Tag Archives: Academic Life

The professional world of political science — the job market, research methodology, peer review, academic writing, the role of formal theory in the discipline, and occasional dispatches from the trenches.

The Slow Burn of Coburn or, “Get The Hell Off My Lawn!”

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So, dispensing with technicalities, the efforts to curtail NSF funding of political science research have apparently succeeded, at least for now.

I think this is a good opportunity to post something that has bothered me over the past few years.  In a nutshell, I am unsure that the “Coburn amendment” is a bad thing for political science.  I will set aside considerations of the direct and indirect benefits of NSF funding, as well as potential crowding out effects such funding might induce in private and corporate donors.  Rather, I want to focus on the virtues of being left alone.

I post here semi-regularly about the substance of my research.  I apply mathematical social scientific models to politics, particularly to political institutions.  I teach courses to undergraduate and graduate students, and I spend a lot of time conducting original research and evaluating the research of colleagues around the world.  I love my job, and I honestly believe that it matters.  This blog is a small instance of why I believe this: I get things wrong, perhaps most of the time, but what I do allows/forces me to think about why and how things work the way they do.  While one can and definitely should think about things in different ways, the attacks on political science are simply nihilistic.

I have made the argument at various points and maybe it’s wrongheaded, but the question of whether an act/profession/interest is relevant or useful in and of itself is typically either ill-posed or easily answered with “no.”  Political science, like every other academic discipline, involves rigorous application of technique to create, assemble, and understand a body of knowledge.  I sleep (very) well at night knowing that what we do as a discipline informs, alters, and shapes the way I think about a broad range of incredibly “relevant” political events and broader phenomena.  Perhaps most importantly, what we do not only allows me to understand these things—it enables me to both be and recognize when I am wrong in simultaneously informative and informing ways.

So, while the jury’s still out about both the long-term prospects and effects of the Coburn amendment, I can definitely say this: I look forward to not talking about it anymore.  I’m tired of being confronted by the loaded question (“Have You Stopped Defending Your Junk Science and Charlatanism Yet?”), especially because my responses are sometimes witty and always unprintable.

But more positively, I am a consequentialist and take a glass half-full approach by recognizing that the die is cast for now and, as a field, we have more fundamental and important work to get back to.  So, ironically, thank you Tom Coburn: may your amendment most ironically refocus us on our science.

Oh, and I leave you with this.

_____________________

* It’s public record, but in the interest of full disclosure, I have some skin in the game.

I Study Political Science. You’re Welcome.

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There is a simmering debate about the science of politics.  For example, here’s a recent uninformed and deliciously uninformative anger-fueled argument that political science does not “serve the public”—a notion that any good political scientist knows is the warm bed of those too lazy to consider the vacuity of the notion of “serving the public.”

That said, social science is, without a doubt, decidedly unimportant to the everyday, snapshot welfare of the average American.  Similarly, basic research in medicine, nuclear test monitoring, TSA screening at airports, and even your usual dental and automotive checkups have incredibly infinitesimal positive impacts—clearly outweighed by the direct cost of any one visit—on your life.  STOP BRUSHING YOUR TEETH.  IT WON’T MATTER….today, at least.

That said, you’re reading this—so you’re not average.  (lost? bored? –ed.)

The reality of the matter is that politics is about many things.  That said, the requisite consideration is whether politics, as a discipline, contains anything that is both not subsumed by another field and is also important.  The answer to that query is undoubtedly “yes.”  Specifically, the study of politics concerns the study of institutions.  And, to be clear and slightly pugnacious, I mean the study of real institutions. To further the pugnaciousness, I mean both the theory and empirics of real institutions.

In a nutshell, there are many regularities of decision-making that can not be understood without thinking in detail about the rules that people have to follow.  The world is replete with rules.  And, continuing the business of bringing/inviting the fight, I mean formal rules.

To understand why and where power resides where it resides in any system, the very first place to look is the rules.  For example, did you know that the Speaker of the House has the power to announce the result of a voice vote without appeal? Or that the Speaker of the House has the absolute power to expedite business through a somewhat arcane but incredibly potent and important route known as “suspension of the rules”?

(Edit: In recognition of the thoughtful (off-line) comments of my friend Brian Sala, I should clarify my ambiguous description of the Speaker of the House’s power with respect to suspension of the rules. This is a formal motion to pass a bill “as is” without amendment and with limited (40 minutes, equally divided) debate. It requires a two-thirds supermajority. It also is in order only on certain days, and at the pleasure of the Speaker. This is an absolute power (essentially of recognition) and allows the Speaker to deny attempts to circumvent normal order. Given that suspension is very commonly used, this gives the Speaker a subtle form of a carrot to reward members. The Speaker’s power, of course, is conditioned on the supermajority requirement. (That, of course, is not by accident.)  Sorry for any confusion!)

What about the intimate and not so intimate details of recess appointments?  When does the President have power?  When has Congress given this power to the President?  Why would they do so?  Should courts care?  Should voters care?

The easy (and accordingly unsatisfying) answer to these broad questions is, “well, it depends…”

Political science is uniquely responsible for telling you what it depends on, how it depends on it, and—if we’re lucky—how you might change things to make these dependencies work in your favor.

So, unless you think that neither Obamacare nor the Keystone XL project are important, the business of institutional details “matter.”  Then, moving to the redundancy worry—maybe political science is merely a secondary backwater of those who might be able to  teach but surely can’t “do”—the reality is that no other social science (not to mention any other discipline) is concerned with the details that matter and how they matter.

Sure, economics and law worry about related issues, but institutional political science is focused on the mechanics of how things work and how they could work.  Law worries a lot in very important ways about how things work, but the reality is that their focus is appropriately focused on the way things “are,” and (more subtly) focused on things that matter to clients (broadly construed).  Clients—be they litigants or lobbyists—are important.  But they are not the same as voters.  Indeed, theoretically motivated empirical studies in political science confirm that they are potentially very different.

To be quick about it, economics is concerned with broad and systematic models of social/economic/political interaction.  There are very many productive and meaningful overlaps between the two fields.  (Indeed, I have a PhD in economics.)  That said, the two fields are distinct for a reason.

(For example, and first and foremost to someone like me, the idea of a “representative voter” is equivalent to assuming away all of politics.  Those of you who know me know that I like to refer to the theorems of Arrow and Gibbard-Satterthwaite theorem (too) frequently. Both show, for related but distinct reasons, that it is difficult if not impossible to sustain the presumption that one can utilize the notion of a “social will.”)

Economics is incredibly useful when it comes to “large numbers” analysis.  But to be honest and utilize the safety of my own blog, there is nothing particularly “economic” about the game theoretic analysis of general institutions.  In particular, mechanism design makes it clear that, in the abstract environment of institutional design, much should be possible—approximation or outright achievement of “first best” (unambiguously efficient) outcomes should be possible.

The difficulty of these results is that they neglect the practical and, appropriately, political realities that hinder (for example) credible commitments in the design of institutions.  For example, governance would be (theoretically) quite easy—and deliciously simultaneously democratic and authoritarian in good measure—if one could simply compensate the “chief executive” based on the measured realization of “social welfare” at regular time intervals during his or her tenure with some sort of fungible numeraire good.

Yes…this is exactly how ZERO countries (that I know of) are governed.  Hell, it’s not even how public corporations are governed.  The recent debate about responsibility, oversight, and transparency in (say) financial corporations is predicated precisely on the difficulty of (for example) measuring “social/shareholder welfare” in a meaningful and credible (i.e., relatively non-manipulable) fashion.

This is not to say that economists/lawyers/etc. do not worry about many of the same issues.  Unlike those who like to throw stones, I don’t need to attack others.  I have too many interesting and—again it’s my blog—important research questions to dive into to waste my time trying to avoid my own glass walls.

In that spirit, I leave you with no silly link this time.  Instead, I prefer to point out that, whenever someone says that rules (for example) are just a bunch of minutiae, you should respond, “you know, the definition of “minutiae” is endogenous.”  Or, combining an old adage and old saw among politicos, “minutiae is defined by those about to screw you.”

So Optimal You Hardly Notice

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I’ve been reading several papers lately that examine the effects of various government policies on various social and economic outcomes.  Increasingly, I find myself wondering what these studies actually conclude with “null” results. (By the way, I am sure that this issue has been raised before, but I’ve been thinking a lot about it lately, and I figured that’s what a blog is for.)

A (justifiably) standard approach in these literatures is as follows:

1. Describe why the outcome variable, y, is important, how it is measured, acknowledge weaknesses in the data, etc.

2. Describe the vector (list) of K independent variables, X, acknowledge they are imperfect, describe why they are still arguably useful, and perhaps link these with a theory explaining why they might affect y.

3. Apply a statistical model to generate estimates of the effect of the various variables in X on y.

For a lot of very good reasons, the standard approach in thinking about (or “modeling”) the effect of X on y is as based on some equation that essentially boils down to the following:

y_i = f\left(\beta_0 + \beta_1 x_1 + \ldots + \beta_k x_K\right) + \epsilon_i,

so that \beta_k essentially measures the linear impact of variable x_k on the outcome variable, y. (The function f(\cdot) captures nonlinearities, particular for situations in which y is meaningfully bounded, like a proportion or probability.)

Then, typically, if the researcher is unable to reject the hypothesis that the estimated value of \beta_{k}, \hat{\beta}_{k} is equal to 0, the conclusion is that there is little or no evidence that x_{k} affects y. This is usually followed by a puzzled expression and an awkward pause.

In many respects, this is perfectly reasonable: this approach is a classical way to model/uncover the relationship between the outcome variable and independent variables. And, particularly in modern social science, it is broadly and well-understood as a means to conceptualize/present results. So, I’m not saying we shouldn’t do this. That said, I am saying that we should think about the political relationship between the outcome and independent variables.

Now, for the sake of argument, suppose that K=1, to focus the discussion. Then, suppose that y is a politically important variable that voters “like” (i.e., want higher levels of), such as per capita income in a state and that x_{1}\equiv x represents a policy controlled/set by political actors. Now, suppose that political actors are responsive to voter demands, so that they set x so as to maximize y.

The first order condition for maximization of y with respect to x is \frac{\partial f(x)}{\partial x} = f^{\prime} \cdot \beta_{1} = 0. In general, $f$ is a strictly increasing function, so that f^{\prime} \cdot \beta_{1} = 0 implies that \beta_{1}=0.

We have reached this conclusion without presuming anything about the true relationship between y and x. Thus, if one is unable to reject the null hypothesis that \beta_{k}=0, isn’t it arguably better to conclude that the marginal effect of x_k on y is zero, given the observed data and behaviors underlying them than that x_{k} has no apparent effect on y?

Put another way, if we find in observed, real-world data that the effect of x on y is unambiguously non-zero, shouldn’t we be more surprised than if we fail to uncover a systematic, non-zero (linear) effect of x on y?

With that, I leave you with this.

Naming Rites

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On the eve of the most universal of American family holidays, I am thinking of the question of names. In particular, the interaction of surnames and marriage.

In the interest of both “setting the stage” and providing at least the appearance of a disclaimer, I should acknowledge, that (1) I am married and (2) my spouse and partner-in-crime, Maggie Penn, has (quite rationally, when you think about it) chosen not to take my last name.

Perhaps as a result of the fact that our naming configuration differs from that adopted by each of our (wonderful, awesome, inspirational, and—to be honest—classically liberal) sets of parents, I have realized that our approach of leaving our names unchanged in every respect after our marriage provides a special, and arguably idiosyncratic, visceral value to me.

I will dispense with the traditional explanation that my spouse is an established scholar on her own.  From such an explanation, instrumental benefits such as citation counts, professional reputation, and other benefits flow from maintaining an independentce in nomenclature above and beyond that traditionally accorded to spouses in years past.

Rather, I increasingly think that there is a very important point inherent in recognizing that names come from birth. And, as an ancillary effect, that marriage “merely” adds to the lineage of one’s life as opposed to overriding the events, happenstances, and detritus that came before (or, perhaps more provocatively, “caused”) the “marital event.”

My own experience suggests that there is significant value in at least two aspects of not having a common marital nomen (or, respecting word order rather than history, cognomen). Specifically, “keeping one’s name” (an idiom that has a distinctly and unfairly selfish feel) is arguably valuable insofar as it (1) reifies (or, perhaps, enforces acknowledgment of) the separate and important paths that led (at least in equilibrium) happily to the betrothal, and (2) puts the potential futures (or, perhaps bargaining positions) of the two equals on suitably equal footing.

The first of these reasons–the reficiation of the independent paths by which the betrothed came to be such–is particularly important when dealing with an instantiated third party.  (Or, for example, in colloquial terms, a child.  But, to be fair this could be a colleague, a neighbor, or a candidate for public office.) In short, when I am dealing with someone, there is a presumption that should be implicit in the conversation, given my wearing a wedding ring, that the whole enchilada of “this” is, barring explicit assurances to the contrary, presumably fair game for conversation with my spouse.  (After all, she and I can have pillow talk about our murder sprees and not be subject to the sovereign’s prying ears in terms of incrimination…So how could you expect to be immune from me telling her about your “secret USB drive” containing each and every one of AC/DC’s songs, ripped by your old college roommate?)

Having different surnames–not by choice but because our parents don’t happen to share surnames (not there’s anything wrong with that, conditional on your surname, of course)–reinforces this very important concept.  My spouse is my equal.  Names don’t matter, except to the degree that they are, in fact, simply external impressions (labels) of who we “are.”  That might be my own weird reasoning, but at least I find it compelling, and I (at least functionally) always have.

Two side points. 1. I say “functionally,” because I used to have a strong aversion to the concept that “labels matter.”  I have since “grown up,” and as a presumptive “relative elder,” I see the wisdom in labels.  Examples include “Professor,” “Unindicted,” and “Silver Preferred.”

2. I have yet to hear a meaningful retort that is not equally consistent with the imperative that, at weddings, we should have a coin toss (probably right after that really fun garter toss) in which the marriage “naming rights” are awarded.  That is, I won’t go too far into the gender inequity inherent in traditional naming conventions, but I’m willing to do so.  Only because an active opposition to my points here suggests that you have an interest in the status quo, not “surname convergence,” as it were.  But, you know, bring your best.

Second, the idea that one partner takes the other’s name, regardless of how that assignment takes place, differentiates the two spouses in terms of future negotiations.  In particular, whoever takes the other’s name is (for the sake of argument, yadda yadda) impaired in future negotiations because he or she (come on, “she”) has, upon introduction, revealed that, at some point in the past, been married. (And, before you say, well, that means he/she must be desirable, note that this effect would manifest itself in people voluntarily adding random surnames to themselves.  I only know of one occasion of this, and that has just been weird, though kinda awesome, too.

In the end, I like to walk into a room, particularly one in my house, and think that we’re all there for the same reasons.  (For example, I would never let a plumber into the pantry, and I would make a cook use the potty outside.) Marriage is collaboration, and I always want not only to know that everybody is there for the same reasons, but also that they know that I’m there for the same reasons.  The “math of politics” point of this post, as silly and introspective as it might be, is that securing for your partners the determinants of bargaining power is not nearly as effective as securing their knowledge of your knowledge of their possession of those determinants.  In other words, it’s not simply about being equals: it’s about both sides knowing that both sides know that both sides know that both sides now that both sides know … that both sides are equal.

With that, I wish you all this.  Happy Thanksgiving! And, more importantly, thank you, thank you, thank you Maggie, for being my partner in crime.

Political, Antisocial, Dismal Science: Economics Getting Cut Next?

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At least among social scientists and their supporters/detractors, there was a fairly active discussion of the House of Representatives version of the Commerce, Justice, Science, and Related Agencies Appropriations Act, passed back in May.  For example, Christopher Zorn wrote this, Ezra Klein presented a well-intentioned take on the issue, Brendan Nyhan presented this defense, and then there’s this misguided & facile, but highly placed piece by Charles Lane. (Apologies for all of those I did not include here.)

I am not going to defend or oppose NSF funding here.  In my opinion, there’s no “right” position on this, and even if there were, there is little reason to suspect that people would agree even on what constitutes evidence.  After all, there are reasonable arguments for and against the government funding any research or, for that matter, education.

I just wanted to note that the efforts to reduce funding for social science research continue. Specifically, as described here in Science by Jocelyn Kaiser, NIH funding for general social science research and economics research in particular is to be eliminated according to the draft appropriations bill the Labor, Health and Human Services, Education, and Related Agencies Subcommittee of the Committee on Appropriations of the U.S. House of Representatives.

In a press release, the elimination of funding for social science research is described as ensuring that “the NIH support only research projects that are highly meritorious, based on peer review processes, and that continue the agency’s historical unbiased position toward specific diseases.

As I said, I don’t take a position on whether social science research funding “should” be cut. I just think it is important to note that the developments make even clearer the irony of sophomoric and facile pronouncements by those who truly don’t have the time,  knowledge, or perhaps the inclination to consider the deeper questions at hand in these budgetary battles.  The use of limitation riders and their ilk has a venerable history of screwing with big politics through the use of disarmingly little screws.

Finally, for those (quite appropriately) more concerned with Big Bird than with Big Science, note that this version of the appropriation bill cuts over $100 million in funding for the Corporation for Public Broadcasting.  It also prohibits funding for Planned Parenthood unless it certifies it will not provide abortions, effectively bars implementation of a new NLRB rule regarding union elections, and eliminates funding for the new Center for Consumer Information and Insurance Oversight, a key oversight office for the Affordable Care Act.  This office is responsible for regulating health insurers (like limiting inflation in insurance premiums and like ensuring that insurers provide enough coverage to their customers), and setting up and managing health care exchanges for states that (choose to) fail to do so on their own.

By appearances, this might seem just another mundane appropriations bill (of which there are typically 14 or so through the year).  But appearances can be deceiving.  Accordingly, I leave you with this.

Vitali Statistics: Measurability Issues in Education

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This weekend, the Olympics drew our attention to those who leave everyone behind, leading us to question the nature of time itself (and I started thinking about algebra). So, I naturally began to think about measurement and education…

Recently, increased attention has been paid to the Obama Administration’s granting of waivers (or, “flexibility”) to states from the provisions of the No Child Left Behind Act of 2001 (NCLB).  The Act has been widely discussed since its passage at the beginning of the century, and I will focus only on one of its provisions (albeit arguably one of its most important).

CYA/Flame Retardant Provision. I am very aware acknowledge that these (both educational reform/performance in general and the NCLB in particular) are important, contentious, and complicated topics.  My point here is to illustrate a specific issue that I believe deserves some thought by those who are considering reform and/or reauthorization of NCLB.  

In a nutshell, NCLB requires states to develop standards by which their schools’ and school districts’ performances will be judged. I have a modest goal here: I will point out and try to explain a subtle but classic paradox hidden within one of the ways the NCLB calls upon states to measure educational success.

A key concept in NCLB is Adequate Yearly Progress (AYP).  This concept is measured at the school level for most elementary and high schools.  Without going into even more arcane details, it suffices to know that demonstrating achievement of AYP is desirable. I want to focus on what achieving AYP requires.

Specifically, in each year, tests are administered to students in reading, math, and science.  Waving at some details as we pass them by, success is essentially measured by the percentage of students passing each of these exams.  More importantly for our purposes, success rates must be measured in several ways.  For a given school, the success rates must be sufficiently high (and, generally, improving) in each of the following categories:

  1. all students,
  2. economically disadvantaged students,
  3. students from major racial and ethnic groups,
  4. students with disabilities, and
  5. students with limited English proficiency.
This design immediately raises the possibility of Simpson’s paradox, which can occur when comparing subpopulations with the population as a whole.  In this case, the relevant point is that an unambiguously improving school can still fail to satisfy AYP (and vice-versa).  Here is an example.
Suppose that a school has 100 students in both Years 1 and 2 and, for simplicity, consider only two “subgroups”: economically disadvantaged (“poor”) and not-economically-disadvantaged (“rich”) students.  Suppose that in Year 1, 20 of the school’s students were poor, and that 10 of these students “passed the exam,” whereas 72 of the 80 rich students passed the exam.  The school’s “scores” for Year 1 are then:
Poor: 10/20=50%.
Rich: 72/80=90%.
Total: 82/100=82%.

Now, in Year 2, suppose that 70 of the school’s students are poor, of whom 42 passed the exam, and all 30 of the rich students pass the exam. The school’s “scores” for Year 2 are then:

Poor: 42/70=60%.
Rich: 30/30=100%.
Total: 72/100=72%.
Uh oh. Viewed from a groups perspective, the school unambiguously improved its performance from Year 1 to Year 2 but viewed as a whole, the school’s performance has (similarly unambiguously) slipped.

The cause for the “paradox” is that the composition of the school changed between Years 1 and 2.  In year 2, the school gained students who had a lower success rate (even though, comparing apples to apples, this success rate increased) and lost students who had a higher (and also increased) success rate.  (Note that you can also construct this paradox only by altering the size of one of the groups.)

In a nutshell, it seems likely that the current construction of “Adequate Yearly Progress” might not measure what some of its proponents think it does.  Put another way, focusing on performance by subgroups (which is probably appropriate in this context and undoubtedly called for by the statute) immediately implies that this is an aggregation problem. Aggregation is a (or, perhaps, the) central question of political science.  But rather than get into that, I’ll simply leave you with this other formulation of Simpson’s paradox.
A Couple of Notes….
1. It should also be noted that others (e.g., Aldeman and Liu), have noticed a connection between Simpson’s paradox and educational testing, but I am unaware of anyone who has noticed the direct role of the paradox in the measurement of progress in the NCLB.
3. There are several other intriguing measurement aspects in both NCLB and the Obama Administration’s “Race to the Top” program.  Maybe I’ll write about them later.

But, Algebra is f(u)=n!

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Putting real politics aside for a moment, I have a few comments on Andrew Hacker‘s op-ed in today’s New York Times, entitled “Is Algebra Necessary?” I will first answer his question.  Then I will discuss a few logical weaknesses of Hacker’s argument.

(In the interest of full disclosure, I am very proud to be a Unicorn, class of 1992.)

1. Wait, did you expect an answer?  Well, in a nutshell, the appropriate answer to Hacker’s tantalizingly ambiguous question is “yes and no.”  Clearly, algebra is not necessary for potty training, survival swimming, navel-gazing, or even fantasy football (though it helps). Strictly speaking, algebra is necessary for an admittedly much smaller set of life tasks.

The more important point is rejecting the false dichotomy put before us by Hacker.  Implicit in his piece is the presumption that something is either “necessary” or it is in need of serious, urgent reform.

The proper way to address whether algebra should be required is to ask what its mastery  does provide.  This is question of sufficient conditions.  In this case, one relevant conclusion is the fact that understanding algebra implies that one knows how to logically solve a problem.  Hacker might have a point (though it would require a lot more work than is evident in this piece) if he made a more measured argument that requiring algebra is too costly a means by which to ensure that high school graduates know how to logically solve a problem.  But his argument is not of that form.  Rather, he implicitly takes the position that “if something learned in a math class is not directly evident in everyday actions, it should not be required.”

Accordingly, Hacker has provided an argument against requiring that people learn about anything other than:

  1. sitting,
  2. Facebook,
  3. blogs,
  4. internet memes involving
    1. kitty cats
    2. Carly Rae Jepsen lyrics
    3. Queen Elizabeth,
  5. Amazon Prime,
  6. keyboard shortcuts, and
  7. Facebook.
  8. And Amazon Prime.

2. Oh, you meant “Is Unnecessary Algebra Necessary?”  Much of Hacker’s argument reminds me of this great correction. See, Hacker doesn’t want us to think that he thinks that we shouldn’t require, you know, useful math.

I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame…

Ummmm.  Okay, so the deal here is….what? Oh, yeah…Hacker wants to get rid only of the math that is not “critical for informed citizenship and personal finance.”  My brain hurts…perhaps because of all that math society made me take.  Exactly what are the bounds of “quantitative skills?”  This is never made precise, though apparently long division is a component.  As will become clear below, Hacker would have students learn how to understand where statistics and quantitative data come from and how they are constructed without having students learn about equations and fixed points.

For example, why is some data best described by the mean?  Why is it sometimes best described by the median?  What purpose does the mode serve?  What the hell is a variance?

Consider this interchange in the future.

Teacher: Suppose we flip a fair coin. If we let “Heads” equal 1 and “Tails” equal 0, the mean, or average, flip is equal to one-half.

Student: But, teacher, what does that mean? I’ve never seen a coin land on its edge.  

Teacher: Ahh, don’t you worry.  Andrew Hacker assures us that you don’t need to understand that.  Now shut up, go balance your checkbook, and vote.

In short, it doesn’t appear to me that Hacker has thought through one of the central  persuasive distinctions in his argument.  He frames it as a practical offering, but there’s very little practical guidance on how to decide what to keep and what to chuck from the curriculum.  On that note…

3. No, seriously, keep the important math. There may be another explanation, of course, but as far as I can make out, Hacker’s argument is either unintentionally incoherent or simply disingenuous insofar as he pretends to still have the cake he just ate.  For example, consider this snapshot of his stream of consciousness:

Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.

This makes no sense.  Let me rewrite this in sailing terms:

Being able to detect and identify the direction the ship is moving is of obvious use. Ours is fast becoming a seafaring age, which raises the bar for informed seamanship. What is needed is not concise summaries of how to sail a ship prepared by experienced sailors, but greater understanding of how various parts of the boat work, and how to actually work them.

4. I went to the bathroom and all I got was this lousy NYTimes Op-Ed. My final salvo is aimed at this passage:

What of the claim that mathematics sharpens our minds and makes us more intellectually adept as individuals and a citizen body? It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x^{2} + y^{2})^2 = (x^{2} - y^{2})^{2} + (2xy)^{2} leads to more credible political opinions or social analysis.

Notice the sleight of keyboard here: Hacker does not address the claim that mathematics sharpens our minds or makes us more intellectually adept.  Instead, Hacker asserts that there’s no evidence that knowing how to expand a quadratic equation leads to more credible political opinions or social analysis.

It is undoubtedly true that mathematics sharpens one’s mind and makes one more intellectually adept.  Indeed, it’s “so true” that one might challenge it as tautological.

In addition, and finally, Hacker’s claim that we should revisit the role of algebra and higher mathematics in the curriculum is based upon his assertion that there is no evidence that such training “leads to more credible political opinions or social analysis.”  Even if one grants Hacker’s concise summary of empirical evidence, this is still sleight of keyboard: neither of these conclusions is “necessary” for requiring algebra, at least no more so than it is for any other component of the curriculum.

As the world comes together to bash algebra and Michael Phelps, I leave you with this.