Cars! Acceleration vs MPG

I don’t own a car. I haven’t owned my own car for about 6 years, though a shared one for the first 4 of those. I’ve lived happily car-free for the last few years. This lifestyle isn’t possible for everyone, so most of us buy a car. But how do we chose? And why do car commercials get to arrogantly advertise their pick up has the best MPG in class of 27 MPG? 27 is a really crappy number. My first car, a 98 Chevy Cavalier got 32 MPG and I was a wild teenager driving that thing. Why have we progressed so little in the past 15 years? Why does a Google search find fuel efficient to mean 30+ MPG and not 50+ MPG?

I sat down to do some research about the historic relationship of acceleration vs MPG in America. We have, as a country, systematically chosen power over efficiency. A blogger, Dan, at put together a wonderful article that I will pull from for this post. He speaks to a big political document called the Light-Duty Automotive Technology, Carbon Dioxide Emissions, and Fuel Economy Trends: 1975 – 2013 (which reads a lot like I imagine the IPCC report reads to non-climate folks…). It’s long and a little tedious to the uninitiated. So, just like I do with the IPCC, I’ll highlight the most insightful graph:

Figure 2.3 from the EPA annual report.

The fuel economy, or MPG, of cars has basically flat-lined since 1980. Without changing much about the vehicles weight, car manufacturers have dramatically increased performance. This graph gives well researched evidence that car manufacturers have no real drive to improve our efficiency. Okay, so why does this happen?

Now here is something really cool that Dan did: he made a lovely correlation plot of efficiency and power. He found that for every percentage drop of fuel economy you give up, you get 3 percentage points of power. This means that it always feels like a better deal to give up a little efficiency to gain a lot of power. Ugh.

Beautiful plot!

What does that power really get you? Wouldn’t you rather save the money at the pump? I don’t expect to change anyone’s mind with this. But it’s worth thinking about. Luckily Obama has some legislation in place that will help efficiency get to were it ought to be. But for now I’m happy to live car free and hopefully by the time I want a car I will have more options for “high efficiency” vehicles.  …and then I found this:

I can’t even tell you how many versions of this meme I found! I have no words…

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Mathematicians in the big-data spotlight

Mathematicians and statisticians, perhaps with a sprinkle of programming and network science, will be as foundational to the modern workplace as numeracy was a century ago and literacy before that.

When I decided to go back to school my father explained to me that all disciplines see their heyday. As a society we are seemingly capable of focusing on only one major field at a time. So recently Biologists, Chemists and Computer Scientists have had their success. But it’s been a long time since Mathematicians have held center stage. In fact, mathematicians have been waiting quite some time to hold the imagination of the public. I can say this because whenever I told someone I was getting a PhD in Math, the first assumption was that I was going to teach. Because math isn’t, you know, good for anything useful. Not on it’s own. Maybe if you add some engineering or chemistry- but not on it’s own! But we, the math nerds, have had some recent success.

The housing market crashed, after years of statisticians and mathematicians wondering how we could continue to support bad investment loans. So good job to the mathematicians for noticing that something wasn’t right. But we didn’t have the clout back then to make a difference. Since then we’ve had other famous moments.

Those look like graduation robes! Maybe that’s because this was the last time math was cool?

Target statistician Andrew Pole famously determined how to identify pregnant women. And lets not forget PRISM and the NSA who hire huge teams of mathematicians. There is some difficulty with working in a field which wields a new tool. Just as staring at the sun took Galileo’s eyesight and the development of the nuclear bomb took the lives of many physicists, Big Data can be used in dangerous ways. But the data will continue to collect in dark musty closets and hard drives. Data which, when one knows the magic words, can open doors to exciting discovery.

Who knows the magic words? Statisticians and Mathematicians. We know the words to unlock the secrets of interlinked data. Mathematicians, Statisticians, and a few others with the knack can dig through the tables and columns to create useful, profitable, and valuable insight. “Every great research team has a mathematician,” I was once told. This may not have been true several decades ago. But now, when everything is data, the long overlooked mathematicians may have an opportunity to see the spotlight of societies gaze.The quote at the top of this article comes from the book Big Data: A Revolution That Will Transform How We Live, Work, and Think by Viktor Mayer-Schönberger and Kenneth Cukier. I recommend it! It’s good!

But, now that mathematicians may be standing in the spotlight, what will we do with the attention when we are so famous for being social rejects? I hope that we’ll take the opportunity to build a new stereotype. And that’s an exciting idea.


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Winter is Coming…

Winter is coming… and going… and coming again here in Minneapolis, MN. I can’t believe this week has low temperatures below freezing. It’s April!

This winter has been colder than normal. I wanted to get some sense of how much colder it was. So I pulled a bunch of data about Minneapolis’s 2013-2014 winter weather off of Weather Underground. I looked at data from November 15, 2013 (the last day the high was above 50F in 2013) through March 30, 2013 (the first day the high was above 50F in 2014). These are the 134 days of my definition of the Minneapolis winter. 134 days out of 365 is almost 40%!


40% is a whole lot more than the 25% percent of the year that is supposed to be “Winter.”  But, what’s cool is that this is basically the Golden Ratio of warmth to cold!! Which makes Minneapolis, MN pretty cool (pun intended).

We had a lot of “below zero” days this year. Currently, below zero days are defined to be days where the low is below zero. These days really suck. They are the days when your snot freezes in your nose, when you need flannel lined jeans AND long underwear, when you overheat as you get dressed and then your sweat freezes to your forehead as soon as you get outside. Suffice to say, these days are less appealing than most to wait for the bus in the morning…


Here’s a graph of the daily highs and lows for the past winter. I have helpfully marked the zero Fahrenheit line on the graph. Because below freezing is bad, but below zero is worse. Perhaps I can provide a more emotionally accurate view:


I’m working on my infographic skills, so let use a cute snowflakes in a bar chart to count these crappy days! I’ll just consider the weeks when there were below zero days. So we are restricting our attention to the dates between December 6th, 2013 and March 6th, 2014.

Days below 0 GraphThat’s a lot of days! 50 days is 13% of the year. For comparison: only 3% of the year is federal holidays and your birthday is only 0.02% of a year. Here’s that percentage breakdown for you with a snowflake to represent the percentage of days which are below zero. I put my birthday on there too… it’s just so small you can’t see it.


Over the same interval (Dec 6 to March 6) there were only 14 days when the high was above freezing. This is why snow that lands in Minneapolis in November tends to still be hanging around in April. The weather is never warm enough to melt anything of consequence.

Days above 32 GraphThis winter has been long. For the last 40% of a year, it’s been cold. Today is still cold with lows below freezing. But not bitterly cold in a below zero kind of way. Is this normal? Well, 50 or 60 years ago, below zero days were much more common than they are now. This is because Minneapolis has been getting warmer over the decades. (Kind of like our planet!)

This winter could be a case of increased climate variability. Climate scientists have been talking for decades about increased variability in our climate due to global climate change. Global warming produces instability in the weather patterns. Thus, while the whole planet is warming on average, certain locations could be experiencing colder than average weather. There are plenty of predictions that these extreme weather events will become more common. So while I would like to end this article with the hope that next year will be better, it’s entirely possible that next year will be just as unpredictable as this one. I know it’s only April, but here in Minnesota I think we should assume that winter is always coming.



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4 tips for non-mathematicians attending math dinners


I think this article is lovely! Attending a math conference dinner is a really hard thing to do. Mathematicians, as a community, are very good at talking about math and very poor at talking about other things. I think this article is a lovely take on that.

Originally posted on Sarah Zureick-Brown:

Seminar dinner, conference dinner, generic math gathering, I want to be there.  This shouldn’t be surprising.  I love eating and drinking, and I enjoy both of these activities even more in the company of smart and interesting people.

Still, at more than one math dinner, I’ve been told, “I’m surprised you’re here.  My wife would never want to do this.”

This makes me feel strange, like some mutant math groupie (which, in truth, I am).

I understand where these other non-mathematician partners are coming from.  Mathematicians can be abrasive, and it can feel isolating when you can’t take part in the dinner conversation because you don’t understand the math.  But there’s a lot of fun to be had at these dinners, and sometimes you have to do it for your partner.  So here are my tips for having a good time…

1) Let people talk about math

Nothing is going to…

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The Yoga of Grading

Grading is like yoga. Over the last six years in which I’ve been practicing the art of grading, I have found there is a belief system to the practice of grading, an ideology. And everyone has their own system. Some people start from 0 points and only add points when I student does something correct. Some graders start from  100% and work their way down as the student makes mistakes. Are you an additive or subtractive grader? A grader goes through phases in their journey to be a paper grading master. I think there are a three main phases which I went through on my journey to grading enlightenment.

Women talking

Phase 1: The conversational practice

When I first started my journey to grading enlightenment, I found myself very talkative. I enjoyed grading with others. It was a social experience. So, on Sunday morning, I would sit in the grading room with 4 or 5 other people and we would share stories about our experiences. We could discuss how best to grade a problem, how to deal with inconsistencies. We could also share the pictures that our students occasionally drew instead of giving a solution!

New Yogis also go through this process. You look around to see what the heck a “Utkatasana” is. And then you spend the next ten minutes wondering why the instructor didn’t just say “Chair pose”- is she trying to be oblique and snobby? This is the social element of learning the craft. Your instructor keeps telling you that your yoga practice is just between you and your mat, but you can’t help but compare yourself to others: “My runner’s lunge is totally better than everyone else’s!” I couldn’t fathom doing yoga at home. Too many distractions and no outside pressure to make me do the work.


Phase 2: The emotional outpouring

As I continued my spiritual grading journey, I found myself really invested in the answers. I would get really upset. “How could they think that was appropriate?”  or “Weren’t they listening in class?” or “Yay! Good job!”. This made the process of grading really hard. It was long and emotional. But, by this point I was in yoga class regularly…

My instructors would reflect on observing but not judging. Yoga is a process of accepting what is happening on your mat regardless of what your brain is judging. “It’s yoga practice, not yoga perfect,” my instructor would say. Let go of the practice thus far. It doesn’t serve you to dwell on it.

So I tried this. And my grading went faster. I was less tired at the end.


Phase 3: The practice of inward focus

Now, I don’t grade in groups. In fact, I prefer to grade at home. I don’t need the feedback. I have accepted that some of my students will do well, and some will do poorly. I know the chants and the rituals of grading. I know what works for me. I try to grade so that a student is less likely to cheat, edit their exam, and return it to ask for more points. Most importantly, I know that a poor student score doesn’t mean I failed. It’s like when I fall out of a big toe hold. My sense of self is not diminished when I fall on my mat.

Sure, sometimes I’ll be inconsistent with my grading. And sometimes I’ll have to re-grade some exams because I goofed up the first time. But, despite the potential for frustration, I (mostly) remain calm. So now I am comfortable with my grading practices… Which is good since I only have a month and a half of grading left before I leave academics for a while. I’m not sure what the moral is here. Better late than never? Finding peace in a yucky task is not wasted effort? Yeah. Both of those sound good; let’s go with those.


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In defense of science: Cosmos!

I love love love that people are freaking out (negatively and positively) about Cosmos, a remake led by astronomer Neil deGrasse Tyson of a mini-series led by Carl Sagan in the late 70’s. People are freaking out and watching it and you should be too.

Science as a field of legitimate inquiry has

come under attack over the last decade.

Think about how the climate change “debate” has continued despite 97% agreement among scientists- just ask NASA. Let’s also remember that New York has a measles outbreak for the first time in decades thanks to people not believing in vaccines.

I’m so grateful that there are people who want to put money into PUBLIC displays of science’s grandeur. If religion can paint emotional pictures to get recruits, then I believe science should be doing that as well. And scientists aren’t always their own best advocates… Cosmos is an amazing example of how science + emotion and art is compelling and understandable. It’s brilliantly done and skeptics should be scared. They should be running for the hills to regroup.

Cosmos has social power. Watch it. Talk about it. Help promote a positive view of science.

As a post script: this remix has been keeping me company as I write the second draft of my dissertation. It’s hilarious and grand.

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What’s in a name?

What’s in a name? that which we call a rose
By any other name would smell as sweet.  – Shakespeare

A name is just a name. We, as mathematicians, are happy to define something to be whatever you want it to be. You want to call that function f? Go for it! Maybe you are in a Γ mood. That’s okay too. We’ll accept a function to have whatever name you want it to have. …up to a point. I mean, you can call it whatever you want. But, you can bet you me that if you name the darn thing π or O (pronouced “Big O”) we will all complain to the end of time.  And Yes, for all you non-mathematical folks out there, there really is a function, or more accurately a notation, called Big O. Ask Wikipedia. Didn’t the folks who first started using Big O notation realize it looks exactly like a zero??

What was I saying? Oh, yes. Freedom of naming. If you want to name your child Jake then people might assume the child is white. Freaknomics famously wrote about this in 2005. But then, they may be wrong? Regardless, what I really want to talk about is the nomenclature of mathematics.

Secretly, every mathematician has strong opinions on the subject. Let’s start with something simple.


The lower case a seems fairly innocuous. Little a has many great qualities. He is the first letter that comes to mind (hehe, it’s a terrible joke but I can’t help myself!). Little a looks great with a bar, prime or hat!


Now here comes the picky part. Little a is for constants. In fact, the first 3 or 4 letters are reserved for constant values. Variables come from the end of the alphabet. Do no vary from this unspoken mandate. To stray is verboten! Thus, a polynomial might be written as:

ax² + bx + c

But what if you need more than four constants? Then, I’m happy to say that little a looks great with indices and subscripts!  Just look:

a2x² + a1x + a0

b2x² + b1x + b0

Looks really great! Indices look great with the second equation of little bs as well! But sometimes we need a random constant. Then there’s trouble. We need an arbitrary index. Mathematicians like to use i, j, and k for this. So, as an innocent mathematician, you pick the first:littleasubiThis is all well and good until you need another arbitrary constant for a different equation…

littleailittlebjAnd anyone who doesn’t see a problem with using the term “bj” in a classroom full of mostly male teenagers is awesome and I appreciate your innocence. But, rude jokes aside, mathematics get very passionate about their nomenclature.  Suffice to say, to a mathematician, a rose by any other name is acceptable, but it would not smell as sweet.

Maybe I can tell you more about this later. Maybe I need to do some social research on the topic…

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