Category — doing the math

For someone who’s long identified himself as an environmentalist, the rise in recent years of the profile of environmental issues, particularly climate change, is heartening. Much of this attention is the result of Al Gore’s An Inconvenient Truth, which concludes, as much of the more optimistic reporting on the subject does, with solutions and steps to avert the prospect of catastrophic global climate change.  An often overlooked but absolutely critical aspect of any of these “greener” ways of doing things is an investigation of the way they scale. Two questions that need to be asked of any proposed solution:

1. Is the idea feasible on a large scale?
2. If implemented on a large scale, how does the overall benefit compare with the magnitude of the problem that the solution purports to address?

We do need to constantly look for ways to lower energy use, to create less waste, to reduce the release of toxics to the environment. An abiding quest to green and re-green our lives should become a universal American value, in much the same fashion that thriftiness was admired during the depression, or that discount shopping was admired in the 1990s. But at the same time, we must be careful not to fool ourselves: there is a real prospect that, if we do not consider the scale of the problems and potential solutions, we’ll stop short, that metaphorically we’ll change a lightbulb and recycle a soda can and think we’re done.

Consumption of energy is the biggest part of greenhouse gas emissions, which is the biggest environmental problem facing us today. Almost universally, in the popular press, there is a widespread lack of awareness of scale involved, which is both understandable and frustrating. It is frustrating because figures on overall energy consumption are unambiguous and readily available from the Department of Energy, yet understandable because the numbers involved are so huge. Large scale energy consumption is measured in quads, or quadrillion BTUs. The United States consumes roughly 100 quads, or 100,000,000,000,000,000 BTUs, of energy per year. The outline of the flow of this energy is brilliantly presented in this graph from the DOE. On average, this amount of energy consumption is equivalent to a power consumption of 3.3 trillion watts.

As a very crude¹ (but illuminating) approximation, suppose that every American, all 300 million of us, turns off a lightbulb and reduces our power consumption by 100 watts. In this approximation, we imagine a bulb which had been on 24/7/365 to now be off. All total, we’d save 30 billion watts. Sounds like a large number, doesn’t it? It’s the output of 30 Gigawatt-sized power plants. Certainly admirable. But it’s just 1% of our overall 3 Terawatt power consumption.

Petroleum constitutes roughly 40% of our energy consumption, to the tune of 865 million gallons per day.²³ This turns out to be 10000 gallons per second;  it takes our country about a minute and 40 seconds to burn through a million gallons of oil. Keep this scale in mind the next time you hear about a great way for our country to save a million gallons of oil: wonderful, but hardly the whole solution.

Of this oil, each day we burn 388 million gallons of gasoline and 175 million gallons of diesel fuel.⁴⁵ It is contemplating these figures that lead us into question 1 above: how feasible are any of the alternate fuels touted as replacements for gasoline?

For the moment, I will just address biodiesel. To make biodiesel, vegetable oil is combined with an alcohol and a strong base to produce a liquid that is similar to petroleum-based diesel fuel. There are serious questions as to the energy efficiency of this whole process, which I will not address in this post. As a reasonable approximation, suppose one gallon of vegetable oil can be turned into one gallon of biodiesel.

The entire annual US production of vegetable oil is about 2.9 billion gallons.⁶  If all the vegetable oil produced over the course of a whole year were converted into biodiesel, it would displace about 5 days of gasoline and petro-diesel use.

I’ve seen (but can’t find at the moment) a figure that roughly 10% of our vegetable oil production ends up as waste vegetable oil. So if we converted an entire year’s supply of  used french-fry oil, etc., to biodiesel, we’d keep our country motoring for about 12 hours and 22 minutes.

This is why I’m more than a little skeptical when conversion to bio-diesel is taken as evidence that someone or some organization has “gone green.”  To replace all our motoring fuel with bio-diesel, we’d have to scale up production by a factor of 70. Even if we set a more modest target of replacing a quarter of our motor fuel with biodiesel, we’d need to produce 18 times as much vegetable oil as we do today. In this context, discussion about whether one method of producing biodiesel is, say, 20% more efficient than another method, or whether one type of biodiesel-burning engine is, say, 30% more efficient than another is really irrelevant. What’s relevant is the scale.

I’ll close with one final calculation that puts the scale in perspective. Just looking at gasoline, 388 million gallons per day is equivalent to 1.3 gallons per person per day. We can see that it makes sense: it’s what you get if everyone drives 30 miles per day. We tend not to think of the volume of gasoline that we consume because we don’t see it: it goes from a tank underground through a hose to a tank under our car. But aside from water, there’s nothing for which each and every one of us consumes that’s on that scale. For a family of four, 1.3 gallons per day is 36 gallons per week: imagine this volume of vegetable oil, every week. Sound absurd? That’s what the bio-diesel solution would be.

1. Crude because it mixes primary energy–like coal and gas–with electricity, which is good for order of magnitude, but keep in mind that only a third of the heat value of the primary energy makes it into electricity. [↩]
2. 1 barrel is 42 gallons [↩]
3. Equivalent to the volume of Lipsette Lake every two days. [↩]
4. distillate fuel oil=diesel [↩]
5. plus 68 million gallons of jet fuel [↩]
6. See Table 6 of any of the reports. Note that production of oilseed and production of vegetable oil are different things; only part of the weight of the oilseed is oil. Here I use a specific gravity of 0.9 to convert from metric tons to gallons, so about 7 pounds per gallon. [↩]

My graduate school was primarily a hockey school, although this year it has made the NCAA basketball Tournament for the first time in decades. In fact, my graduate institution plays my brother’s graduate institution in the first round (I don’t predict mine to win), and one of my grad school friends has his undergrad, graduate, and (present) faculty schools all in the tournament. (Take a look, though, at Chad Orzel’s bracket based on the strength of physics graduate programs: Cornell would win!)
While in grad school, I didn’t really follow the basketball team, and I don’t think I even went to a single game. But even though I don’t really, nor have I ever really followed college basketball, I will say that March Madness is the greatest sporting event in the world. Sixty-four games and they all matter.

My brother has, for a number of years, run the only March Madness pool that I participate in. Compared to the rest of my family at least (and sometimes his other friends as well) I tend to do rather well: I’ve never won but I have placed second twice. My general strategy is to pay as little attention to college basketball as possible during the regular season. This works: in our family, at least, there does seem to be an inverse correlation between the number of games watched and performance in the pool. Once, in graduate school, I tried to pick a bracket by flipping a coin, and it was absolutely dismal. I turn to two strategies, then, to fill out my brackets.

Statistics

There are two strategies with statistical bracket-picking methods. The first is to try find the characteristics (such as average winning margin or number of times the coach has been to the tourney) that historically have led to success in tournaments, and to see which of the current teams best meet the characteristics of historically successful teams. Pete Tiernan is the highest-profile guru of this sort of work and he’s put together a set of phenomenological models that predict success at all levels of the tournament, from choosing a final four to picking the 6-11 upsets. Of course, I’m too cheap to actually pay the $20 to buy full access to his research, nor do I want to buy ESPN insider to read his in-depth articles there. And the big question here is whether the methods actually work: compared with all the brackets on ESPN’s tourney challenge, a model (he has about a dozen) that hits the high 90’s pecentiles one year very often hits the 30 percentiles the next. So it may like picking winning lotto numbers: the winners don’t win because of the strength of the model, but because if there are enough entrants, one will be the best.

The second statistical approach is to construct models of team skill, and either rank the teams or put them head-to-head. An amazing amount of free analysis is available from Ken Pomeroy and I’m sure there are other sources as well.

For bracket construction, it’s actually pretty boring to just use somebody else’s ranking list to fill out a bracket. I’ve put together one bracket that’s a sort of half-hearted attempt to use Tiernan’s guidelines (at least the ones you can read for free) combined with Pomeroy’s Pythag numbers. What I discovered is that, more often than not, the simple guidelines don’t give clear-cut results, so doing this thoroughly requires sifting through an awful lot of data, which itself requires a good deal of effort to find. And although I’m a numerically-minded person, my interest does wane after a while.

Pundits

The method I like the most for bracket-picking is to see what all the sports pundits have to say. This year, at least, 5 writers for CNNSI and 5 writers for CBS Sports put their entire brackets up soon after Selection Sunday, and ESPN had 5 pundits with their Elite Eight picks. (CBS Sports has added two more brackets that I didn’t look at.) Sports pundits watch an awful lot of college basketball. To be a national-level sports pundit, you have to pay attention to all the conferences and a wide swath of teams. (This is where I think basketball enthusiasts stumble: they generally have their favorite teams and conferences upon which they focus their attention, and as a result overlook and underestimate the rest of the teams.)

What was interesting to me is the variation in pundit picks. All 5 of the CNNSI writers picked UCLA to win the tournament and none of the ESPN pundits did. All of the CNN pundits pick 13-seed Siena to upset Vanderbilt, while only 1 CBS pundit did. Four of five CNNSI pick 11th-seed St. Joseph’s to beat Oklahoma, while only one CBS did, while 3 CBS writers picked 11th-seeded Marquette to beat Kentucky, while only 1 CNNSI writer did. Out of all ten full brackets, there was only one prediction of a 14-over-3-seed upset: CBS writer Brian De Los Santos picked Georgia over Xavier.

In addition to sending them to my brother, I posted my brackets to the Washington Post Tourney Tracker: Search for thm_A_exp for the pundit-derived bracket, thm_C_stats for the statistics-derived bracket, and thm_B_pyth for the (boring to construct) bracket filled out strictly based on Pomeroy’s pythag statistic. I’m curious how each of these strategies fares in a wider pool of competition.

Sunday’s Super Bowl was an interesting game: the lead changed several times and until the very last seconds of the game, it seemed like either team could win.

Emotionally, at least, there’s a similarity between watching election night returns and watching sports: as the votes tally up, one can form a mental picture of a literal race, and if your favored team or candidate is behind, you cheer when the gap closes. Of course in sports, the actions of the players determine the course of the game, and crazy things can happen. In elections, it’s all over once the polls close. Barring irregularities like the 2000 presidential election in Florida, it really doesn’t matter what order the votes are counted in, and once the votes start to be counted, there is nothing anyone can do to get more votes. Cheering doesn’t give anyone a boost.

Of course, for all those involved in a political campaign, it also ends once the polls are closed, especially for the losing candidate. But even for the winning candidate, the dynamic of everyone involved changes dramatically. Those hours of uncertainty, after the polls close but before the winner is known, are the only possible time to have one last gathering of the campaign, and it might as well be a party, and you might as well find out how you’ve done.

And for everyone at home, watching the election returns can be entertaining, to know as soon as possible what happened. So as thoughts of Super Bowl turn to thoughts of Super Tuesday, I present my rudimentary election watching spreadsheet.

The television networks often project a winner even when it’s mathematically possible for either candidate to win, and the spreadsheet I offer here lets you play along, too. It only uses three pieces of information: the number of votes each candidate has, and the percent of precincts that have reported.

If we make the approximation that all precincts will have the same number of voters–not generally true, but hard to get a better number without detailed precinct-by-precinct data–then we can project the total number of votes that have been cast, and from that calculate the number of votes remaining to be counted, and of those the number each candidate would need to win, and finally, what percentage of the remaining votes each candidate would need.

These percentages are really illuminating: if you calculate that a candidate who has 45% of the vote so far would need to have 67% of the remaining vote to win, then you could call the election for the other candidate with a fair degree of confidence.

To use, just put the most recent vote counts in cells A3 and B3, and the percentage of precincts reporting in C3. The rest is calculated automatically. Use the Fill Down command to create multiple lines for running progress.

Watch Returns

I was 34 years old when my son was born; my father was only 29 when I was born. Yet despite the fact that more time will have elapsed between my childhood and my son’s than between my father’s and mine, my perception is that while the world in which I grew up was fundamentally different than that in which my father grew up, my son is growing up in a world that is a slow, gradual evolution of the world of my childhood. Perhaps it’s because it’s only relatively recently that I’ve self-identified more as an adult instead of as a young person, and have wanted to categorize more years of advancements as belonging to my youth than I would acknowledge belonging to my father’s youth. I don’t really know what the right comparison to make is–Matthew is several years away from an age against which I can compare any real memories. And when he’s old enough to think about it, I could imagine Matthew reasoning that the lack of digital photography, a ubiquitous internet, and the need to buy music on physical media all as evidence that my youth was stone-age by comparison. We don’t really know what the world will look like when Matthew is old enough to remember it, but we can make some comparisons about the years in which we were born.

First, transportation. Amtrak was formed in 1971: passenger rail when Matthew was born is roughly the same as when I was born, and completely different from when my father was born. At some point before I was born, the passenger-miles of the airlines overtook that of the railroads. The present Interstate Highway system, begun in 1956, is similar to when I was born.  

So I think its fair to say that the transportation world in which I was born was fundamentally different than that in which my father was born, but Matthew’s transportation world is similar to mine.

For sports, my dad grew up in the era of the original 6 NHL teams, and before interleague play in Major League Baseball, but looking at the figures per 100 Million population is interesting:   

So while the NHL has definitely grown in each era, there was more football per capita when I was born than either now or when my dad was born. Most significantly, there was more baseball per capita when my dad was born than either now or when I was born. Sort of makes me wonder about all the hand-wringing that goes on about how baseball expansion is supposed to have diluted the available pitching talent.

One other facet that I thought was different about my dad’s youth, but isn’t really, is candy. I remember my dad telling me about ads for Clark bars when he was a kid–even though they’re still available, they really aren’t heavily advertised, nor were they when I was young. But according to this timeline of American candy bars, it looks like the golden age of candy bar inventions were the 1920s and 1930s; pretty much the same selection had been available for my dad as for me, and Matthew benefits from the rather small handful of candies (Whatchamacallit, Twix, Skittles) that were introduced during my youth.

A few years ago, for Christmas, we got a fondue set from my brother and sister-in-law. With everyone here for Christmas this year, we decided to echo a tradition of the sister-in-law’s family and have fondue on Christmas day; as per our family’s tradition, we do the turkey Christmas eve so that we aren’t spending all of Christmas day roasting a turkey.

We did discover that a sterno-powered fondue pot, although fine with cheese and chocolate fondue, in which you coat a piece of bread or fruit or cake with a thick yummy liquid, isn’t up to the broth (or oil) fondue in which you actually cook a bit of meat or vegetable in a simmering liquid. We were thinking, though, that it would have been nice to have had an electric fondue pot as well, but unless you’re really into fondue, do you really want to have two (or more) fondue pots around all the time?

Wouldn’t it be nice, that is, if there was some sort of small appliance “library,” or community registry of small appliances that people could borrow for a day? Crock pots, chafing dishes, large coffeemakers: all things that are very useful on occasion, but I don’t know that I want to devote shelf space to all of them.

Grating the Gruyere and Emmentaler, I realized that the density of grated cheese can vary tremendously, and was sort of annoyed that the recipe in my Fondue cookbook gave only volumetric measures for cheese, not weight. I looked up two other cheese fondue recipes, and found, for the basic ratio of cheese to white wine:

• Fondue cookbook: 4 cups cheese to 2/3 cup wine
• Joy of Cooking: 1 pound cheese to 2 cups wine
• Fannie Farmer: 1 pound cheese to 1 cup wine

Fannie Farmer further states that 1 pound of cheese is “about 2 1/2 cups.” In the back of the Joy of Cooking, you can find that 1 pound cheese is 4 cups grated, and this ratio, 4 ounces grated cheese per cup, is also given in several Cooks Illustrated recipes, although they don’t have a cheese fondue. Thus it looks like all the fondue recipes are talking about the same amount of cheese, but with a factor of 3 in the cheese:wine ratio. 

In a sense, it is this wild variation in recipes from trusted, standard sources that leads Cooks Illustrated to try 50 variations of a recipe before publishing the one they find to be the best. But there’s another lesson here, which I eventually took in: if you melt some swiss cheese with some wine, and throw in a bit of kirsch and a little nutmeg, salt, and paprika, you’ll get something very tasty, and if you’re still worrying about the ratio of cheese to wine, then you haven’t had enough wine yourself.

One of the biggest changes moving from academia to being an employee of the U.S. Government was that I now have to keep track of vacation days–I get 19.5 per year, in addition to the 10 federal holidays. So I don’t always take the entire week between Christmas and New Year’s off, but this year I did, using up four vacation days to get an 11-day stretch at home. (The President was gracious enough to give Federal employees Christmas Eve day off.)

As with most vacations, I had anticipated making progress on a whole list of projects, but, as is also usually the case, I hardly touched most of them.

Let me say right off that the first problem is that the ‘to-do list’ mentality is not really the appropriate way to describe spending time with my son. I played with him and photographed him and read to him, and the fact that I didn’t get to cross any of these things off a project list is really irrelevant.

But still, it does seem like a whole bunch of time went by without much productive being done. And I think it’s partly because even though I do have some to-do lists made up, I didn’t really plan my vacation.

Planning might seem line anathema for vacations, an unwelcome imposition of order onto what ought to be relaxing, but I’ve come to differ. You must, at some point, plan your time: one way or the other, you’re going to have to figure out what you want to do. At the most inefficient, you can use up your vacation time deciding what to do, and in the end I think I don’t think that ends up very satisfying.

I think our sense of elapsed time–whether a vacation has flown by, or seemed like a good break–is strongly correlated with the number of changes we experience throughout. A “leisurely” day–getting up late, eventually eating and getting dressed, thumbing through the newspaper, and then thinking about what to do, to be followed, perhaps, by actually doing something in the afternoon–does not put one through very many changes, and seems to go by quickly. (This does describe a large number of my eleven days off.)

By contrast, I think of two-day conferences I’ve been to, with separate events in the mornings, afternoons, and evenings–lots of changes–and recall that they usually end up feeling satisfying, or at least, I can’t recall feeling like time flew by with nothing being done.

Planning out vacation time in advance becomes more important if you’re traveling somewhere, because then, your time at your destination is very rare and very expensive. What a waste to spend your time sitting in a hotel room flipping through a guidebook!

When my wife and my mother-in-law and I went to Korea, we did a lot of planning: to know what the bus and train schedules were, and what days the museums we wanted to see were open, and how to get from a hotel to a site of interest. And the planning paid off: we still marvel at how much we saw in ten days. Quite a contrast to this year’s eleven days of holidays.

Perhaps the best reason to listen to Sierra Club Radio is to hear the fascinating guests that come on the show, who often manage to say something insightful despite host Orli Cotel’s bubbly demeanor and loaded questions. But one theme has come up in two recent programs–indeed, you hear it often from the Sierra Club–that really gets to me: the notion that the answer to the problem of our nation’s oil consumption is to “go farther on a gallon of gas” by raising fuel economy standards. Since raising fuel economy standards is just about the only progressive thing left in the energy bill that made it through Congress, much has been made of this phrase of late.

It seems simple enough: increase the fuel economy, and our fuel use goes down. But there’s a really big if here: that’s if the number of miles driven doesn’t go up. I will argue in this post that there’s no evidence to support the notion that the amount of driving will stay fixed. This is the problem with the phrase: “going farther” implies more driving, by using the same amount, “a gallon,” of gas.

From the standpoint of an individual, many environmentally-minded folks buy high fuel economy cars in order to achieve “guilt-free” driving. When faced with a transportation decision: whether to travel, and if so, which mode to choose, the fact that one has a car with higher than average fuel economy certainly makes it easier to choose to drive. This is actually a well-known phenomenon known as the Jevons paradox: improvements in efficiency of consumption of some good leads to a larger overall rate of consumption of that good, because use of that good becomes feasible for more uses as the efficiency grows. It’s the same reason you spend more time online when you have a faster Internet connection. Overall, America’s gasoline consumption is analogous to a (faltering) dieter who eats a whole box of fat-free cookies because they’re “healthy.”

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Americans throw out 100,000,000,000 plastic shopping bags each year. This is the figure given in Katharine Mieszkowski’s article about plastic bags in Salon.com, which I first heard about when Sierra Club Radio Interviewed her.

I won’t repeat what’s in the article: that’s what links are for. Suffice it to say that plastic bags wreak havoc on the environment. But let’s explore the numbers.

As I write this, the Census bureau estimates the US population at 303,384,903: that means that, on average, each American throws away about 330 plastic bags each year, or just one bag per day most days of the year. Five bags of groceries plus two other purchases a week would do it; this tells us there’s no reason to doubt the 100 billion figure. In fact, thinking about all the double-bagging that goes on at supermarkets, and not to mention all the other shopping that’s going on all the time, the figure seems a bit low. And unfortunately, there isn’t one evil industrial polluter to which we can assign the blame: what seems like a normal number of plastic bags times a whole lot of us means a whole lot of bags.

Producing the 100,000,000,000 plastic bags apparently takes 12 million barrels of oil. One barrel of oil is 42 gallons, so you can make about 200 bags from a gallon of oil, or about 2/3 fluid ounce of oil per bag.

According to the US Department of Energy, the US uses 20.7 million barrels of oil per day, or 7.6 billion barrels of oil per year. Of this, roughly 3/4 goes to transportation fuels. So if we took all the oil that presently goes into plastic-bag production, and used it instead for moving around, it would last about 19 hours.

Which means: plastic bags are awful for wildlife, and very ugly when they’re littered around, but they’re not really a significant part of our dependence on foreign oil. If someone comes up with a scheme to recycle plastic bags into an alternative fuel for cars, then perhaps it will be clever, but it won’t really be anything like a solution.