Primes and Probability

At the suggestion of a colleague, I recently started reading Charles Wheelan’s Naked Statistics: Stripping the Dread from the Data. So far, it’s a fun, demystifying sort of book, the kind I hope my students will enjoy (watch out Lafayette Economics, I’m coming, and I will make you read). It rests on the twin ideas that statistics can be fun and statistics are incredibly useful to explain, to tell stories.

The book was high in my mind this morning when I read this deliciously accessible Slate piece by Wisconsin professor Jordan Ellenberg about an advance in prime numbers by a University of New Hampshire mathematician. Economists like to make lots of bad jokes about how they are failed physicists, who are in turn failed mathematicians, so while it interests me, I wasn’t expecting to really understand the discovery when someone riffed on twitter about primes.

What’s so wonderful about this really intense mathematical discovery, at least according to the mathematician author of this piece, is that it’s really about statistics, which I can totally get my head around. The theory goes that primes come in infinitely many ‘twin pairs,’ like 3 and 5 or 17 and 19, and the intuition lies in that we can think about primes as random numbers.

And a lot of twin primes is exactly what number theorists expect to find no matter how big the numbers get—not because we think there’s a deep, miraculous structure hidden in the primes, but precisely because we don’t think so. We expect the primes to be tossed around at random like dirt.

Zhang didn’t quite prove the twin pairs theorem, but he made an important step towards proving it, it seems, and understanding probability and statistics is key to getting there.


On cell phones and twitter in the classroom

Yesterday afternoon, a guest speaker was in a Gettysburg College sociology class to discuss the role of social media in the Israel-Palestine conflict. When I asked how it went, having run into the speaker and professor at the local Irish pub, my colleague replied, “it was going great until Boston.” In moments, it seemed, Boston had transformed from a city to an event. While we still wait for the details to shake out, calling it anything in particular seems premature, but also reflected, probably, an unwillingness by my colleague to internalize what had happened.

Upon reflection, I am now struck by my lack of surprise that a news event would so wholly disrupt a class. No one came running into the classroom to tell them about it, but rather all her students were on twitter. This class is a bit particular because it is on the study and practice of social media, but all the same, I’m sure the same situation played out throughout campus as students are now constantly on their phones.

Just over eleven years ago, when planes struck the World Trade Center buildings, I was in class. Though someone had mentioned a plane when we walked in, we held class, entirely oblivious to what was going on just a few states away. The next time that class met, the professor apologized for having kept us; he just didn’t know. And how could he?

The subject of cell phones and twitter in classrooms proved to be a popular one throughout the evening (It’s a rare event that gets a group of eight or ten professors out on a Monday for purely social reasons, but last night happened to be just that. We still talked mostly about students and research, if you must know). All present seemed to have much higher levels of tolerance for use of phones and computers in the classroom than I had imagined. I still remember professors answering their students’ phone when they rang in class, confiscating laptops and phones, and now all that seems unimaginable. I don’t expressly prohibit cell phone use in my class. I know that my students are texting or reading sports scores when they look down at their shorts and not at me, but I’m not going to stop them either. Some students are legitimately looking things up, finding definitions, trying to figure out whether Palestine is a country or a city, or any number of other activities. Some are probably on facebook, too. In some cases, it’s just their choice. Some claim they listen better with something in their hands, but all the same, I’m not on a rampage confiscating iPads, and neither are these colleagues.

We all seem to have just accepted it. I guess technology is here to stay, so how to work it in appropriately is inevitable.

My condolences to the families of those affected in Boston.

Mental labor of the always connected

Amanda Marcotte has an excellent piece out on the mental labor that falls more heavily upon women in the household. While chores may be more evenly split, women are still the ones exerting the effort to split the work, to nag when it doesn’t get done, and finally, likely to do it if really doesn’t get done.

Though perhaps unrelated to gender, the piece prompted me to think about how my workload has changed over the course of my short teaching career. In particular, I find myself spending a lot more time with my students than I did when I first started, and more time fretting about them getting their work done. This is my invisible work, keeping track of student assignments, making sure they’re on track to finish their research papers, worrying about their sick grandmothers, and more. It reminds me of my college roommate, who since we’ve aged and mellowed a bit, has reminded me several times how stressed out I made her through my procrastination while students at Duke. As the years have gone by, students seem to want more of my email time, and at all hours of the day, even as the face time has not changed much. Like many professors, I try to limit my time on email. There are many activities and conversations that can be more efficiently performed in person. For instance, if you email me asking how to calculate Adjusted R squared and ask why it’s different from R squared, I’m going to ask you to come talk to me instead of typing out those equations. I promise you’ll learn it better and it will take both of us less time.

More and more of these emails seem to come in the middle of the night, before exams, before homework assignments are due, etc. I tend not to answer those late night emails and I don’t accept them as excuses for not doing work. I have a policy about late work; It’s in the syllabus. I’m not going to remind you of it a million times either. It’s your job to keep track of your work.

I do this partly for my own sanity (avoiding mental labor at least a few hours of the day), but also because I believe that as an educator, I should be preparing my students for the real world. They need to learn to produce timely work—even if it’s not perfect—to manage their time, to realize that help is not available at all hours. That’s the real world, right?

More and more of what I hear though, is that it’s not. One serious problem that professors have is that they don’t live in the real world they’re trying to prepare students for. The only jobs I’ve worked outside of academia since 2006 have been consulting, hardly indicative of day-to-day office jobs that are commonplace for recent grads (when they’re getting jobs, that is). While some friends assure me I don’t want to be there among the unwashed masses, it’s a real liability for professors, especially if a whole new economy has popped up around being constantly available and connected and cheap, as some are claiming.

In response, some universities are advertising for positions to be just that for students: constantly available, connected, and (likely) cheap. This Western Governors University position wants a PhD economist to be available essentially 24/7 to tutor students who are struggling. I admire them being honest about the hours and expectations, but is that really the most efficient use of a PhD’s time? Answering the same email over and over again at 3am about opportunity costs? And they have similar positions open in almost every field. Is it really in students’ best interests to reinforce that work should be round-the-clock? That someone will be there to answer questions all the time?

Marissa Mayer, the CEO of Yahoo!, was recently lambasted by any number of individuals and groups for telling telecommuting employees that their flexible work schedule days are over and that employees can’t work from home anymore. While I disagree with the fundamentals of the decision for reasons that have to do with supporting working parents and caregivers, I’m sure she has internal reasons for her actions and the point about separation is important. It’s ridiculous how many of us check our email at the bar, respond to a client in the middle of dinner with another client, interrupt play time to read another message from our bosses. The WGU positions mentioned above actually erase all of those boundaries between work and home, keeping us constantly connected, constantly answering emails. There is no office, no in-real-life contact with students. It’s not teaching, but “mentoring,” and it reinforces the idea that someone should be working constantly. If you’re a student, it’s you and your professors. If you’re in the workforce, it’s you and your boss. If you’re the boss, it’s you and your employees.

College is kind of a special time. If you’re not up all night writing a paper, you’re up all night debating philosophy, or driving to the nearest Krispy Kreme, or or doing all manner of legal, illegal, silly, and serious things. There’s a reason that we don’t continue that madness (or at least some of us don’t) into our 20s and 30s, and especially not into our work.

And if work is really now 24/7, how the heck do we get it to not be? Certainly not by hiring people specifically for that purpose.

Thanks to @katinalynn for comments on a first draft of this post.

Correlation is not Causation, clearly

Repeat after me:

Internet Explorer vs Murder Rate Will Be Your Favorite Chart Today

We discussed causation and correlation in my Methods class this morning. I generally use the ice cream sales and murder rates example, but since this has been floating around the internet lately, I figured I would throw it in. It got a few chuckles out my class, from those who also wanted to insist that ice cream made people deranged and thus more likely to murder someone, but a good reminder nonetheless. A regression of murder rates on ice cream sales or internet explorer market share will have a positive and statistically significant coefficient estimate, but it doesn’t mean that either is causing more murders to occur.


Why study social sciences?

Monkey Cage Blog has a great post up in response to criticism of his exhortations to study social sciences. He makes a broad argument about the validity of social science research because it has effects on the way that people live their lives. To be selfish for a moment, he highlights some important questions that I examine every day:

Families.  What makes families more or less successful?   What makes marriages more successful?  What makes them fail?  What are the effects of divorce?  Does it hurt the children of divorce?  How much, in what ways, and for how long?  A medical doctor can treat the effects of family dysfunction and divorce—say, with anti-depressants or therapy and so on—but we can learn and know more about how to prevent some of this dysfunction from doing social science.

The post is really about funding for social science research rather that defending my everyday work. It’s also not really about teaching undergrads social sciences, but clearly, we have train undergrads in social sciences if we eventually want some of them to do research in the social sciences. I think there’s a point to be made about how learning about these wide-reaching social phenomena—families, schools, economies, politics, attitudes, networks and norms—forces students to think about cause and effect in a nuanced way. When it’s not clear how X might affect Y or how Z has effects on X that in turn effect Y, it takes creativity and imagination and critical thinking to sort it out. It’s not that social sciences can do this exclusively, but the nature of the topics student lends itself to varied analysis and the development of skills that are useful in many careers.

The Beltway Deficit Feedback Loop. Or, why we should all commit to reading various news sources

Last week, I was surprised by my students’ apparent belief that debt and deficit spending was high during the first Obama administration and that it was the first thing they thought of when asked about the effects of government spending.

By way of explanation, Greg Sargent of The Plum Line takes on the current Joe Scarborough vs. Krugman (and the world of economists) debate via the Beltway Deficit Feedback Loop.

The relentless bipartisan focus on the deficit convinces voters to be worried about it, which in turn leads lawmakers to spend still more time talking about it and less time talking about the economy, a phenomenon that is self-reinforcing. This is exacerbated by some commentators and news orgs, who continue to treat the deficit scolds with a great deal of deference, while marginalizing the opinion that we should prioritize boosting the economy and job creation as a means of getting the country’s fiscal problems under control over time without savage spending cuts that will hurt a lot of people. Back in 2011 one study actually confirmed that newspapers were spending far more time talking about the deficit than the economy — at a time when the recovery was in serious peril.

h/t @EJDionne

Dramatic changes (or not) in government spending

I’m teaching Methods again this semester, this time two sections with a total of 24 students. They’ll all be blogging again, so if you’re curious, I do recommend you check out their blogs. Links are forthcoming in the sidebar.

We started class this week with a little data work and a statistics refresher using data from the Bureau of Economic Analysis. It’s probably the only macro example I use all semester in great depth, but it serves to help students link their past work to what they are going to do in this class as well as give me the opportunity to show off impart some Excel shortcuts and basic data analysis skills and tips while reviewing statistics.

Since we use the entire set of GDP data from the NIPA tables, I like to take a bit of the class to talk about a few major events in economic history and highlight the idea that an action such as increasing government spending can both increase GDP and decrease it, according to economic theory. Which effect is bigger determines the outcome we see, even when both are happening.

Most students know that federal spending went up as a result of wartime production in the early 1940s and as a result of the New Deal in the mid-1930s, but I was surprised at how students answered my question of what effects does government spending have. Several students in both classes answered “debt” before anything else, and no one came up with “crowding out” (where government spending replaces private consumption and investment or drives up interest rates such that firms don’t invest but save) without significant prompting.

Once I said it, of course, they all recognized what I had been getting at, but I think it’s so indicative of the current political and news climate that students would default to an answer that’s not particularly true as a result of having heard it over and over again. Government spending, as anyone who was alive in the 90s knows, doesn’t have to result in more debt. A balanced budget is not outside the realm of possibility, and while crowding out is not necessarily a foregone conclusion either, it should fit much more nicely into students’ understanding of theory and a review of national income accounting. I know that Prof. Weise or Prof. Hu taught them about crowding out. It’s amazing how hammering on a subject can replace an outcome of an action in one’s mind. I was surely told over and over again that government spending caused crowding out, so it’s always first. These students have clearly been told that government spending causes debt. Weird. (As a side note, the Chronicle has a great article on how students struggle to transfer skills learned in one class to others.)

I’m getting away from the initial trajectory of this post, though. In addition to forgetting about crowding out, my students wanted to tell me that government spending had accelerated over the past few years. I immediately shot down the idea, saying how spending growth had slowed dramatically since we had officially left the recession, even if there had been an initial spike.

I was a little nervous when I said it that I had misspoken, but was grateful to come back to my office to this Krugman post: “the narrative that says that spending has surged under Obama is just wrong – what we’ve actually seen is a slowdown at exactly the time when, for macroeconomic reasons, we should have been spending more.” Ah, sweet vindication and relief.

How to email your professor

It’s day one of my fourth semester at Gettysburg. It’s also Martin Luther King, Jr. Day. I hope you all are enjoying a day of remembrance. If you’re looking for something different to read, might I suggest former NC state attorney general Hampton Dellinger in the Atlantic on the MLK memorial? I’ll be reading syllabi and teaching my new students how to blog.

For all the students out there, a little primer on how to email your professors.

Happy first day!

The advent of conversations I thought I’d never have

Even teaching at a place like the University of Colorado, marijuana use was never something I discussed with my students or professors. It didn’t really come up among my fellow graduate students (except the ones who played Ultimate, let’s be honest). Outside of one friend who owned a medical marijuana dispensary and a few pothead friends (mostly my guitar teacher, who taught me some Bob Marley before anything else), it just wasn’t something I talked about that much.

The passage of Amendment 64, however, has suddenly turned the conversation on its head in ways I never thought possible. More than once this semester, I have had my principles of micro students ask about marijuana legalization and how we tax it. (The answer was I didn’t know, turns out that in Colorado it’s taxed at a higher rate (regular sales tax) than other pharmaceuticals (exempt from sales and use taxes), which, from an elasticity and deadweight loss perspective in a simple supply and demand model, is certainly the way to go).

Another student asked me this afternoon about moving to Denver after graduation, where he might have a job opportunity. I, of course, lauded Denver’s many highlights and, to my surprise, added, “well, and you can smoke pot legally if you want.” He responded it was not his thing, but we then delved into a conversation on the relative economic merits and costs of legalization. I know that people have been having conversations like this forever, it just seems like they’ve suddenly become much more mainstream.

Finally, on Saturday, I got together with some friends and one friend’s very conservative, elderly, immigrant parents, perhaps the last people on Earth I thought I would have a conversation with about marijuana. But, they grow orchids, and according to the new law, her dad told the group, he can grow six plants and so can his wife, so why not get started? He didn’t want to smoke it, he said. I’m still not sure what he planned to do with it, sell it, keep it just because he could, give it away? But both of my friend’s parents were extremely excited about the possibility. We went back and forth on the specifics of the law all while laughing uproariously at the insistence of two elderly Chinese that they wanted to grow pot and were looking for a consultant to help them, while their daughter tried to convince them not to because she didn’t want to take care of the plants while they’re not in town.

Not your run-of-the-mill cocktail chatter, for sure, but suddenly, it is. Brave New World.

Back to School

It’s the first day of classes here at Gettysburg College and I am working hard (as I’m sure are many) to get back into the swing of things, to readjust to the humid Pennsylvania weather, and to find my rain jacket and galoshes only to have the sun come out while I’m in class.

I’m done with my first day and I’m happy to report that my students will be blogging again. This time, there will be two different classes, Quantitative Methods and Labor Economics. I’m really excited to have my Labor students reading BLS jobs reports every month and getting them as addicted to on-the-spot analysis as I am…I mean, well, moving on. Hopefully, we’ll get some good conversations going this semester.

For my part, I’ll be back up and running soon. I owe you all an explanation of what I was doing in Venezuela. It’s forthcoming and will be cross-posted at Caracas Chronicles, so might have a slightly different feel to it than what I usually write here. After that, I should be back to a normal posting schedule. My apologies for a slow August. Good luck to all going back to school with the new semester and talk to you soon!