more than $25 billion in December’s $750 billion pork-fest. Do they really need $600 million more? Does the federal government really need $600 million worth of new cars?

---

If only Mr. Saracino understood some of the more arcane functions of his calculator, he would see that $600 million is 20% of $3 billion (assuming he gets the troublesome decimal place right; percentages are tough). I'll admit that $600 million is real money (as Everett Dirksen might have said), but 20% is not staggeringly large. (I'd like a 20% pay increase, please, but it won't make me a millionaire.)

Bill eventually has mercy on us: “I could go on—oh, how I could go on—but I think you get the ugly picture.” Yes, we get the ugly picture. You're an innumerate propagandist for the right wing. But just to show there's no hard feelings, here's a nice calculator trick that you'll enjoy.

Moving the goalposts

But it's still the same game

Joe Soucheray needs my help and cries out for my assistance in an opinion piece published in the St. Paul Pioneer Press:

What we need is a margin of victory that is mathematically bulletproof, not one-half of 1 percent. I don't know what that margin is, but a mathematician could come up with it based on vote totals.

---

As a civic-minded mathematician, I hasten to answer his call. Joe probably won't appreciate it, though, since my response boils down to little more than, “Wow, Joe, you sure are a dumb-ass, aren't you?” Under those circumstances, it's easy to see how he might think I'm not being very helpful.

I just said “he might think.” Now that, you see, would have made a difference. Soucheray believes that the hassle in the Minnesota senate race could have been resolved by setting a new standard for victory.

Nonsense. And you don't have to be a mathematical genius like me to realize that. You just need to give it a tiny bit of thought. Soucheray didn't:

Out of 2.9 million votes cast, there would have to be a margin of victory that could not be automatically challenged as questionable. One vote below that number would call for the coin flip—yes, a coin flip.

---

Now that is just dumb-squared. Not the bit about the coin flip. That's a perfectly respectable way to break a tie. It's Joe's comment about “one vote below.” Freaking hilarious. Can you imagine the hassles and lawsuits every time the results teeter on the boundary of Soucheray's new margin-of-victory standard? It doesn't matter how many wise mathematicians and statisticians choose the new standard. Any time you put a dot on a number line, the question arises whether you're on one side or the other. It makes no difference whether the standard is “more votes than the guy in second place” or “a margin of at least one percentage point,” the tally will be disputed and adjudicated every time it's close.

You can't fix this problem any better than Minnesota already did. A bipartisan panel looked at each disputed ballot that made it through the process (some, of course, were disqualified at earlier stages and a batch of those are under litigation) and voted, usually unanimously, to allocate the vote to Franken, Coleman, or neither. The whole thing played out on live video, complete with images of each questioned ballot. You can't improve on that a great deal.

It doesn't matter whether you're trying to determine who won a simple plurality (as in the current Minnesota contretemps) or if some arbitrary margin of victory was achieved. In the end it comes down to counting individual ballots and trying to figure out what side of the line you're on.

Even the proposal for a run-off election suffers from the same potential problem. Saxby Chambliss thought on election night that he had avoided a run-off in the Georgia senate race. He later found out that he had not quite won an outright majority and had to face the Democratic nominee in a second round of balloting before he secured re-election. If the margin in the first round of voting had been within one or two votes, you can be sure that Sen. Chambliss would have been in court seeking to declare himself the majority-vote victor who did not need to risk a second ballot.

The notion that some new definition of victory will solve all of our problems is a delusion on the part of Joe the Columnist. It is, frankly, quite illogical.

Are you smarter than Ann Coulter?

Take this easy test!

I haven't written about Ann Coulter in quite a while. For one thing, she had grown boring and no one seemed to be paying any attention to her during the presidential campaign. Coulter continued to write her syndicated rants, but her public appearances apparently ceased. Perhaps the reports that Coulter had had her jaws wired together were true. Whatever the situation, I have not been wasting any words on her, the has-been pundit best known for her confusing advocacy of both family values and recreational fornication. No one among my vast dozens of readers has complained about her absence from my posts.

But Ann has caught my attention again, if only briefly. An example of Coulter's reasoning power plopped into my e-mail in-box and I inadvertently read a few lines. It was probably the title that hooked me: “One Plus One Equals 20 Extra Votes for Franken.” Coulter, you see, has taken up cudgels on behalf of threatened incumbent Norm Coleman, who is at risk of losing his U.S. Senate seat to Al Franken. It all depends on the result of various court challenges and the tedious Minnesota recount. Coulter wants to stir up confusion with accusations that will make it easier to declare the election “stolen” if Franken triumphs in the end:

The day after the November election, Republican Sen. Norm Coleman had won his re-election to the U.S. Senate, beating challenger Al Franken by 725 votes.

---

Coleman “had won” the election? That's a presumptuous bit of phrasing when there were plenty of ballots left to count, as well as a mandatory recount pending. But Coulter's intent is plain: Paint Coleman as the victor so that any recount is necessarily a vile attempt to steal his victory. According to Ann, the minions of evil got to work quickly:

Then one heavily Democratic town miraculously discovered 100 missing ballots. And, in another marvel, they were all for Al Franken! It was like a completely evil version of a Christmas miracle.

---

And by the time the various counties in Minnesota had finished checking their tallies and correcting their election-night reports to the secretary of state's office, Coleman's tentative lead was further reduced:

Then another 400-odd statistically improbable “corrections” were made in other Democratic strongholds until—by the end of election week—Coleman's lead had been whittled down to a mere 215 votes.

---

Frankly, my dear, I don't give a damn what Coulter thinks is “statistically improbable.” I've seen enough examples of how mathematically incompetent right-wing Republicans can be. Coulter's argument suggests that she is well-nigh innumerate, as I will now demonstrate.

Perhaps you're smarter than Ann Coulter. Consider, if you will, the following number. Examine it closely.

And now for something completely different. Please examine this second number. Scrutinize it with the full power of your keen intellectual faculties.

Did you notice how it differs from the first number? Did you? If not, I'll give you just a little hint:

Now do you see? Aha! The second number has an additional digit. The numeral 1 appears in the location famously known as “the hundreds place.” That is, the number 1 actually represents the quantity 100. The omission of a single digit—even one as small as a 1—can have a significant impact. This was observed in Minnesota's Pine County, as noted in a post-election report in The Pine City Pioneer:

On Thursday, Pine County announced they had made an election night mistake—something that happens commonly and is fixed in the following days by the county's canvassing board. But due to the closeness of the race for U.S. Senate, the error caused more drama that it normally would have.

On election night, Partridge Township reported their results correctly. Al Franken had received 129 votes in the township. Because of a county data entry error, only 29 votes were reported to the Secretary of State's Office.

Another 100 votes added to Franken's total means he is within .011 percentage points—236 votes—of Republican U.S. Sen. Norm Coleman. Coleman received 143 votes in the township.

Pine County Auditor Cathy Clemmer said the mistake was nothing out of the ordinary. It's up to the canvassing board to take care of any discrepancies in the days following the election.

“This is the normal process—this is usual,” Clemmer said. “It’s nobody's fault. That's why we have in place in what we do in the state of Minnesota.”

---

Ms. Clemmer is obviously trying to sound like the sweet voice of reason so that we don't suspect her of collusion in the great international communist conspiracy to deny Norm Coleman a second undistinguished term in the U.S. Senate. We're supposed to believe that a single-digit error in a tally of Franken votes could change Franken's total by a 100 votes—with none for Coleman! This astonishes Coulter, who can't imagine it occurring innocently. She's already explained to us that the extra 100 votes for Franken are a miracle. They're statistically improbable. The only explanation must be some dastardly partisan plot! At least, that's what Coulter would have us believe.

That is, unless you're smarter than Ann Coulter. And the chances of that are pretty good.

Roller-coaster polling

Keep your barf bags handy

I like to follow political polls and I'm encouraged that my preferred presidential candidate continues in most reports to hang on to a significant lead. Nevertheless, I am heartily tired of the constant “analysis” of nonexistent volatility. It's a pseudo-drama ginned up by a combination of deep ignorance and ratings-driven sensation mongering.

It's polling, suckers. It's a statistical art with well-documented error bars. The results are not five-decimal-place scientific calculations. They're probabilistic estimates. The numbers are going to jump up and down even if nothing changes. Got that?

For purposes of illustration, suppose that a poll's accuracy is described as being within 3 percentage points 90% of the time. Got that? Then about 10% of the time it will be off by more than 3 points. If two candidates are within about 5 points of each other, taking 3 points away from the leader and giving them to the other guy will reverse the race! Only not really, because the poll would be in error in that instance. These flukes are not avoidable and they provide grist for the mills of the talking heads who will then scream about upsets and stunning surprises. They're just idiots. Or ignoramuses. Maybe both.

Let's take the illustration a few steps further. We can use a normal distribution (“bell curve”) to model the results of polls whose errors are less than 3 points 90% of the time. With the assistance of Excel's random number generator and built-in normal distribution functions, I ran two dozen trials and plotted the results of the simulated polling errors:


The model calls for the errors to fall within plus-or-minus 3 points 90% of the time (in the long run, mind you). Ten percent of 24 trials is 2.4, so we should expect maybe 2 or 3 results to fall outside the plus-or-minus 3 band. In this little experiment, it happened four times, twice going high and twice low. Please note the dashed line marking the −2.5 boundary. Whenever the leader's margin was underestimated by at least 2.5 points (in a race with an actual 5-point margin), the lead changes hands—according to the poll, not reality. Imagine the breathless reports that would immediately blossom on the cable news networks, newspapers, radio talk shows, and blogs. Panic! Or elation!

Another thing to keep in mind: The model did the exact same randomized calculation each time, assuming no actual change in the electorate. You still get variation, an inevitable consequence of sample-based statistics. You're stuck with it and you have to live with it. And pundits love to live with it because it gives the illusion of motion even when none exists.

People should just calm down.

I swear that I did not cherry-pick my results in order to present one that looked especially dramatic. The graph above shows my initial run. I cranked out some more examples, just to see what they looked like. These appear, together with the original experiment, in the graph below. Does it look chaotic enough for you? (Only the blue graph failed to produce an artificial swap in the lead.) See? Major developments in the campaign! We have headlines!

More equal than others

Wobegon math in Washington state

A friend up in Washington state—I'll call him “GW”—writes with exciting news he received from one of his U.S. senators. Patty Murray is irked that her state's citizens are being shortchanged in Medicare reimbursements from the federal government. She says Washington state is being punished for its highly efficient Medicare program. Murray may have a point: It's much too easy to fund certain programs based on percentages of prior expenditures, meaning that every dollar wasted today becomes an extra bit of funding tomorrow.

The senator's remedy, however, comes straight out of the Lake Wobegon playbook (where “all of the children are above average”):

Last week, I joined with Congressman Adam Smith (WA-9) to introduce the Medifair Act, a bill that aims to fix national Medicare reimbursement disparities that hurt Washington state. The bill raises Washington state's Medicare reimbursement rates to the national average and ensures that all states receive at least the national average of per-patient spending. This will encourage doctors to provide Medicare in more areas and will improve access for our state's seniors.

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GW is, of course, delighted by Sen. Murray's determination to help him and other Washingtonians obtain better health care, but he admits to being puzzled by her larger objective:

[S]he says that the act “ensures that all states receive at least the national average of per-patient spending.”

How can that be? You can't have some states or some doctors getting more than the average, while everyone else gets the average! Is that just typical wishful thinking (i.e. pandering) on the part of a politician?

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Hmm. Is it wishful thinking? Is it pandering?

Can't it be both?

Numb and number

Jobs & number games

Spring is the traditional hiring season for teachers and professors. Eager job-seekers file their applications, a lucky few are called in for interviews, and an even luckier fewer are called back for a second round. The sad condition of the state budget (and the governor's suggested cuts in education spending) puts a damper on the process this year, but our schools still set their hiring priorities and we work our way down the list as funds become available.

At my school, as at most colleges, the business of hiring faculty members is an intense multi-level survival-of-the-fittest contest. Each department carefully monitors the retirement plans of its members and crunches its enrollment numbers, ready at any opportunity to justify how many replacement or expansion slots it needs to fill. All sorts of factors come into play, although some of the most important cannot be voiced aloud (like the crying need to hire a tie-breaking third faculty member for the two-person department whose two professors hate each other).

Numbers play a huge role: enrollment, productivity, full-time equivalents (FTE), weekly student contact hours (WSCH), etc. It's never clear whether the less numerate departments are actually at a disadvantage in their quest for new faculty hires; their inability to crunch numbers sometimes produces spurious but impressive data that gives them the appearance of outpacing other academic areas. There is, naturally, constant second-guessing and auditing of each other's numbers. I suppose that's the main reason that departmental hiring request forms now require as much cross-checked information as your basic 1040 form.

Some of the numbers, however, are subjective in principle. These are the ranking scores from faculty members and school administrators who set priorities for the college. (It doesn't matter if your electronics department has the best productivity numbers if the campus as a whole elects to become a fashion and design school.) The ranking numbers have, on occasion, been used and abused to distort the process. One abuse was sheer innumeracy, which wiser heads (belonging to math faculty members) caught in time to avoid scandal. A different abuse was of the more numerate kind, and was perpetrated by a math professor with an impaired conscience.

Hurray for zero

The innumerate mistake was obvious once it was pointed out, but it came as quite a surprise to many participants in the ranking process. Each year the college's faculty senate meets to pass judgment on a stack of departmental petitions for faculty positions. The senators pore over the petitions, listen to brief presentations from each petitioning department, and then cast ballots that rank the petitions in priority order. The ranking numbers for each petition are added up and these totals are used to create an aggregate ranking by the faculty senate of all of the hiring requests. As in golf, a low score is better than a high score, since low scores indicate a lot of senators ranked you as 1, 2, or 3 rather than as 18, 19, or 20.

Several years ago, a few innumerate senators (most of whom didn't bother to attend the faculty senate at other times of the year) cast ballots to favor their own departments' requests (not an unknown phenomenon). Having accomplished their mission of ranking their parochial interests as number 1 (and 2 and 3 if multiple positions were requested), some of them got bored and left the rest of their ballots blank, as evidence they didn't care about the other positions. Just their own. By the logic of the aggregate ranking system, however, they thereby scored all the other positions with zeros ... and zeros outrank ones! In effect, all the positions they left unranked were treated as their top choices—beating out their own departments' positions.

They never made that mistake again, either because they learned better or because their departments chose to elect different senators the next year.

And the last shall be first

A canny member of the math department twisted the ranking system in the opposite direction, using his insight into the process to attempt to hijack it. He was an outspoken technophobe and dreaded the growth of our computer science department. One year the computer science people got ambitious and requested four new faculty positions for the next school year. While most of us chuckled at computer science's audacity (and agreed that the department's numbers justified two hires, but probably not three and certainly not four), my technophobic colleague was outraged. I think he took it as a personal affront.

As the senators filled out their ballots, most of us were ranking Computer Science #1 right near the top of the priority list and Computer Science #2 somewhere in the middle. Computer Science #3 and #4 were often relegated to ranks in the twenties (which was at or near the bottom because there were only 25 requested positions to rank in priority order). My sly colleague, however, voted to give Computer Science #1 last-place priority, writing a 25 on its ballot line. He similarly voted to give Computer Science #2 the next-to-last place by ranking it 24th. By giving the worst possible vote to computer science's first hiring request, my colleague had dramatically increased the score it would get when its rankings were totaled. He thus single-handedly pushed Computer Science #1 down several positions in our aggregate ranking, since most of us had given it 1's and 2's, so his 25 was like an elephant in the room.

Alas. His cleverness was for naught. That year our budget was good enough to cover most of the hiring requests and we worked our way further down the list than usual. Computer science got their two faculty positions. Another factor frustrating my colleague's machinations involved the actual disposition of the priority list generated by the faculty senate. It was submitted to the president's office, which then compared the faculty's priorities with a separate ranking created by the college's deans and vice presidents. A compromise priority list was then created by melding the faculty and management rankings, producing a list that looked the same as the management list.

They had already decided we were going to hire two computer science professors.

Postscript

My clever colleague's ploy was banned the following year, when it was agreed by the faculty senators that no one could rearrange the rankings of multiple requests from a single department. Shortly after that the math department voted him off the senate.

Crushed by the weight

Innumeracy strikes again

My student was deeply concerned. Deeply and unduly. She was worried about her quiz scores in our prealgebra class and beside herself with concern over the points she had lost. I hastened to set her mind at ease. I failed signally.

Many of my colleagues and I like to give frequent short quizzes to keep our students alert and to underscore the topics we mean to emphasize. Most of us, however, choose to give rather little weight to quizzes in computing the semester grades. After all, they're used more as learning tools rather than proficiency assessment tools. I like to give quizzes at the beginning of the period, after which I immediately solve the problems on the board. Since the students were just struggling with the selfsame problems, it's often a teachable moment. If the students pay attention, they'll be ready to acquit themselves well on the exams. Quizzes ought to count, but not too much. These days I've been weighting quizzes at 15% of the course grade. (The bulk of the weight is allotted to the chapter tests and final exam.)

My students, unfortunately, tend to have difficulty with the concept of weighted averages, and those who most need to understand it are the least able to puzzle it out. My prealgebra student is a case in point. She sees the points assigned to the quizzes and tests and cannot help but consider them equivalent. Since I grade quizzes on a 20-point scale, she figures that five quizzes must be as important as a 100-point chapter test. In reality, if I were to try to grade quizzes on a scale that takes into account the relative weights of quizzes and exams, the quizzes would be only about three points each. Of course, that would make grading them quite difficult.

Perhaps I should make the exams each worth 600 points instead. Some of my colleagues have decided to do something like that, simply making all points equivalent. They accumulate them throughout the term and assign grades to students on the percentage of points earned. Such a system, however, is not to my taste; if you decide to give more quizzes, they automatically count for more. By prescribing their weight in advance, I can control their impact on students' grades.

The downside, of course, is clear. The students don't understand the grading system because weighted averages are too complicated for them. Rats. Nevertheless, I'll take another run at explaining the weighting system after we've done the prealgebra unit on percentages. I'm a math teacher. Hope springs eternal.

Running numbers in Reno

Counting on the caucus

PiD decided to participate in the Nevada caucuses last weekend. He and his wife went to support John Edwards. The experience was, in a manner of speaking, quite educational. PiD phoned me Sunday to recount their adventures. Innumeracy was a big part of it.

The organizers soon found themselves facing a challenge: counting the participants. The leaders of the Clinton, Obama, and Edwards factions decided to go about the room pointing at people, who were supposed to count themselves off. Complications arose when the triumvirate did not always point at the same person. One trouble-maker suggested having each table of participants report its number to the leaders, who could then add up the results. This was deemed too complicated, as well as relying on the honesty of each table. The leaders persisted in the point-and-count technique. After three tries, they finally decided there were 146 attendees.

Then came a new problem, also numeric. The threshold for caucus participation by a candidate was 15% support among the attendees. Most people were in the Clinton or Obama camps, but the Edwards people faced possible elimination of their candidate. But how to compute 15% of 146? While some folks yelled out “twenty-two,” the leaders conferred in nervous agitation, trying to puzzle out the computation algorithm included in the caucus guidelines. “No, we have to be sure,” they said.


PiD and other participants were getting exasperated, but it appeared that computing a percentage was a major problem. Some people tried to explain: “Ten percent of 146 is 14.6. Add half again to get to fifteen percent: 14.6 + 7.3. You get 21.9, so the result is 22!”

The explanation didn't help. The leaders finally obtained a calculator and worked through the math several times. It was finally announced that 15% of 146 was 22. There was much rejoicing. (Well, not really.)

Although their ranks had been reinforced by a few Kucinich stragglers, the Edwards cohort did not reach the 15% threshold. The Clinton and Obama leaders pounced quickly: “Okay, you have to choose sides. You have to pick Clinton or Obama.”

The edict was not well received. PiD said, “What if we don't want to?”

“But you have to.”

Diplomacy was not the order of the day, but the Edwards people did understand that their candidate was out of the running in the day's caucus and that they were up for grabs.

“Okay, so why should we pick one candidate over the other?”

Although that might have sounded like an invitation to offer some persuasive arguments to attract the Edwards supporters, it was instead taken as an excuse to engage in mindless chanting. The Clinton forces yelled “Hillary!” over and over while the Obama troops shouted “Obama!” The Edwards cohort resisted the compelling pitches. Eventually the leaders realized it was time to talk. PiD listened to their paeans to their preferred candidates. The Clinton leader was not doing her candidate a lot of good. PiD had met her the day before when she was walking precincts to drum up caucus attendees. One of her arguments was that Hillary was not “as liberal” as her husband. That was sure to confirm PiD in his support for Edwards. Fortunately, the Clinton leader did not offer her opinion about Clinton's relative liberality again and the Obama leader was a weak advocate for his candidate.

PiD ended up moving to the Clinton side of the room while his wife took up with the Obama forces.

It was time for the calculator again. The leaders discovered that a couple of caucus attendees had slipped away. They counted up the the tally anew and determined that the Clinton forces comprised 59% of the remaining caucus participants. Someone pointed out that this meant Obama had 41%. The leaders balked. No, they had to be sure. They computed the numbers for Obama and seemed surprised to get 41%. Imagine that!

I asked PiD whether he had found the three-hour caucus experience rewarding. He told me that his first caucus would definitely be his last.

Fun with percentages

Sins of omission and commission

A pair of posts at Language Log reminds me that I have had my own close encounters of the innumerate kind when it comes to working with the concept of percentage. Some people find the notion of hundred-based fractions to be arcane in the extreme. You mean that 50% is the same as 50/100? And that's the same as 1/2? The brain explodes!

Bill Poser's Language Log post is about innumeracy among reading specialists—the folks who tell us if our children is learning to read. In the case cited by Poser, the specialists have to rely on a math crib sheet to work out the percentage changes—but the crib sheet is wrong. Are students' reading scores going up or down? It seems that no one knows.

Mark Liberman's post tells us about an on-line calculator that one can use to compute percentage change. (Someone please clue in those reading specialists!) Liberman saw a pitch to the community of public relations specialists that touted the on-line calculator as a way to avoid “feeling really old and decrepit.” (As we all know, the ability to compute percentages is one of the first things to go.) Imagine all those press releases put out by PR specialists. Can we trust any of the numbers in them? I would have said “no” in any case, but now it appears that even the PR people don't know if they're lying or not!

The pay increase

Years ago I was having lunch in downtown Sacramento with a friend who was working for a legislative tracking service. In those days it was still a growth business (before easy on-line access to legislative information wiped out most of those companies). He was looking around for a new position because his job satisfaction was exponentially declining toward zero. The latest straw had come in the form of a pay raise.

“The board of directors approved an across-the-board increase of 10% in the compensation package for employees in my unit.”

“That sounds pretty good. Congratulations!”

“It turns out, though, that I'm only getting one percent.”

“Beg pardon? That doesn't make much sense. Does your manager have it in for you?”

“Oh, no. She likes me just fine, although I do have some issues with the assistant manager. No, the manager was told she had discretion in actually implementing the pay increases. That's the problem. She was told she could go up to ten percent, depending on merit, and she doesn't understand percentages.”

“I'm still not following. If she can go up to ten and she gave you only one, she must not appreciate your work.”

“Well, this is the ‘good’ part. She thinks that the increases she awards have to add up to ten. I got one percent. Another guy got one half. The biggest increase she gave was two and a half to her assistant manager. There are seven people in our unit and she doled out increases that ‘add up’ to ten.”

“But the board authorized up to ten percent across the board! She could give each person up to ten percent!”

“Don't yell at me! I explained that to her several times. Or tried to. I'm in a bit of dutch with her right now because she thought I was trying to trick her into going way over budget. I have got to get a job working with smarter people!”

Soaring costs

A few years ago I had occasion to investigate property management companies to find out about their services and their rates. A realtor of my acquaintance recommended a company, telling me it retained 8% of the rent it collected on any property it managed, passing on 92% (less repair and maintenance expenses) to the property owner. I dropped by the company's local office to pick up the management contract and verify the rate.

The desk clerk cheerfully informed me that the company was now charging a 10% management fee.

“That's a pretty significant hike over what you were charging recently. Didn't it used to be 8%?”

“Yes, you're right,” she agreed. “But rents and costs kept going up, so we had to increase our rates.”

“But your rate is a percentage. Your revenues automatically go up in step with rents. And costs tend to keep pace with rents, right?”

“Well, yes, I guess. But they went up.”

I decided to visit a different property management company.

Sin of commission

A friend of mine was working in the home remodeling business, earning his income on a commission basis. One day he dropped in at the central office to pick up his paycheck and to touch base. The office administrator clucked her tongue at him and chided him gently:

“Robert is bringing in way more leads than you. People are noticing.”

“Leads don't matter. Sales do. How many of Robert's leads are turning into sales?”

“Well, let's see. Last month he brought in 100 leads and we closed sales on 12 of them. See? That's nearly one in ten!”

“No, it's more than one in ten. It's actually one-point-two in ten. Or twelve percent, if you prefer.”

“Wow! How did you do that? Anyway, it's pretty good. Robert's bringing in a lot more leads than you.”

“If you look at the numbers, you'll see that I brought in 64 leads last month and we closed on 22 of them. My closing rate is over 33%. And I'm outselling Robert in absolute numbers, too. That's saying nothing, by the way, about the time the company wastes in trying to close bad leads. I bring in good leads.”

“Well, I guess. But they've noticed how Robert brings in a lot more leads than you.”

My friend doesn't work for them anymore.