Posted tagged ‘Arithmetic’

Pink Himalayan Calculator Problems, Part (n)

January 10, 2013

Further to DougJ’s catch over at Balloon Juice this morning:  last night I actually found myself reading (why, oh why, dear FSM?) the McArdle post in question, a bit of fappery in which she paraded her above-the-fray disdain for the idea that the Obama administration might take action to clean up a mess the Republican rump plans to deposit on his lawn.  (No linky ’cause I’m not in the business of giving any hint of value to McArdle’s employers/enablers.)

It’s really a sad effort, in which McArdle attempts to complete a ~1,600 word piece on the failure of governance implied by a discussion of a platinum coin on the US balance sheet without implicating anyone other than President Obama.  She does make a couple of nods in the direction of “both sides do it” faux-balance, chiding the Republicans for their role in the last debt-ceiling debacle and noting that the GOP side of the aisle seems even less prepared for the consequences of actually blocking the measure this time around.

But those are head fakes.  She reserves the full blast of McArdle scorn (as always, queue Denis Healey’s “savaged by a dead sheep” line here) for Obama in particular and the Democrats in general (whodathunkit!).  Her chief complaint: Obama’s election campaign went pitiably small (an argument that relies on ignoring most of what Obama discussed on the trail), and that he and his party simply ignore the “fact” of federal over-spending.

I’m not going to do my usual obsessive 4,000 word fisk on all the failings of fact and logic that permeate this, as so many of McArdle’s effusions.  Life is too short; I’m on (self-imposed) deadline; and frankly, the slow erosion of McArdle’s career makes the task less pressing, at least to me.  The Daily Beast ain’t The Atlantic, and while the site itself may still command more traffic her old home (I’m not sure of that, but it was true a while back) you can see the impact the difference in audience makes.  I actually waded into the comment thread on the post in question (the shallow end — didn’t have the stomach or the time for the deep dive) and there were plenty there heading for Red State territory.


There’s no doubt in my mind that McArdle is unlikely ever to want for a reasonably well-paying gig; she’s pretty well situated on the Wingnut Welfare railroad.  But there is a big difference between those who intone their harmonies inside the Wurlitzer and those who play out a bit, and it seems to me that she’s heading the wrong way on that particular arc.  Could be wrong, of course, and constant vigilance and all that.  But really, there are bigger fish to fry (looking at you, BoBo, et al.).

So, in the interest of everyone’s time, let me here just take note of the fact that McArdle’s calculator is performing as well as ever.  Her post’s coffee-spray-on-the-screen moment came on reading this gem:

For a while, Democrats could pride themselves on being the reasonable ones. Now they, too, are choosing words over math.  “We don’t have a spending problem,” President Obama apparently blithely told the Speaker of the House.  Which is technically true . . . if we’re willing to raise the government’s tax take to north of 50% of Gross Domestic Product. [ellipsis in the original]


Just to dot the “i”s: 2011 GDP?

$14,991,300,000,000.  Call it $15 trillion. (via the World Bank.)

2011 federal spending?

$3,598,000,000,000.  Call it $3.6 trillion. (Via the CBO.)

Now, I don’t know about y’all, but I’m not sure I even need to pull out my slide rule to see that 50% of $15 trillion is $7.5 trillion.  And I can probably get by without digging up a working model of a Curta to confirm that $3.6<$7.5.

But perhaps I should do the calculation anyway.  Using the rounded numbers, it seems that federal spending in fiscal 2011 amounted to ~ 24% of GDP.  Or, for those of you keeping score, right in the range  Bernard discussed yesterday.

All of which is to speak the obvious; McArdle’s number is simply bullshit.

I actually have no idea what she was thinking there; it really is one of the least well hidden secrets in US budget discussions that the feds spend a bit under one quarter of GDP.  That’s a number that’s been out there a lot, not least in the context of not-exactly-obscure proposals like the Ryan “Path to Prosperity”* budget plan, which called for long-term government spending to fall to 19% of GDP.

Just to belabor the point:  getting this proportion scaled right is not rocket science — it’s just part of the assumed knowledge of anyone talking US fiscal stuff.  Which is to say that anyone can, of course, screw up and type a number in error.  But then, if you’re numerate at all, you get that tingle that tells you there’s something just off — and you fix it.

Which leaves me with the usual McArdle conundrum:  is she simply so tone-deaf quantitatively that she really didn’t catch the absurdity of the claim?  Or is she so reckless a polemicist that she did, and didn’t care?

One last thought.  Back when McArdle was securely perched at The Atlantic, I often ended these rants by pointing out that her work colored the output of the whole site.  Sometimes I called out the writers I did (and do) admire there to make that criticism more pointed.  The same obtains today:  McArdle’s work is a measure of The Daily Beast.  If they choose to publish her, they own whatever good she may produce — and all the bad, with every bit of reputational and credibility damage that may result. In which context, whatever your feelings about Andrew Sullivan, I’ll say this:  he’s not stupid about his career.  It’s not (or not just) the manner of his leaving Tina’s playpen; it’s the fact of that abandon-ship that, to me, speaks volumes.

*Doublespeak alert

Image:  Agostino Carracci, Hairy Harry, Mad Peter and Tiny Amon, between 1598 and 1600.  I have used this before, but it really seems to fit here.

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

What Does the Public Really Need To Know?: Science/Math edition.

July 14, 2008

So, last week I have the good fortune (a) to junket in LA (thanks, History Channel — look for their latest Einstein documentary sometime between October and the new year) and, thus geographically advantaged, the chance to raise a glass or two with Sean Carroll and Jennifer (new digs) Ouellette (familiar haunt) — two of the brightest lights among those who blog the physical sciences.

Among much other discussion (how to do good science on television, whether there is any useful algorithm available to help navigate LA traffic) we drifted into that hardy perennial: what, really, does the general public need to know about science. Not for the greater good of science, not to secure more complaisant support for big accelerators or stem cell research, but for them/ourselves?

There are lots of facts that I think would give people pleasure — I love knowing that Albert Einstein patented a hearing aid (with Rudolf Goldschmidt); that chimpanzees fashion tools in the wild; that the first reaction written down in something like the modern form of a chemical formula was that describing the fermentation of alcohol. There are ideas that are enormously powerful — and some of them are clearly of value as part of anyone’s mental apparatus in confronting daily life. (Natural selection, offers insights well beyond the history of life, for example, (though great care must be taken, as we know, to our sorrow) and as general a heuristic as Ockham’s Razor would help people deal with silly season stories like this one.)*

But while these and much more are part of what I think any education should provide, the question I asked over something-or-other in martini glasses last week,** and re-ask here, is what the minimal body of knowledge is that every adult should possess.

Regular readers of this blog will guess the answer I gave: the bare minimum is arithmetic, or more broadly, a grasp of quantitative reasoning and a set of simple rules to apply such reasoning in everyday life.

For example — these posts sought to illustrate of the value of remembering to do something as basic as converting a cardinal number into a percentage, to make it possible to compare different data points.

Another example: the habit in this country of focusing on miles-per-gallon as a measure of fuel efficiency leads systematically to bad decision making. If we instead looked at gallons-per-mile (or hundred miles), it would make it clear that replacing a 16 mile per gallon SUV with a 20 mpg station wagon is a much better choice than replacing a 34 mpg compact with a 50 mpg hybrid, assuming equal miles driven for each vehicle. No one reading this needs much help figuring out why — but for the details, listen to the NPR story from which this particular example came. (See — I had to say something nice about NPR after slagging them for their Shakespeare follies.)

In sum: I’ve been at the popular science game for a quarter of a century now. I’ve written about climate change and physics and cancer research and precision guided weapons and big telescopes and the origins of the pentatonic scale and I can’t remember it all now. I hope everything found some audience who got something out of it. But more and more now I look for stories that in their telling express some of the basic habits of scientific thinking — whatever the body of facts with which I may be dealing.

There is much more to such habits than a quantitative turn of mind — notions of observation, of framing answerable questions and lots besides . But more and more the starting point seems to me to be conveying how much mastery of the world one can get from astonishingly simple acts of counting and comparing.

What do y’all think?

Update: See Chad Orzel’s recent post on John Allen Paulos’ Innumeracy for another swipe at the same problem. (h/t Bora)

*For an antidote to the “Who wrote Shakespeare” tomfoolery, you can begin here with James Shapiro’s latest — one of the best of a spate of Shakespeare-as-window-on-the-birth-of-the-modern books that have appeared recenlyy.

**Fortunately, the waiter in the very chic bar in which the three of us chatted had never heard of what I tried to order, a French 75, which is the only reason I remained unfogged enough to have any kind of a conversation that night. Just the mention of it makes me feel a little shaky. Enjoy, but at your own risk.

Image: Codex Vigilanus, 976 C.E., in which Arabic numerals first appeared in a Western European manuscript. Source: Wikimedia Commons.


Get every new post delivered to your Inbox.

Join 7,801 other followers