Archive for the ‘Arithmetic’ category

For A Good Time On The ‘Tubes (Self Aggrandizement Alert)

August 29, 2012

Just a quick heads up for fans of smart (I hope) talk.  In just about an hour, at 5 p.m. EDT (10 GMT, 2 PDT) I’ll be trading views with science writer Jennifer Ouellete (AKA Jen-Luc Piquante), proprietor among much else of Cocktail Party Physics, which gig gives me the excuse for this pic:

The conversation will take place over at my more or less regular monthly gig on Virtually Speaking Science.  Listen live or later here. Alternatively, come join the virtually live audience in Second Life.  Podcasts of VSS, including the work of my co-host, Alan Boyle, can also be downloaded at the iTunes store.  Lots of back issues there — of particular current interest, you might check out my conversations with climate scientist Michael Mann; science studies scholar Naomi Oreskes, and science journalist and “framing” advocate Chris Mooney.

Jennifer and I will be leaping off from the impulse that led her to write her most recent book, The Calculus Diaries. That’s her account of being an admitted math-phobe coming to grips with the beauty and practical value of what is truly one of the handful of greatest human inventions ever.  As I blurbed for her — calculus allows one to think rigorously about change in time and space; it just doesn’t get bigger than that, really.

We’ll go from the book to the latest kerfluffle about what kinds of math should be taught in school (see the algebra controversy sparked by this piece. For a good reply, see this.)  More broadly we’ll use the question of how to present the actual importance of thinking mathematically in everyday circumstances to think out loud a bit about an issue that is bugging me more and more these days.  To put it in personal terms — I’ve been doing science writing/film making for public audiences for just about 30 years now.  Looking at the convention of one of our major political parties in which that party declares its denial of anthropogenic climate change, evidence based medicine, investments in science education and research and so on and on and on (without even going into the anti-evolution lunacy, nor the pseudo-science with which it justifies government regulation of ladyparts and … you get the picture) — looking at all that and more, it’s depressingly easy to conclude that my career has been a net negative.

Yes, I know, correlation is not cause, which is why some of us still believe that milk drinking does not  lead to heroin addiction. But really, for all that we live in something of a golden age of popular science writing and communication other media, it is past time, in my ever-so-humble opinion, to think about what, if anything, we should be doing to reach a mass audience we clearly have not fully attracted, much less persuaded.

Finally, Jennifer is near the end of a book that has proved much more challenging to write than she blithly thought going in.  I’m just starting a book I’m convinced I have got under control. (Thus every folly begins, in innocent confidence…) So we’re going to talk just a bit of shop:  how every book project trips you up, and what you can do about that terrible moment when you are finally, utterly, deeply certain that you computer is going to reach through the display and throttle you; just put you out of your and everyone else’s misery.

Should be fun.  Check it out when and as you have a notion.

PS:  As a DEW — Sunday, September 9, 8 p.m. EDT, 6 p.m. MT, I’ll be talking one of my old books, Measure for Measure: A Musical History of Science with the incomparable Desiree Schell on Skeptically Speaking. I’ve been on the show once before as a guest of Marie-Claire Shanahan, and it was a lot of fun.  Desiree is a fabulous interviewer, so I’m looking forward to this one too. But it’s relevant to the post above, if only because the book that both nearly killed me and most taught me to write was Measure…in which I succumbed to what I have decided is the dreaded second book syndrome.  More to come…

Image: Edgar Degas, L’absinthe, 1876

In the Integer-Based Community

June 21, 2011

I’ll give that unnamed Bush staffer credit.*  It is possible to create an alternate reality — if only for a time — given the willing complicity of all those watching (and transmitting) the useful fantasies of the powerful.  Just look at the success the Koch brothers’ subsidiary political arm, aka the GOP et al. have had in persuading so many that wealth transfers to the rich are the solution to all ills.

Hence the significance Bruce Bartlett’s entry today in The New York Times Economix Blog, in which the former Reagan, Bush I, Ron Paul and Jack Kemp policy advisor writes that, in essence, the entire Republican presidential field is lying about taxes to the American people.

He doesn’t quite put it that way — but he comes pretty close:

For years, Republicans have [said] …over and over again that taxes in the United States are exceptionally high and the primary obstacle to growth, and that a huge tax cut would do more to raise growth than any other policy.

For example, former Gov. Tim Pawlenty of Minnesota, a candidate for the Republican presidential nomination, has proposed reducing the top statutory income tax rate on individuals to 25 percent and abolishing the taxation of interest, dividends and capital gains. The Tax Policy Center estimates that this plan would reduce federal revenues by $8 trillion over the next decade.

Governor Pawlenty contends that unprecedented growth will result — to such an extent that there will actually be no revenue loss at all.

I am not picking on Governor Pawlenty; all of the candidates for the Republican presidential nomination support similar policies, and not one has criticized him for making outlandish claims.

Yup — that’s as card-carrying a conservative (per commenter wvng below) stalwart as you can get, stating as fact (which it is) that the fundamental Republican position on tax policy is “outlandish.”


Now this is, or ought to be obvious.

Bartlett here is actually responding to critics of an earlier post in which he made the following points:

The economic importance of statutory tax rates is blown far out of proportion by Republicans looking for ways to make taxes look high when they are quite low. And they almost never note that the statutory tax rate applies only to the last dollar earned or that the effective tax rate is substantially lower even for the richest taxpayers and largest corporations because of tax exclusions, deductions, credits and the 15 percent top rate on dividends and capital gains.

The many adjustments to income permitted by the tax code, plus alternative tax rates on the largest sources of income of the wealthy, explain why the average federal income tax rate on the 400 richest people in America was 18.11 percent in 2008, according to the Internal Revenue Service, down from 26.38 percent when these data were first calculated in 1992. Among the top 400, 7.5 percent had an average tax rate of less than 10 percent, 25 percent paid between 10 and 15 percent, and 28 percent paid between 15 and 20 percent.

The truth of the matter is that federal taxes in the United States are very low. There is no reason to believe that reducing them further will do anything to raise growth or reduce unemployment.

Remember, this is just propaganda from  your typical liberal conservative economist with longstanding ties to reliably anti-tax members of the Republican party.  Also, note, that along the way in that post Bartlett called out the conservative punditocracy as, again, liars:

Stephen Moore of The Wall Street Journal recently asserted that Democrats were trying to raise the top income tax rate to 62 percent from 35 percent. But most of the difference between these two rates is the payroll tax and state taxes that are already in existence. The rest consists largely of assuming tax increases that no one has formally proposed and that would be politically impossible to enact at the present time.

Ryan Chittum, in Columbia Journalism Review, responded with a commentary that called the Moore analysis “deeply disingenuous.”

Nevertheless, one routinely hears variations of the Moore argument from conservative commentators. By contrast, one almost never hears that total revenues are at their lowest level in two or three generations as a share of G.D.P. or that corporate tax revenues as a share of G.D.P. are the lowest among all major countries.

This is what apparantly appalled Bartlett’s readers, and this is what prompted him to … well, not defend himself, but to double down on the key point:

A typical middle-class family, on the other hand, is paying less in federal taxes than it has since 1967. Its marginal rate is also down substantially since it peaked in 1982 at 31.7 percent. The well-to-do family, too, has seen its average and marginal tax rates decline substantially.

Of course, these data do not prove that taxes are not too high. That is a subjective judgment related to issues of fairness and the value that people assign to the government benefits they receive in return. Many in the Tea Party talk as if the value of government is zero; consequently, they would probably complain about any tax level above zero.

Nevertheless, it is clear that federal taxes have not been rising and are, at least in historical terms, lower for most taxpayers than they have been since the 1960s.

There is a famous line from the history of mathematics:  “God made the integers.  All else is the work of man.”

That quote has had plenty of glosses, but let me appropriate it here to describe what Bartlett has just done.  We have real numbers about taxes.  We know what they are, and Bartlett in both of the cited posts provides handy historical references to allow any reader to trace the trajectory of those numbers.  They are facts, chunks of experience quantified, and they have autonomy:  Moore’s claim that a 35% rate is really a 62% rate is not a matter of interpretation; it’s just wrong.

But, of course — as Moore’s sin illustrates — what we do with such numbers,  the calculations we perform, the conclusions we draw from them, the interpretations we derive or force on them, why, all those are down to us.  It’s no god’s nor FSM’s fault when we turn the actual knowledge we have into fashion accessories cloaking choices too ugly to pass unadorned.

That’s what Bartlett, seemingly now irrevocably committed to the reality — or perhaps, better —  the integer-based community, is actually saying here.  To reiterate:  a leading conservative policy thinker and economist has just demonstrated that the entire Republican presidential field is talking nonsense about fundamental economic policy.  The implication couldn’t be more clear:  if these views gain direct power over US policy, WASF, even more than usual.

The question, which so far answers itself, is whether or not the media as a whole, and not just some (albeit prominent) blog-contributor, will pick up on this theme, and present the choice in 2012 as that between destructive fantasy and reality.

I live in hope, but not in expectation.

Bartlett himself demonstrates why.  This is the very last line of his post:

Those who assert that taxes are rising or are at confiscatory levels simply do not know what they are talking about.

That may be true of some — but people like Pawlenty or Romney or Gingrich, any of them, really, have no such excuse.  Pawlenty governed a state for two terms.  Romney, we are told, is a smart money man.  You get the point.  They do know what they are talking about, and they choose to divorce themselves from the facts.

These are not potential Presidents.

Factio Grandaeva Delenda Est.

*Said to be Karl Rove.

Images:  Vincent van Gogh, The Corridor at the Asylum, 1889.

Martina Schettina, Fibonacci’s Dream, 2008.

Attack of the Mutant Ninja Fiscal Conservatives

May 16, 2011

Oh Noes!

Via TPM:  the GOP-led budget insurrection over the six-month spending bill in March actually boosted spending over that period by $3 billion, according to the latest CBO analysis:

“Total discretionary outlays in 2011 will be $3.2 billion higher as a result of the legislation, CBO estimates–an increase of $7.5 billion for defense programs, partially offset by a net reduction of $4.4 billion in other spending,” reads a just-released report from the Congressional Budget Office — Congress’ non-partisan scorekeeper. Analysts there conclude that increase is due in large part to the fact that the six month spending bill shifted defense spending to more immediate activities, which means the bills will come due sooner than later.

It is true that the bill will, if unchanged in any future budget, lead to about $122 billion in spending reductions…(wait for it)….over the next ten years.

That’s barely more than what the Republicans road into office swearing they’d cut this year alone…not to mention that $122 billion out of a truly unrealistically conservative estimate* of ten year expenditure of $25.4 trillion dollars amounts to a rounding error — a reduction of on the order .5% over a decade.

Way to go!

The initial reports of $38 billion in cuts, by the way, were Teabagger bait, which means that the Republican party has some ‘splainin to do to its base, and the rest of us should help tell that story as much as we can.

Here’s how the scam worked:

the approximately $38 billion in advertised cuts spanned the entire federal budget, including locked-in “mandatory” spending programs, and it reflected reductions in “budget authority” — how much the government is allowed to spend — as opposed to projected “outlays” — how much the government truly will spend.

Ah, that old problem for the GOP and its voters — the difference between what the tooth fairy promises, and what actually happens in the real world:

When viewed more narrowly — how many fewer dollars will the government spend this year as a result of this bill — the results flip.

Which is to say, the GOP rookie congresscritturs and the Tea Party electorate were promised one thing, and got…played.

The moral, dear faux Minutemen:  the GOP’s central command has exactly no interest in actual lower-case “c” conservatism.  They serve different masters…or to put it another way:

If you can’t tell who the patsy is at the table, it’s you.

*That number comes from the simple-minded multiplying the (pre-stimulus) 2008 numbers — an arithmetical gesture of maximal kindness to our GOP arithmetic-challenge friends.

Image:  Follower of Hieronymous Bosch,  The Battle Between Carnival and Lent, (A subject sometimes titled The Dance of Fools, Carnival.), c 1600-1620.

Give The Man One White Chip*

April 15, 2011

Via the NYT we learn what constitutes “big” to a Republican congressman.  (No, children…don’t go there.)

(Hell.  This is the internet.  Go there if the spirit moves you.)

By now, just about everyone with a pulse and an interest in politics knows that the budget debate produced much more kabuki than actual cuts.  Rather the reverse in fact:

According to a Congressional Budget Office comparison, the bill would produce only $350 million in tangible savings this year, in part because cuts in domestic programs were offset by an increase of about $5 billion for Pentagon programs.


When projected emergency contingency spending overseas is figured in by the budget office, estimated outlays for this year will actually increase by more than $3 billion.

There are longer term effects that restrain spending.  Albert Einstein is said to have said that the only true miracle in the universe is compound  interest.  That’s apocryphal, of course, but it is true that cuts in baseline expenditures in discretionary spending will propagate through the years to come:

The agreement does put the brakes on what had been a steady growth in spending by federal agencies. Future savings would be greater as the cuts took hold — a point Republican aides emphasized by noting that the plan is estimated to cut spending by $312 billion over the next decade.

Sounds like a lot of money.  At least, so says those members of the GOP, who quail before the wrath of the pitchfork brigade that they’ve turned into their base.  Hence nonsense like this:

“Big stuff,” said Representative Tom Price, a Georgia Republican and leading conservative.

Yeah, I know.  A billion here and a billion there and pretty soon you’re talking real money.

Except that $312 billion, for all that it could buy is …


…a rounding error — or an example of the kind of numerical trick that confidence men use to gull the unwary, the inattentive, the numerically illiterate.

I’ve beaten the drum elsewhere for the importance of getting minimal quantitative reasoning into the electorate.  I’m not talking much math here.  I’d be happy if we got folks using arithmetic on a daily basis  to test claims like Price’s above.  If the country could do that, then there are lots of cons that would become brutally obvious, even to folks as frightened of numbers as tools of reason as our Village press corps.**

Hell, Price isn’t even trying to hide the tell:   that really big, scary number $312 billion. Sitting there, all by itself like a fresh cow patty steaming on a patch of meadow grass.   Everyone here knows what’s wrong with this:  it ain’t the numerator that matters.  It’s the denominator, dawgs.

And this is where both Obama and the Democrats, and the in-the-bag-for-big-money GOPers (most of the Congressional caucus) made marks of the Tea Party.  Even though we don’t know what the 2012 budget will be, much less spending levels of a decade hence, we can still construct a pretty good picture of the whole load of nothing going on:

Just work through a wholly unrealistically low set of assumptions on spending over the next decade.  Take level budgets from the FY 09 request — George Bush’s last budget — of $3.1 trillion.  That’s below expenditures by about a trillion, by the way, for a variety of reasons, and it is substantially under today’s numbers, which are, of course, the baseline for future cuts.  But hey — let’s make the GOP look as good as it can.

So multiply $3.1T by 10, and you get -the implausibly low figure of $31 trillion.

Price’s “big stuff” — $312 billion — is 1% of that fictitious total. One [more] minor war over the next decade and it’s gone.   A few disasters.  An economic downturn, with its upward pressure on social welfare expenditure.  And so on…

Big stuff.

Oh — by the way, I sent a draft of this post to an economist friend of mine  as a check against slips of my calculator or my logic (not an American, btw, so someone who can look at this with at least some a- or be- mused distance).  He reminds me that it is always useful to contextualize public finance numbers by a per-capita measure.  Given that the most recent population figures show the US as home to just a skosh over 310 million people, the projected budget reductions of $312 billion work out to no more than $100/person.  In my friend’s words:

I think most people can see that is not a gnat’s fart but it’s not going to solve anything. Put another way it’s of the order of 1/500 of GDP in round terms.

Consider this another episode in Percentages:  How Do They Work?…

Or else, see it as a reminder of what the GOP is really all about.  Hint:  it ain’t the deficit.

*This title comes from story I heard once, no vouching for its accuracy, about the time some industrialist — a metals guy — came to Detroit to announce his company’s entry into the car business.  He told the assembled automobile journalists about his plans, and his willingness to spend what it would take to compete.

He was, he said, prepared to invest $25 million in the venture.

From the back of the room, an old car hack piped up:

“Give the man one white chip.”

**Numbers as fashion accessory — as above — that’s fine.  But actually thinking with them…

Images:  Victor Dubreuil, Barrels of Money, c. 1897

Gerard van Honthorst, The Cardsharps, before 1656.

Yup, I Do Need A 12 Step Program: McArdle’s Calculator Is Acting Up Again, Social Security edition.

February 18, 2011

Oh boy.  Speaking of faux hawks, Megan McArdle yesterday decided to start getting serious about the deficit.*

In McArdle’s playpen, that means we’ve got to eliminate Social Security for the middle class (and the rich), shifting instead to covering only low-lifetime earners.**  There’s more:  She offers a Medicare budget “plan” designed to replace the lower cost provider of medical care with more expensive private insurance ones.  I’m not going to bother applying a beat down to what she suggests on health care because it is (a) at least partly incomprehensible — what is “long term care insurance for the carriage trade?”*** and because I really do have a day job and thus don’t have the spare minutes to do my usual John Foster Dulles on this subject right now.

No, here I just want to offer one more ranging shot in my ongoing attempt to demonstrate that McArdle’s serial errors of journalistic craft, large and small, are on their own, divorced from her politics, sufficient reason to dismiss her as a particpant in any civic conversation.  That such failings support her disastrous views is, to be sure, a feature and not a bug — but what continues to amaze me is that she doesn’t even meet the minimum threshold for the career in which she has had such institutional success.  It’s as if she were a cop who never got the hang of that radio thingy.

So what is it this time?  Try this passage:

But people looking at percentages of GDP are dramatically underestimating the scale of what’s involved.  For example, I was on a panel where someone told me that “all” we had to do to salvage Social Security was lift the cap on social security earnings. My reaction was:  all?  That’s a fifteen percentage point tax hike on all income above $106,000, much of which is supposed to be taxed, as of 2014, at 39.5%.  On top of the 55% marginal tax rates you’re proposing on top incomes, you need to add in state and local taxes, and the already uncapped Medicare taxes, plus the Medicare surcharge, pushing the marginal tax rate on  those incomes well over 60%.  To look at it from the point of view of the wealthy, you’re proposing to slash their current after-tax salary income by about a quarter in one fell blow.

What’s wrong here?  Well, to be going on with, there’s an elementary mistake about the Social Security portion of FICA.   Lifting the cap on earnings taxed for pensions would increase tax levels on those extra dollars by 12.4 %, not 15 %.****  That would be because, as McArdle seems to remember in a sentence or two, 2.9% of the payroll tax total of 15.3 % goes to pay for Medicare, and already is not subject to an income cap.

It’s a little error, I’ll admit, perhaps genuinely a careless one.  It is notable (at least to me) that the error falls on the side of making the case for the poor worse and the concern for the rich greater — all SOP in McArdle’s stuff.  But maybe this truly was just a slip of memory, an instance of sloppiness rather than malice.


In the end, of course, the question of rhetorical intent doesn’t matter much, at least not from my perch as an observer and teacher of writing for the public.  If you can’t get things right, big or little, to some quite high level of performance, you just shouldn’t stay (or be allowed to remain) in this business.

Still, as so often with McArdle, there’s more to this mistake than meets the eye.  She accepts her interlocutor’s premise that it would take a really big tax — whether her 15% or the real 12.4% number — to restore Social Security to perpetual balance.  But is this true?

No. (Surprised?)

I don’t have the full range of calculations in front of me, but it happens that last year Rep. Robert Wexford (D-FL) asked the Social Security Administration to calculate the effects of imposing a 6% tax on all income above the current cap.

The results: that change alone would eliminate more than half of the projected shortfall in Social Security as of 2083.  In that context, relative minor changes to the benefit structure (e.g. a change in the indexing calculation to shift the index applied to higher earners from wage growth measures to the consumer price index) would render the system in balance indefinitely.

Now, apply Wexler’s six percent number and get rid of McArdle’s double counting of the Medicare charge, you get to a federal maximum marginal income + FICA rate of 48.4 %.

Next, to return to McArdle’s  calculation:  the Medicare surcharge McArdle mentions for those above the current Social Security income cap level of $106,000 will run from about $1,000 a year to about $3,200 for the highest earners.  Which means we’re  talking about maxing out at a marginal, not total, federal tax burden of about 50% — instead of the McArdle preferred rate of roughly 44%.  The difference between a take home of 50% of (marginal) adjusted gross income as opposed to 56% is, of course, a big chunk less than one quarter.  Which is to say that McArdle’s calculator is broken again.

I’ll reiterate that the Wexler number doesn’t entirely close the 75 year gap. But it gets damn close — and the point is that McArdle postulates in her post that we have to kill Social Security (as a universal program) to save it.  Not so:  real calculations with honest numbers show that much less drastic treatments can cure the pension program’s ills.


The point:  yup, Social Security has a long term solvency concern.  It is, as everyone here knows, far from the biggest budget issue we face — that would be health care costs — and there are a number of paths out there to get to decent outcomes for the aged.*****


Enough.  You get the idea:  McArdle fails on the elementary journalistic task of reporting the most basic facts within her story correctly.  Those errors support larger failures of interpretation and intellection, to the detriment of her own reputation, to the discredit of her venue, and to the disadvantage of the republic.

And with that I’m off the McArdle beat for a while, except for tying up the loose ends of kitchen folly. I’m just not going there for as long as possible.  There is a whole web out there; why spend any more time than one must mucking about in the swamp?

*Yes, I know.  I need a twelve step program.  I promise that this is the last McArdle post for a while, but for my promised response to her bit of silliness attempting to excuse her kitchen follies. But she does provide such a tempting target…

**This is the kind of manure advanced by  folks who either no nothing about a subject or whose real goal is not the stated one.  In this case:  look at national support for transfer payments to the poor and ask how long Social Security transformed into a welfare payment of the elderly poor will remain unscathed.  This is pure opinion, of course, but it is a historically informed one:  Social Security works because the middle as well as the poor understand its value.  Erode that, and the whole structure is at risk — and grandma will count herself lucky if she can dine on cat food. Whether this is a bug or a feature for McArdle I’ll leave for others to ponder.

***McArdle’s full “plan” (sic-ed) for health care cost containment:   “You put tight(er) means tests on Medicare and Medicaid to encourage the development of markets for private health insurance and long term care insurance for the carriage trade.” Because our private market for health care has tested out so well already, no doubt.

****For 2011, the total SSI tax rate goes down 2% under the tax deal reached during last year’s lame duck session.  It won’t last.

*****You can see a wider range of options of both benefit cuts and payroll tax increases in another calculation that the SSA ran in response to a National Research Council/National Academy of Public Administration study.****

Images: Laurent de La Hyre Allegory of Arithmetic,  c. 1650
Theo van Doesburg, Study for Arithmetic Composition, 1929-1930.
Francisco de Goya, Old Man and Woman Eating Supper, 1821-1823.

How Hard Are Fractions, Really: Elizabeth Warren Scares Her/Megan McArdle Is Always Wrong Chronicles, Cont’d.

July 28, 2010

Update: some edits to make the post read like someone without a grudge against English syntax wrote this post. Nothing substantive — a couple of cuts, a couple of verbs supplied to verbless “sentences.”

I guess I just can’t quit that Ms. McArdle.

I vowed to give myself a break from looking at the work of someone who seems to me to be trying to live up to fitness report number 12 on this list (or perhaps, better, number 4…oh hell, actually, a whole bunch of them).*

But then I read on, and I can’t help myself.

In my last post on this subject, I compared elements of her hatchet job on Warren to the techniques Andrew Breitbart uses in his war on progressives, Obama, and random African Americans who drift into his sights.

This time, it’s a little different:  McArdle is here simply trying to confuse the issue, apparently in the hopes that each bit of noise and nonsense that she can generate around Elizabeth Warren will damage her chances to become the first director of the he new Consumer Financial Protection Agency.  It’s an example of what I’ve called in the past McArdle’s monkey-in-the-zoo approach, in which she flings anything that comes to hand against the wall and hopes some fraction of it will stick..

To recap McArdle has promised the world a second part to that first post that attracted much uncomplimentary attention, but, as Susan of Texas notes it’s been a while.  In the meantime, she has outsourced the task, excerpting a Wall St. Journal op-ed of some years ago, which she presents under the title, “More Weird Metrics for Elizabeth Warren.”

What is so weird to McArdle?

Expressing tax liabilities as percentages of income.

No, really.

As in:  a single-earner family with an income of $38,700 facing a tax burden that claims 24% of that total.

As in: a two-earner family with earnings of $67,800 facing a tax burden of 33%.

Stating tax bills in this manner is apparently a dreadful sin, a willingness to mislead or a confusion about the underlying data.

Or so says the WSJ item’s author, Todd Zywicki, who in the passage quoted by McArdle complains that Elizabeth Warren and her co-author Amelia Warren Tyagi express certain items in raw dollar terms — $5,140 on car expenses for the single earner example, for example, vs. $8,000 in the two income family — but state tax liabilities only as percentages.

To Zywicki, this amounts to an obvious attempt to confound “an “apples to apples” comparison of all expenses.”

He corrects this, in his mind, by performing what he seems to regard as the utterly impenetrable magic act of performing two calculations:  .24*38,700 and .33*67,800, to yield dollar figures for the tax bills the two families in these examples owed.**

But beyond this en passant swipe at the eternal mystery that is the Wall St. Journal op-ed operation, our real concern here is McArdle.

She too, apparently, finds expressing a quantity as percentage of another, specified quantity, somehow suspect, a “weird metric.”

More, she regards this example as somehow dispositive of a systematic misuse of data, a demonstration of either Warren’s incompetence or her dishonesty.  McArdle writes,

Does it matter if we have a regulator who can use data consistently?  A lot of commenters seem angry that I would suggest it might.  As for me, I don’t know which is worse:  the notion that Elizabeth Warren understood what she was doing, or the notion that she didn’t.

My question would be, were I the publisher of The Atlantic, does it matter if we have an economics writer who can, apparently, neither read nor count?

Now that’s harsh, and I know it, but look at what happens if you read Warren’s and Tyagi’s examples in good faith, with a view to understanding what they are actually trying to say.

Well, long ago I wrote about the importance of such simple calculations as percentages to raw data in the context of Iraq War casualties.

The point there was that doing so allowed one to make comparisons across disparate bodies of data or historical examples.  If you want to understand the implications of  600,000 casualties among Iraqis, it helps to express that as a percentage of the population affected, which then allows you to compare it to, say, the deaths suffered by combatant nations in World War I or the American Civil War.  Thinking about the comparisons those enabled provided the frame for the moral of that post:  that the application of even veryy simple arithmetical/mathematical ideas to the raw experience of the world can prove enormously useful.

So, what might persuade Warren and Tyagi to present housing expenses or car costs as dollar numbers but  tax burdens as percentages?

Well, if I were to guess, it would be to make a point central to their larger argument:  that there are systematic increases in costs that accompany the increase in earnings in as you move from one income to two — but that different kinds of cost increases behave differently, have different scales of impact on the outcome for a two-earner family.

That is — increase in car costs like most family expenditures are basically linear:  if you go from one car to two, you pay a bit more in payments, insurance, and maintence, and that’s it.  If you take on a larger mortgage, the same applies and so on.  As Zywicki notes, apparently with some sense of being deceived, this results in such costs consuming a smaller percentage of the gross family income for two-earner households compared with single earner ones.***

Update:   note commenter Jim Bales analysis below.  Zwicki’s sins are worse than what I, in my haste to get this up, fully recognized; Jim does the due diligence.

But I think every sentient American knows that taxes don’t behave like housing or car payments.

In fact, I find it hard to believe –absurd, in fact — that McArdle, of all people, a self proclaimed libertarian, doesn’t grok the point Warren and Tyagi are trying to make as clearly as possible by using an expression for the tax burden faced by their two families in percentages.

After all, the book is about the two income trap.  And one of critical elements of that trap, as we all know, is that marginal tax rates go up at higher income levels.  This is, of course, something that McArdle has written about –notoriously quite recently, in her “calculatorgate” post.

In fact, in every context but the one in which she attacks Warren, McArdle grasps the implications of a progressive income tax, and she should, of course, given the fact, noted above, that every American who has ever looked at a tax table recognizes that the last dollar of income above minimum thresholds is taxed at a higher rate, a higher percentage than is the first.

So, quite the contrary to the charges leveled against them by Zwicki and McArdle:  Warren and Tyagi weren’t obscuring a fact that anyone — probably even McArdle’s calculator! — could obtain in seconds from the raw data they povided in full.  Rather, they were making the point that their own argument required in the best form they could — which, I meekly say, as the writer of this and that myself, is the essential core of an author’s job.

And that argument, the one that Warren and Tyagi developed across a couple of hundred pages, turned on explicating the fact that two incomes do not bring wealth proportional to the effort expended to acquire them.

Which is what would be understood, pretty clearly, I believe, by any reader unburdened by a willed desire not to get it.  How hard is to grasp that marginal tax rates in progressive taxation systems — which are generally pretty well expressed as percentages — act as a drag on the aspirations of two earner families?

This is not a raving radical position.

I believe I’ve heard some conservatives lament this very fact.

All of which is to say that there was nothing “weird’ about Warren and Tyagi’s metrics– unless asking a reader to do a quick bit of mental arithmetic (what’s one quarter of 39K vs. one third of 68) is somehow a malicious act by authors bent on deceit.

That McArdle might find that task daunting I find plausible, barely, given her recent trouble with long division.

But really, I know that she’s perfectly capable of handling fractions.  This is pretty clearly a case of willful misreading to a malicious end,  a baffle with bullsh*t moment.

So, with that,  I’m left here with is her own question, again rephrased for those in charge at The Atlantic. Does it matter if your “Business and Economics Editor” cannot consistently grasp the simplest of calculations, the most elementary of analyses?  Is it worse that McArdle understands what she is doing, or that she doesn’t?

*My personal favorite has always been number 2, but that’s just me.

**…Then, seemingly oblivious of the hilarity that thus ensues, Zywicki converts a number of the other quantities into percentages to make comparisons of the relative weight of different expenses possess in the two family’s budgets.  Seriously.  Oh well.  That was long ago, in a country far, far away, and besides, the kvetch is dead.

***He seems to think Warren and Tyagi are concealing this fact, as if it is beyond the ken for someone to notice that $8,000 is a smaller chunk of around 68K than roughly $5,200 is of $39,000. Truly, this just isn’t that hard.

Images:  Jan Massys, “At the Tax Collector,” 1539

The title pages to two arithmetic texts published in Germany in 1514

Megan McArdle is Even More Always Wrong Than Usual: Arithmetic is Hard/Mostly Outsourced edition

July 22, 2010

By now most everyone who cares (a swiftly dwindling number, I hope) has heard of Megan McArdle’s spectacular meltdown when confronted by arithmetical and analytical errors of the most damning sort.

By far the best account of this comes in a spectacular fisking of McArdle by her own commenters, as organized by the invaluable (and stronger-stomached-than-I) Susan of Texas over at The Hunting of The Snark.

I’m not going to bother linking to McArdle herself. Why reward her with even the mote of traffic that might come her way, when SoT provides the complete text with commentary.  A veritable Talmud of McArdle.(I’m not sure I can really get my head around that concept–ed.)

In short form:  Ms McArdle can’t count, and she can’t think either — but those errors of argument are rather more strategic than they appear.  (She can’t deal with criticism either, which leads to much hilarity in this instance.*

So, to begin with, McArdle mistakes $250 for $25, and then uses the lower number as her estimate of how much money could flow to each American if taxes on the wealthiest were allowed to return to the levels experienced in the last epoch of budget surplus and sustained job creation and economic growth.**

She then went on to make an claim in large part based on that error: that the stimulus effect of choosing to recapture foregone revenue from the rich would be tiny, given that $25 buys no more than “one pizza dinner per person.”

Now, you can get the full takedown on the serial sins of fact and logic that McArdle made at Susan of Texas’s place.  Here, I just want to add two thoughts.

For one, McArdle’s first order claim — that redistributing to the population at large the money that is now earmarked for tax cuts for the rich will have no effect because the sums involved are trivial — allows her to ignore the reality of class and economic life as it is lived by most Americans.

In fact, as the upper-middle-class McArdle chooses not to know, the difference between a $100 supplement to income for a family of four and $1,000 boost is potentially life-changing, especially at the economic margin.

That’s roughly one month mortgage payment or better at median house prices right now.***

That’s one more month of high-deductible health insurance for the family in my home state of Massachusetts.

That’s the food budget for about a month and a half.

You get the idea.

More broadly, the real failure lies with her claim that one basically can’t figure out whether or not spending money on unemployment insurance is good for the economy (and not simply struggling individuals) as compared with retaining the current tax structure.  She writes:

it assumes that the rather optimistic estimates of Mark Zandi about the size of the stimulus multiplier are correct. Estimating stimulus multipliers is incredibly difficult when you try to do it at the macro level (how much spending equals how much extra GDP), and even more difficult when you try to figure out whether food stamps are better than a jobs program–the examples are fewer, and the amounts are smaller, making it hard to pick up direct effects.

I.e., you can’t figure out what a given policy will do (according to McArdle, ex cathedra)…and worse — even if there were a discernable impact, it wouldn’t matter. Why not?  Because the measures of success are meaningless:

It also assumes that any measured increase in GDP measures some improvement in human welfare. It is trivially true that if you increase one component of a measured variable, that variable will get bigger. It’s much harder to know that any particular increase in GDP represents a real change in human welfare, or merely moving chess pieces around the board.

Now that last statement is simply nonsense, as stalwart McArdle commenter Zosima pointed out. measures may be imperfect for all kinds of reasons, but that doesn’t mean that they are devoid of meaning.

But McArdle, I think, doesn’t really care if she’s wrong or risible.  Her real goal is to advance the notion that government action informed by reason and empirical knowledge is impossible.

Hence the value (for her) in repeating stuff like this.  This isn’t about the stimulus, in other words, or appropriate tax policy.  It’s about the impossiblity of governance.

In that light, the key fact to remember is that McArdle’s lapses of reasoning and fact are features, not bugs.   Remember the mission as declared by her home institution: “TheAtlantic – shaping the national debate on the most critical issues of our times, from politics, business, and the economy, to technology, arts, and culture.”

McArdle is indeed trying to shape the debate, to constrain what might be possible in the exercise of government power.  Mere logic, paltry fact may not be permitted to get in the way.  She is Always Wrong™ — by design.

*Here I shamelessly steal from Susan, uber smart serial commenter Aimai’s summary dismissal of the divine Ms MM on McArdle’s comment thread:

Hm, lets see if the site lets me post. Can I ask whether this long, incoherent and off point attack by Megan on poster zosina is, in fact, by Megan? I mean, look–for one thing the “Megan” in this post claims to be the child of academics when the real Megan, as far as I know, is the child of a former public employee turned lobbyist and a realtor. Second of all the real Megan presumably grasps that “being the child of academics” doesn’t actually amount to an argument. No, really it doesn’t. Actually, and for real, I’m the child of a Nobel Prize winner and for kicks I’ll add I’m a third generation Harvardite. So what? This really, really, really, never comes up in academic arguments which are actually won and lost not by some kind of bizarre blood test but by concrete arguments. The “you are tedious and lack charm” argument is also one that I have yet to see adduced in a respectable discussion. Certainly, on the basis of the evidence from this thread, its hard to tell which of the two of you, the “megan” poster and the zosina poster is the younger. If I didn’t know that the real Megan is 37 I’d have had to award this avatar the palm for most juvenile approach to intellectual discussion. Finally, I have yet to see the imaginary comments “Megan” refute any of Zosina’s points. If this thread “Megan” isn’t the real Megan I think the real Megan might want to step in and clean up the comments by deleting her. But if she is the real Megan I think the Atlantic might want to step in and jerk the blog entirely. This is a positively craptacular piece of incoherent special pleading on Megan’s part, from the first post to the comment thread. Really, its shameful. And you don’t have to be the “child of academics” to know that.


**McArdle later tried to excuse herself by noting that her calculator could not handle the millions – billions quantities in the division.  To which I respond that it one of the skills we train our students in at the MIT Science Writing Program is that of estimation, and the honing of a nose for suspect numbers.  I would have thought that someone so inordinately proud of her role as “Business and Economic Editor of The Atlantic” would have cultivated the same.  If she hasn’t, then I would respectfully suggest that this is just one more piece of evidence that she is unqualified for the position she now holds.  I mean, dude — was it so hard to reconfigure the 75 billion/.3 billion raw number into 750/3?  There.  That wasn’t so hard.

***That statement is based on the following calculation:  take the median price for a new home as of Q1 2010, subtract 10 percent for a down payment and come up with a mortgage balance of $195,000 (give or take a buck).  At the current 30 year mortgage rate of 5.36%, you get a principal and interest payment of $1090 and a couple of cents.)

Image:  Francisco de Goya “Old people eating soup,” 1819-23

Last, for now, to Galt’s Gulch. A Libertarian Commenter Proves Mah Point…

February 3, 2010

Jim K., in this comment thread takes issue with my claim that anti-tax glibertarianism is (a) one of the root causes of Colorado Springs’ current predicament and (b) is powering a potentially deep decline in American wealth and power.

The issue, he says, is not the shortfall in taxes, but the “abomination” — his word — that city employees are overpaid,  excessively well-benefitted, and inflexibly secure in their jobs.  This labor greed and rigidity, and not the collapse of tax revenues in the context of anti-tax politics is to blame for the loss of police and fire jobs, the darkening of city streets and so on.

In Mr. K.’s words:

The argument that folks like me (who are apparently wrecking the American way of life) have is not with government provision of services per se but the fact that a great proportion of the dollars we are paying into the government these days is going to support unsustainably high compensation schemes for government employees.

To demonstrate how iniquitous is this burden, he offers some numbers:  a presumed final salary after 40 years of work of $75,000 that would, he claims, linking to the Colorado public pension system’s benefit calculator page, yield a 100% pension — the equivalent, he asserts of an annuity that would cost one million dollars and change to buy on the open market.

And wait! it gets worse:

Additionally, most state employees do not fund any contributions to their pensions from that 75K.

Sounds bad, I guess — except for two problems that are to me illustrative of the absolute intellectual poverty for what passes for libertarian argument in this country.  First, such arguments are usually deeply empirically challenged, as they are here.

That is:  Mr. K.’s key numbers are wrong, apparently simply made-up.  It may be true that if you, as Mr. K. says he did, “plug some numbers” into the the benefits calculator you get a retirement payment equal to your salary at retirement.  But no actual Colorado public employee does.

Instead, as Mr. K. would have discovered had he employed his mad intertube skillz just a little more rigorously, the retirement benefit ranges runs by yearly steps from 10% after five years of employment to a maximum of 87.5% at thirty five years of service and above.  Significantly that percentage is not calculated on the final, and commonly the highest paid year of service, but on a formula that provides for a lower figure and that, in essence, prevents any sweetheart raises from skewing the retirement payout. (All this can be found by clicking on this link and then downloading the relevant benefit explanations.)

There’s more, of course.  Mr. K. asserts that most state employees don’t contribute to their pension plans.  Maybe in his universe, but not in this one.  The Colorado plan, PERA reports that in 2008, employees contributed $717 million to the plan, while employers provided $863.5 million. You can, I suppose, argue about the appropriate ratio — but the key message is that, of course, Mr. K. said something flat out wrong that, conveniently, supports his myth of the leech-like viciousness of public servants.  In the real world, the employees of Colorado Springs have been paying significant amounts to their own future compensation.

At the same page, you’d find that the average monthly retirement benefit for 2008 was $2772, which annualizes to all of $33,264 — not nothing, truly, but hardly the caviar and Cadillac compensation of Mr. K.’s fever dreams.

Enough: you get the point.  Mr.K., like many of the anti-government crowd I’ve argued with in the past, feels free to assert what he is convinced must be true.  That’s behavior I recognize as I raise my small son — but it is something that, thankfully, at age nine, he has begun to outgrow.  It seems a developmental disorder afflicting much of the body politic that a similar progression has not taken place amongst too many alleged adults.

The problem with such invention is that it has real consequences.  In this case, Mr. K. wants to see Colorado Springs employees taking one for the taxpayer:

What else am I forgetting? Health care benefits, much better job security, and hours and holidays most of us would envy….What is really destroying the American way of life, the unwillingness of some of us to pay ever more to support this abomination or the fact that we have created a class of citizens who demand ever more of our money in return for keeping the streetlights on?

Hey! I thought class war was for my side!

This is the second problem with glibertarian discussions of the evils of government.  They really do believe in magic ponies.  Streetlights good.  People who go up on lifts to change them? “This abomination.”

I don’t doubt that there is waste and sloth and indifference in government service.  Hell, I’ve seen it in every business  or institution I’ve owned or worked for, so I don’t see why the public sector should be any different from the private and non profit ones.

I also know some folks high up in big-city government so  I know (a) problems exist and (b) very smart and dedicated people work like hell to deal with them.  And I know and or receive services from a lot of not-so-high up folks.  And what gets me is the way that folks like Mr. K. seem to think two things:

First, that contracts may be binding for thee and me, but not if your contract happens to be collectively bargained and between an individual and the state.  The cop who started work ten years ago signed on to a challenging, difficult and sometimes dangerous job in exchange for a defined compensation package.  Now we should throw this away?  I don’t think so.

Second, that whatever we pay our civil servants is always too much, and hence ill-gotten, which is why it is OK to cut people’s pay  while expecting them to provide the same labor.

Here’s the horrible truth:  we don’t pay civil servants very much, really.  A Colorado Springs police sargeant makes, broadly, between $55,000 and $70,000 — or roughly $27.50 to $35 an hour. That’s for an experienced person in a supervisory role, working a job that requires considerable expertise and specialized skills, not to mention acceptance of the risk inherent in police work.

Why do skilled and smart people do the work — be they cops, teachers, whatever?  Because they like it, one hopes, but also because they accept a bargain — they’ll take a constrained wage in exchange for security and good benefits.  Take some part of that bargain away, and you’ll lose folks.  Usually the best ones, if you accept free market notions of rational self-interest, which I do.

So you have to ask yourselves:  Do you feel lucky today?  How much do you cut before these kind of people say f*ck it, and move on?

Seriously:  you can always cut something.  But you lose something when you do.  And if you have so committed yourself and your community to the idea that government is an abomination, it should come as no surprise that the cuts start to hurt.  But it does, which is why folks like Mr. K. have to make stuff up to get the horrible facts of real life out of their heads.

To which I say — move to Colorado Springs!  Show us what paradise can be.  I double dog dare ya.

Image:  Vincent Van Gogh, “The Potato Eaters,” 1885.

Quickie math (arithmetic)/journalism peeve: I don’t think “party lines” means what you think it means/NY Times edition.

August 7, 2009

Update: a couple of changes below to try to make the point I thought I was making.

From today’s NY Times article on the Senate vote to extend the Cash for Clunkers program:

In the end, the bill passed largely along party lines, with 51 Democrats, 2 independents and 7 Republicans voting for it.

What’s wrong with that?

This phrase:  “largely along party lines.”

Let’s do the math, shall we?

7 Republican senators voted with the majority to pass the bill.  4 Democrats joined the minority opposing the bill.  So the Democrats did come close to holding party lines on the bill; only 6.7 % of the Democratic caucus defected.

But 7 Republicans?   That’s 17.5% of the rump opposition party.  That’s a substantial defection, a significant breach in party discipline, especially given the record of GOP monolithic “no-ness” on most major votes this year.  Even more so when you consider that this is in essence a small supplement to the economic stimulus bill, and as such would naturally be a target for a Republican party that has pushed a lot of chips onto the table betting against the success of Obama’s economic policies.

Numeracy matters — and it does so not just at the level in which an understanding of statistics in any kind of deep way might be helpful, but even at this simplest level of fifth grade math.

I’ve written before on the importance of distinguishing between raw numbers and some representation of the data that permits comparisons to be made across different circumstances or events.  See this post for a much sadder example.  But the point keeps getting made by the way journalists handle numbers.  Simply the act of deriving a percentage from the tally sheets is way too often a bridge too far.

Why the failure to count on one’s fingers at such an elevated institution as the Times?

I don’t know for sure, certainly — I wasn’t in Matthew Wald’s head when he wrote the piece, nor the room in which his editors ran their eyes ove rhis copy.  But I do note that the running journalistic line for weeks now, significant especially in the context of the health care debate, has been that the Democrats have failed to meet promises of bipartisanship, and that hence, their legislative agenda and even their (our) legitimacy is in doubt.

If that’s the story line, then clearly each significant vote must be characterized as evidence of the ongoing division between the parties, and the inability of the Democrats to construct legislation attractive to a rumored center and the mostly mythical moderate wing of a party dominated by Limbaugh dead-enders.

And so, even in this case, when Democratic legislation on a high profile economic and environmental* program attracts a significant number of Republican votes, enough to release some Democratic senators to cast what may be either or both politically useful and or principled nay votes, the Times still feels compelled to assert, in essence, that this Democratic — and partly Republican — legislative victory was in fact yet another blow to bipartisanship.

The moral of this story:  this is how destructive tropes get made.  In the construction of myths epithets matter.  Little phrases, rote characterizations —  “the wily Oddysseus,” “loose-tongued Thersites” — they frame the reader’s interpretation of all the action surrounding the thus-labeled person or event.  They serve as received wisdom, a collectively agreed value judgment, to speed the plot.

And here, the phrase approximating an epithet, “party lines,” is the tell that the writer has substituted such prior qualitative interpretation for thought.  The cash for clunkers bill saw close to one fifth of the opposition party break ranks.

But to say so, to recognize that a Democratic policy initiative was sufficiently successful/popular that a significant subset of the GOP senate caucus chose to embrace it would have forced the writer (and editors) of the Times’ story  to break out of that sweet sleep in which there is no need to actually do the simplest bit of arithmetic.

Image:  Jan Breugel the Elder, “A Fantastic cave with Odysseus and Calypso,” c. 1616.

Sunday Links

June 7, 2009

Running late — deadlines on three (3!) pieces by tomorrow at eleven at the latest.

So far I have one in draft, one that I will conjure out of another piece of writing on the same subject for a different purpose, expanding by 60% (all good stuff, no groats for fillers) and a third that is but a gleam in my eye.

Plus it’s Sunday and my son wouldn’t mind having his dad share the same spacetime coordinates with him, and nor, emphatically would his father.

So not much today, except to thank all those who listened to my appearance on Ira Flatow’s NPR TOTN:  Science Friday to discuss Newton and the Counterfeiter— and especially those who mentioned the gig beforehand on Twitter or in their blogs.  (I haven’t managed to send my personal thanks to all those in the latter group yet, but I will.)

If y’all missed it, you can hear my dulcet tones here.*

So just to demonstrate that I’m only mostly about me, and not solely, I’d like to point folks to a running series  of cool over at Daily Kos, Orinoco’s “Fundamental Understanding of Mathematics” farrago, now up to its eighteenth installment.

As long term readers of this blog know, I’m a big proponent of evangelizing the idea that injecting the most basic and simple of mathematical ideas into one’s own reasoning and into public discourse pays enormous benefits.

I’ve given a few scattered examples over the 18 months or so I’ve been writing this blog — e.g. the conversion of raw numbers into abstractions like percentages** but Orinoco, a school teacher who has taught math to young kids, is doing a wonderful job in building a systematic appreciation for both the constructs and habits of mind of mathematics accessible to just about anyone.  Highly recommended — and especially if you read through the comments where a number of math and computer geeks expand on Orinoco’s themes.  This is what I love about the internet:  spontaeneous collective creativity.

Anyway, here’s the link to diary one, and you can find the rest by navigating through Orinoco’s diary page.

*And yes, on the higher traffic day of Monday, I’ll give this another plug — I enjoyed it; I think it went well; and I’d like people to hear it.

**And yes again, I know that numbers are themselves abstractions.

Image: William-Adolphe Bouguereau, La leçon difficule (The Difficult Lesson), 1884