# Are Teslas greener? (And why ‘average’ and ‘marginal’ can be confusing terms).

From the Union of Concerned Scientists (UCS):

Global warming emissions occur when manufacturing any vehicle, regardless of its power source, but battery electric vehicle (BEV) production results in higher emissions than the making of gasoline cars— mostly due to the materials and fabrication of the BEV lithium-ion battery. Under the average U.S. electricity grid mix, we found that producing a midsize, midrange (84 miles per charge) BEV typically adds a little over 1 ton of emissions to the total manufacturing emissions, resulting in 15 percent greater emissions than in manufacturing a similar gasoline vehicle. However, replacing gasoline use with electricity reduces overall emissions by 51 percent over the life of the car.

A full-size long-range (265 miles per charge) BEV, with its larger battery, adds about six tons of emissions, which increases manufacturing emissions by 68 percent over the gasoline version. But this electric vehicle results in 53 percent lower overall emissions compared with a similar gasoline vehicle.

In other words, the extra emissions associated with electric vehicle production are rapidly negated by reduced emissions from driving. Comparing an average midsize midrange BEV with an average midsize gasoline-powered car, it takes just 4,900 miles of driving to “pay back”—i.e., offset—the extra global warming emissions from producing the BEV. Similarly, it takes 19,000 miles with the full-size long-range BEV compared with a similar gasoline car. Based on typical usages of these vehicles, this amounts to about six months’ driving for the midsize midrange BEV and 16 months for the full-size long-range BEV.

The key figure from the report:

Such analyses require deciding whether to use the marginal or the average GHG intensity of electricity production. Ma et al argue for the marginal approach:

for a true assessment of the overall CO2 impact of the growth of electric vehicles, it is more relevant to consider the ‘marginal’ grid intensity than the average grid intensity. Marginal electricity is the incremental electricity that must be brought on stream to meet the additional demand from BEVs. In this context, it is important to note that low GHG intensity electricity such as nuclear or wind power is typically used to 100% of available production for various reasons, particularly the low short-run marginal costs.

However, UCS note that this marginal approach can lead to paradoxical-seeming results:

For example, if over some time period 25 percent of electricity generation in a region moved to renewable sources, fossil fuel power plants may still be the only electricity sources on the margin responding to instantaneous increases in demand for electricity. So an EV powered on a grid with no renewables and one with 25 percent renewables might still have the same emissions profile using this type of marginal emissions analysis.

At this point it becomes useful to ask: exactly what intervention are we modelling? Is it one individual buying an electric car, electic car subsidies, or Elon Musk’s decision to start Tesla? This makes the average/marginal controversy fall away. In each case, we want to know what happens if we buy a car, enact subsidies, or start Tesla, compared to the counterfactual. In the car case, it’s pretty clear we would call this the marginal change, but what do you call the effect of going from zero to one Teslas? It’s marginal in a sense because Tesla is (or was) the marginal electric car company, but average in the sense that we are averaging over thousands of small decisions that led to the existence of Tesla. And what would it even mean to evaluate the average effect of electric car subsidies? Average according to which reference class? The set of all pro-electric-car policies? Let’s not go there. It’s just much clearer to ditch talk of marginals and averages, and instead be clear about our counterfactuals.

A more mathematical way to put the same point: if $f(x)$ is the amount of value as a function of our actions $x$, the marginal approach looks at $f'(x)$, the average (usually) looks at $f(x)-f(0)$. But both are special cases of looking at $f(n)-f(c)$, where $n$ is the value of $x$ after we act, and $c$ is the relevant counterfactual.

All three of these interventions have both a short-run effect (increasing electricity demand at the margin) and a long-run effect (affecting which types of electricity-generating plants are built, and how many). In the case of purchasing a car, it can appear not to have a long-run effect, but this turns out to be an illusion, as I wrote elsewhere.

So we want to analyse both short-run and long-run effects. UCS, calling such an analysis a “long-term marginal” approach, write:

The long-term marginal emissions approach, or a consequential life cycle approach, evaluates how the electricity grid responds over a longer time period. This approach can estimate what would happen to the grid without new electricity load being added and then contrast this outcome with what would happen under a the new load. For example, an analysis could estimate electricity demand between 2015 and 2030 assuming no EVs and then what demand would look like with several million EVs added (EPRI and NRDC 2015). This type of modeling approach allows long-term changes in the electricity grid to be evaluated, including power plant retirements, new electricity generation, and changes in EV demand. Importantly, it also allows for the evaluation of policies to reduce emissions from both the transportation and electricity sectors, as well as for estimates of the cumulative impact on emissions from both sectors. For example, one could use this approach to examine the impact of the increased EV deployment triggered by implementation of the EPA’s Clean Power Plan.

UCS point to Weis, Jaramillo, and Michalek 2014 as an example of this kind of approach.

# Fluidics

Logic gates can be built that use water instead of electricity to power the gating function. These are reliant on being positioned in one orientation to perform correctly. An OR gate is simply two pipes being merged, and a NOT gate (inverter) consists of “A” deflecting a supply stream to produce Ā. The AND and XOR gates are sketched in the diagram. An inverter could also be implemented with the XOR gate, as A XOR 1 = Ā.

Diagram:

The two gates AND and XOR in one module. The bucket in the center collects the AND output, and the output at the bottom is A XOR B. When exactly one input stream is on, then the stream hits the other side of the tank and falls towards the bottom. When both input streams are on, then they collide in the middle and fall down to be collected by the bucket.

# How we talk and think about probability distributions

From InfoProc, my emphasis:

Many people lack standard cognitive tools useful for understanding the world around them. Perhaps the most egregious case: probability and statistics, which are central to understanding health, economics, risk, crime, society, evolution, global warming, etc. Very few people have any facility for calculating risk, visualizing a distribution, understanding the difference between the average, the median, variance, etc.

A remnant of the cold war era curriculum still in place in the US: if students learn advanced math it tends to be calculus, whereas a course on probability, statistics and thinking distributionally would be more useful. (I say this reluctantly, since I am a physical scientist and calculus is in the curriculum largely for its utility in fields related to mine.)

In the post below, blogger Mark Liberman (a linguist at Penn) notes that our situation parallels the absence of concepts for specific numbers (i.e., “ten”) among primitive cultures like the Piraha of the Amazon. We may find their condition amusing, or even sad. Personally, I find it tragic that leading public intellectuals around the world are mostly innumerate and don’t understand basic physics.

The Pirahã language and culture seem to lack not only the words but also the concepts for numbers, using instead less precise terms like “small size”, “large size” and “collection”. And the Pirahã people themselves seem to be suprisingly uninterested in learning about numbers, and even actively resistant to doing so, despite the fact that in their frequent dealings with traders they have a practical need to evaluate and compare numerical expressions. A similar situation seems to obtain among some other groups in Amazonia, and a lack of indigenous words for numbers has been reported elsewhere in the world.

Many people find this hard to believe. These are simple and natural concepts, of great practical importance: how could rational people resist learning to understand and use them? I don’t know the answer. But I do know that we can investigate a strictly comparable case, equally puzzling to me, right here in the U.S. of A.

Until about a hundred years ago, our language and culture lacked the words and ideas needed to deal with the evaluation and comparison of sampled properties of groups. Even today, only a minuscule proportion of the U.S. population understands even the simplest form of these concepts and terms. Out of the roughly 300 million Americans, I doubt that as many as 500 thousand grasp these ideas to any practical extent, and 50,000 might be a better estimate. The rest of the population is surprisingly uninterested in learning, and even actively resists the intermittent attempts to teach them, despite the fact that in their frequent dealings with social and biomedical scientists they have a practical need to evaluate and compare the numerical properties of representative samples.

[OK, perhaps 500k is an underestimate… Surely >1% of the population has been exposed to these ideas and remembers the main points?]

…Before 1900 or so, only a few mathematical geniuses like Gauss (1777-1855) had any real ability to deal with these issues. But even today, most of the population still relies on crude modes of expression like the attribution of numerical properties to prototypes (“A woman uses about 20,000 words per day while a man uses about 7,000”) or the comparison of bare-plural nouns (“men are happier than women”).

Sometimes, people are just avoiding more cumbersome modes of expression – “Xs are P-er than Ys” instead of (say) “The mean P measurement in a sample of Xs was greater than the mean P measurement in a sample of Ys, by an amount that would arise by chance fewer than once in 20 trials, assuming that the two samples were drawn from a single population in which P is normally distributed”. But I submit that even most intellectuals don’t really know how to think about the evaluation and comparison of distributions – not even simple univariate gaussian distributions, much less more complex situations. And many people who do sort of understand this, at some level, generally fall back on thinking (as well as talking) about properties of group prototypes rather than properties of distributions of individual characteristics.

# The Copernican Revolution from the inside

My friend Jacob started a blog, and the first post was awesome (I even worry that he won’t be posting as much as he could because now he feels that every post has to live up to that standard. Don’t think that way, people!).

First, if you lived in the time of the Copernican revolution, would you have accepted heliocentrism? I don’t mean this as a social question, regarding whether you would have had the courage and resources to stand up to the immensely powerful Catholic Church. Rather, this is an epistemic question: based on the evidence and arguments available to you, would you have accepted heliocentrism? For most of us, I think the answer is unfortunately, emphatically, and surprisingly, no. The more I’ve read about the Copernican revolution, the less I’ve viewed it as a key insight followed by a social struggle. Instead I now view it as a complete mess: of inconsistent data, idiosyncratic mysticism, correct arguments, equally convincing arguments that were wrong, and various social and religious struggles thrown in as well. It seems to me an incredibly valuable exercise to try and feel this mess from the inside, in order to gain a sense what intellectual progress, historically, has actually been like. Hence a key reason for writing this post is not to provide any clear answers — although I will make some tentative suggestions — but to provoke a legitimate sense of confusion.

[…]

The ability of the Ptolemaic system to account for these phenomena, predicting planetary positions to within a few degrees (Brown, 2016), was a key contributor to its widespread popularity. In fact, the Ptolemaic model is so good that it’s still being used to generate celestial motions in planetariums (Wilson, 2000).

The kicker (but wait, it gets better!):

In order to get the actual motion of the planets correct, both Ptolemy and Copernicus had to bolster their models with many more epicycles, and epicycles upon epicycles, than shown in the above figure and video. Copernicus even considered introducing an epicyclepicyclet — “an epicyclet whose center was carried round by an epicycle, whose center in turn revolved on the circumference of a deferent concentric with the sun as the center of the universe”… (Complete Dictionary of Scientific Biography, 2008).

Pondering his creation, Copernicus concluded an early manuscript outline his theory thus “Mercury runs on seven circles in all, Venus on five, the earth on three with the moon around it on four, and finally Mars, Jupiter, and Saturn on five each. Thus 34 circles are enough to explain the whole structure of the universe and the entire ballet of the planets” (MacLachlan & Gingerich, 2005).

These inventions might appear like remarkably awkward — if not ingenious — ways of making a flawed system fit the observational data. There is however quite an elegant reason why they worked so well: they form a primitive version of Fourier analysis, a modern technique for function approximation. Thus, in the constantly expanding machinery of epicycles and epicyclets, Ptolemy and Copernicus had gotten their hands on a powerful computational tool, which would in fact have allowed them to approximate orbits of a very large number of shapes, including squares and triangles (Hanson, 1960)!

Despite these geometric acrocrabitcs, Copernicus theory did not fit the available data better than Ptolemy’s. In the second half of the 16th century, renowned imperial astronomer Tycho Brahe produced the most rigorous astronomical observations to date — and found that they even fit Copernicus’ data worse than Ptolemy’s in some places (Gingerich, 1973, 1975).

Kepler:

At the turn of the 17th century Kepler, armed with Tycho Brahe’s unprecedentedly rigorous data, revised Copernicus’ theory and introduced elliptical orbits [6]. He also stopped insisting that the planets follow uniform motions, allowing him to discard the cumbersome epicyclical machinery.

[…]

Spurred on by his observations, Galileo would soon begin his ardent defense of heliocentrism. Despite the innovations of Galileo and Kepler, the path ahead wasn’t straightforward.

Galileo focused his arguments on Copernicus’ system, not Kepler’s. And in doing so he faced not only the problems with fitting positional planet data, which Kepler had solved, but also theoretical objections, to which Kepler was still vulnerable.

Consider the tower argument. This is a simple thought experiment: if you drop an object from a tower, it lands right below where you dropped it. But if the earth were moving, shouldn’t it instead land some distance away from where you dropped it?

You might feel shocked upon reading the argument, in the same way you might feel shocked by your grandpa making bigoted remarks at the Christmas table, or by a friend trying to recruit you to a pyramid scheme. Just writing it, I feel like I’m penning some kind of crackpot, flat-earth polemic. But if the reason is “well obviously it doesn’t fall like that… something something Newton…” then remind yourself of the fact that Isaac Newton had not yet been born. The dominant physical and cosmological theory of the day was still Aristotle’s. If your answer to the tower argument in any way has to invoke Newton, then you likely wouldn’t have been able to answer it in 1632.

Holy shit:

Spurred on by his observations, Galileo would soon begin his ardent defense of heliocentrism. Despite the innovations of Galileo and Kepler, the path ahead wasn’t straightforward.

Galileo focused his arguments on Copernicus’ system, not Kepler’s. And in doing so he faced not only the problems with fitting positional planet data, which Kepler had solved, but also theoretical objections, to which Kepler was still vulnerable.

Consider the tower argument. This is a simple thought experiment: if you drop an object from a tower, it lands right below where you dropped it. But if the earth were moving, shouldn’t it instead land some distance away from where you dropped it?

You might feel shocked upon reading the argument, in the same way you might feel shocked by your grandpa making bigoted remarks at the Christmas table, or by a friend trying to recruit you to a pyramid scheme. Just writing it, I feel like I’m penning some kind of crackpot, flat-earth polemic. But if the reason is “well obviously it doesn’t fall like that… something something Newton…” then remind yourself of the fact that Isaac Newton had not yet been born. The dominant physical and cosmological theory of the day was still Aristotle’s. If your answer to the tower argument in any way has to invoke Newton, then you likely wouldn’t have been able to answer it in 1632.

[…time for thinking…]

Now if at the end of thinking you convinced yourself of yadda yadda straight line physics yadda yadda you were unfortunately mistaken. The tower argument is correct. Objects do drift when falling, due to the earth’s rotation — but at a rate which is imperceptible for most plausible tower heights. This is known as the “Coriolis effect”, and wasn’t properly understood mathematically until the 19th century.

For the Corliolis effect, here’s a good explanation of the physics.

It goes on, but I’ll stop quoting everything Jacob wrote and let you read the post.

# Cuisine and Empire

One of the best EconTalk episodes.

On wheat:

Russ: It’s an amazing thing that someone thought to do that. I mean, I assume that in the beginning people just chewed it, and it wasn’t very good or very appealing.

Guest: I think if they just chewed it–really the grains passed through you. Their cover was a little hard-skinned on the outside. And you can’t get much nutrition from them unless you break them up. And we have speculations about whether or not they were made into popcorn by just simply eating a popped wheat, puffed wheat; whether they were sprouted and made into beer; whether they were ground; whether they were boiled. You have to do one of those things. It’s a really cute debate: Did humans start agriculture in order to have beer because they wanted beer so much? But I think that misunderstands the extent to which people were experimenting. I think long before agriculture–by about 20,000 B.C., humans are experimenting with grains. And I think they did absolutely everything to them. They treated them, they heated them, they ground them, they treated them with lye, they popped them. They probably treated them with acid. They sprouted them. Anything to be able to get access to that nutrition.

Russ: And one other thing I want to mention in passing that runs through the very earliest part of the book is the power of that kind of transformative process. In particular, cooking. And I think modern people tend to think of cooking as it makes food taste better. We have a modest experience with raw foods: we eat sushi; we might have steak tartare; we eat raw vegetables with dip at cocktail parties. But you point out that the really important part of cooking is it saves time in chewing. Can you explain that? Because that’s remarkable.

Guest: Both chewing and digesting. Animals, if you think of the standard picture of a cow, they first of all spend a lot of time wandering around, chewing grass, which is tough. And then they have stomachs and they spend much of the day digesting this food. It takes a huge amount of energy to digest food. So that when you cook, what you are essentially doing is outsourcing digesting–chewing and digesting–into the kitchen. And doing it previously. And that saves a lot of energy for the humans who are lucky enough to eat the cooked food. Of course, the energy has to come from somewhere, and part of it is from the thermal energy of the fire; but part of it is from the energy of the people or animals or later on wind or water or steam that are doing the hard work of grinding.

Burgers and French cuisine: