All Talk

There Is No Such Thing As Unit-Free!

*Diogenes With The Lamp Looking For An Honest Man* (c. 1780) by Johann Tischbein

Percentages have been getting on my nerves since I started economics.

Picture this. An economist is describing their model, which outputs some change in a mysterious metaphysical substance like GDP or utility. ‘We observe a hundred million dollars-worth of GDP growth.’ ‘Utility goes up by a thousand utils.’ Without more context, the statements are meaningless. The second obviously so, but the first isn’t much better. What is a dollar’s worth of stuff? (A 1966 dollar or a 2023 dollar? Who can spend the dollar? Where can they spend it?)

The economist then acts as though this problem can be side-stepped by talking in relative terms instead of absolute terms. Don’t say GDP grows by a hundred million dollars, say that it grows by 0.05%. Don’t mention a thousand-util increase, call it a fifty percent increase in utility.

In econ101, they even demonstrate to you why we use percentages to get rid of units. It’s all just basic arithmetic! Let $u$ denote your unit (dollars, utils, etc.). An increase from $M$ units to $N$ units is given in percentage terms by

$\frac{N u - M u}{M u}\times 100 \% = \frac{N - M}{M}\times 100\% .$

Like magic, the $u$ just disappears!

But $u$ never really disappears. Because magnitudes are never unit-free. There is no analogy between a country that goes from producing a trillionth of a barrel of oil to one barrel of oil, and a country that goes from producing one barrel of oil to a trillion barrels of oil. A fifty percent increase in utility is as meaningless as a thousand-util increase in utility.

Moral: you can’t create knowledge about the world just by rearranging a fraction.

Well, except for Bayes’ law…

Seven Dos and Don’ts of (Economics) Grad School

Illustration from *The House at Pooh Corner* (A. A. Milne, 1928) by E. H. Shepard

At the start of the year, I was fortunate to receive PhD offers from a few good schools. This meant a unique window, between desperate applicant and despairing grad student, in which the bargaining power was mine. Eager professors tried to woo me (never again will I receive so many generous interpretations of the inane and stupid things I say!), along with a press gang of their PhD students.

After a couple meetings with people from any given school, I’d have learned basically everything that was relevant to my decision, and in subsequent meetings I struggled to think of questions to ask. But it felt wrong to turn down a meeting, and I had to figure out something to say.

So, I did the banal thing of asking how to make the most of grad school. I didn’t really expect to hear anything enlightening (I believed Agnes Callard’s argument that non-trivial non-technical advice requires a long-term relationship between the advisor and the advisee). I thought everyone would just tell me to work hard-but-not-too-hard, and if I was smart, I’d do well, and if I wasn’t smart, I wouldn’t do well.

But the advice I got was actually very enlightening. Here are the seven tips that struck me the most. I hope that writing them down here plants them a little deeper in my mind. Each one sounds easy, maybe obvious (if it’s here though, it wasn’t obvious to me), but they are all very hard, and I’m already doing a bad job of sticking to them.

For advice on how to get into econ grad school, the only two posts that I found useful (but I found them incredibly useful) were Rachel Meager’s and Ben Davies’. For an article of unconventional PhD advice that I really like, check out Ariel Rubinstein’s Experienced Advice for “Lost” Graduate Students
in Economics (one of the few readers of the blog was sent this article, and he didn’t like it ;), ah well, I think it’s great). If economics grad school is stressful, and you’d like to spend twenty minutes reading about how it’s a hundred times more stressful in the humanities, read this post by Bret Devereaux.

Anyway, here are seven dos and don’ts of econ grad school. To be clear, I am just trying to synthesise the suggestions I received. I personally have no clue what I’m talking about.

1. Read, read, read, read, read

Read a lot. Read broadly. Read consistently. Read economics. Read outside of economics. Read, read, read!

2. Don’t let the great be the enemy of the good

When you have a research idea, pursue it. Don’t obsess over causal identification and sampling errors. Don’t jump around between various half-baked ideas, committing to nothing. Focus on what you have, and see it through.

We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil.
Donald Knuth

3. Spend time on ideas, not busy work

The most boring work is the most pleasant. When I’m writing code, proving lemmas, cleaning data, solving problem sets, I get immediate, positive feedback. The setbacks are always surmountable, and I feel smart when I surmount them. When I’m doing something interesting, I feel slow and stupid. I go weeks without progress, and when I do make a breakthrough, I feel even more stupid for not having made it sooner. In the short-run, I’m always tempted to allocate more time to the boring busy work, and less to reading hard papers and understanding concepts.

But great economists are great at thinking about complicated things. I have no idea how quickly Daron Acemoglu can make a heatmap with Python, or how well-formatted Amartya Sen’s .bib file is. You get good at what you practice. You want to be good at doing interesting things.

4. Courses matter, grades don’t

Everybody I spoke to told me that coursework was really important, and that you should put a lot of effort into really understanding the material. The first couple years of grad school are your last shot at mastering the fundamentals, so make the most of it. One (very) famous professor told me not to do any research at all in first year, and just think about courses. Now, most people recommended an interior solution to the research-coursework trade-off, but they almost always weighted coursework more heavily in the first year.

That doesn’t mean you should care about your grades. They (finally) do not matter. Focus on learning, not on scoring points in exams (see no. 3 above).

5. Figure out how you generate ideas

In economics, unlike other fields, research is divorced from idea-generation. In maths, you come up with your next idea by answering the question that puzzled you the most when you tried to prove your last idea. And the success of the sciences is in large part because of this tight inspiration-research feedback loop.

In economics, you can’t always depend on the day-to-day work to generate new ideas for papers. The best ideas often come from far outside the immediate frontiers of what is known. Every economist has their own approach to seeking them out. Some talk to people outside the university. Some talk to people in other parts of the university. Some read economics papers. Some read history. Some read psychology. Some read the news. Some immerse themselves in a particular economic environment for a long time. Figure out what works for you.

“But it isn’t Easy,” said Pooh to himself … “Because Poetry and Hums
aren’t things which you get, they’re things which get you. And
all you can do is to go where they can find you.”
A.A. Milne, The House at Pooh Corner

6. Explore through research

It’s typical for an economist to enter grad school with no idea of what they want to specialise in. In my case at least: truly, embarrassingly, no idea. I want to try a bit of everything, before Isettle down. But I’m being paid to do research. How do I get the breadth I feel I need, while producing the work that’s expected of me? It would be nice to delay research until I’ve taken every course in the department (and a good helping outside), but the PhD time-horizon is finite. Solution: explore through research! Which leads to…

7. Co-author with your classmates!

You can learn a lot from your classmates, so co-author with them. Make sure to discuss work expectations explicitly. You don’t want the tension that comes from asymmetric effort. But most people describe co-authoring with their classmates, or even just brainstorming with them, as the best part of doing a PhD. Savour it.

A Weird Bayesian Argument About Animal Sentience

*Fish (Still Life)* (1864) by Edouard Manet

I tried not to give too much weight to the thing about the fish, but after a while it started to get me down anyway.
Elif Batuman, The Idiot

Now that I have established my seriousness with an insipid book review post, I can let my hair down and go full eaforum-core. I apologise for keeping this post’s word-count below five figures, and for being too lazy to respond to every possible counter-argument in footnotes. But hopefully this won’t compromise the nausea. Enjoy!

I have been vegetarian for roughly eight years. For two of those years, I was vegan, and I’m still pretty sure that vegans are in the right. I think killing animals is probably always wrong, and also that modern animal agriculture is very bad for all the usual gut-wrenching reasons.

The argument of this blog post challenged my righteous confidence in vegetarianism. It came to me last year (I think after listening to the box argument in Ajeya Cotra’s 80k interview), and I have not been able to shake it off. Of course, I don’t actually believe it. I’m not crazy!

It is very important to vegetarianism that we think animals are sentient. But it’s not trivially obvious that they are. Humans are unlike any other animal we know to have existed. We are very, very smart, we have language, we have abstract ideas. All of these are necessary conditions for knowing that we’re conscious. Are they also necessary conditions for being conscious? If they are, vegetarianism might be just a waste of time. And while I doubt they are, I don’t know for certain that they aren’t. There are smart, well-informed people who think that only humans have sentience.

Let’s call the possibility that Only Humans are conscious $OH$ . We’ll use $\mathbb{P}(OH)$ to denote the probability this theory is true. Since we can’t say for sure that $OH$ is false, $\mathbb{P}(OH)>0$ .

What is the relevant alternative possibility to $OH$ ? I don’t really care about the theory that only humans and chimpanzees are sentient, or that only humans and great apes are sentient, or that only humans and great apes and dolphins and parrots are sentient, etc. Nobody I know wants to eat chimpanzees, great apes, dolphins, and parrots. Serious vegetarianism rests on the assumption that consciousness goes down at least to pigs and cows. My own vegetarianism goes all the way to fish and crustaceans. (I personally have always believed sentience bottoms out somewhere around insects.)

For my vegetarianism to make sense, it must be the case that basically All Vertebrates are conscious. We’ll call this possibility $AV$ . To decide between $OH$ and $AV$ , I have access to exactly one datum. Me. A priori, ‘I’ could be any conscious thing. I could disprove $OH$ by just being something other than a human. Let’s use $IH$ to denote the event that I’m Human.

What is the probability of $IH$ ? If $OH$ is true, then $IH$ must be true, since the only I’s are humans. That is, $\mathbb{P}(IH \mid OH)=1$ . If $AV$ is true, then $IH$ may or may not be true. By the principle of indifference, I will assign equal weight, a priori, to my being any conscious thing. So, the probability $\mathbb{P}(IH \mid AV)$ is just equal to $H/V$, where $H$ is the total number of humans and $V$ is the total number of vertebrates.

Assume for convenience that after a careful study of the evidence, we’ve figured out that the only two viable theories are $OH$ and $AV$ . For example, suppose we have narrowed down the natural substrate of consciousness to either language (in which case $OH$ ), or that the vertebrate brainstem (in which case $AV$ ). This implies that $\mathbb{P}(OH)=1-\mathbb{P}(AV)$ .

It turns out that $IH$ is true. So, we can use Bayes’ theorem to calculate the posterior probability of $AV$ , given my humanity.

$\mathbb{P}(AV\mid IH) =\frac{\mathbb{P}(IH \mid AV) \mathbb{P}(AV)}{\mathbb{P}(IH \mid AV)\mathbb{P}(AV) + \mathbb{P}(IH \mid OH)\mathbb{P}(OH)}$

$=\frac{\mathbb{P}(AV)}{\mathbb{P}(AV)+ \frac{V}{H}(1-\mathbb{P}(AV) )}$ .

Remember that the number $\mathbb{P}(AV\mid IH)$ represents the confidence a human should have in vegetarianism being a moral duty. We have re-written $\mathbb{P}(AV\mid IH)$ in terms of two variables. One is $\mathbb{P}(AV)$ . This represents the strength of the theory that all vertebrates are conscious. A higher value of $\mathbb{P}(AV)$ implies more confidence in vegetarianism.

The second term is $V/H$ , the number of vertebrates per human. Determining the value of $V/H$ is a purely empirical exercise. And while I doubt we’ll ever have even a rough approximation of $V/H$ , we do know one thing about it. It is very big.

To get a rough idea of how big $V/H$ is, we’ll ignore all vertebrates other than fish. This will give a lower bound on $V/H$ . Well, there are plenty of fish in the sea. Economists Alexis Carlier and Nicholas Treich put the number at somewhere between 125.3 trillion and 354 trillion. Let’s go with the lesser.

Fish have been around a long time, about 530 million years. Let’s assume that fish numbers have stayed roughly constant since the big diversification of fish in the Devonian period (aka THE AGE OF FISHES!) 419 million years ago. Based on the estimate of ecologist Edward Houde, the life-expectancy of a typical (late) juvenile fish is less than a year. Let’s be conservative and set fish life expectancy to a year (higher life expectancy corresponds to a lower estimated number of fish). Then we obtain an estimate of about 52.5 sextillion total fish since the Devonian. We’ll use this as our lower bound on $V$ .

Given data scientist Max Roser’s estimate of 117 billion humans to have ever lived, we arrive at a fishy lower bound on $V/H$ equal to roughly 450 billion. This means that if I want my level of confidence in vegetarianism to be at least 1%, then I need to be over 99.9999999% sure of $AV$ .

The take-away is a profound asymmetry between the two theories $AV$ and $OH$ . Accepting only the platitudes that there are way more vertebrates than humans, and that I am human, the burden of proof is overwhelmingly on those who want to show that all vertebrates are conscious.

I don’t believe the argument. I’m going to give a cursory summary of some good counter-arguments.

We shouldn’t be counting conscious beings, we should be counting instances of consciousness. Suppose ‘I’ refers to an instance of consciousness, rather than the temporally extended thing that is conscious. Then $V/H$ should count the number of vertebrate instances of consciousness over the number of human instances of consciousness. If humans are conscious much more of the time, then it is possible that $V/H$ is quite small.

For example, suppose that the annual number of instances that of consciousness is equal to a function $C(N)$ of their neuron-count $N$ , multiplied by their life-span $L$ . I’m going to set human life-expectancy at 30 years (this is meant to be a rough conservative estimate based on Our World In Data).

Our calculations produce 52.5 sextillion fish-years, and 3.51 trillion human-years. Using philosopher Will Macaskill’s neuron count numbers (80 billion for humans, 20 million for fish), we get

$\frac{V}{H} = \frac{C(20 \text{ million})}{C(80 \text{ billion})}\times 14.957 \text{ billion}$

The consciousness function $C$ does not need to be all that convex for $V/H$ to become quite small. For instance, if $C(N)=N^{2}$ , we get $V/H \approx 935$ . (However, mammals and birds have many more neurons than fish, so the number could jump up if we were to incorporate these into our count. A springbok has 2.72 billion neurons, only a fortieth that of humans.)
*Yawn* I’m a pescatarian, I only include tetrapods in $V$ . We focused on fish because they make up the overwhelming majority of vertebrates. We could re-run the argument with land vertebrates or mammals in place of vertebrates. I doubt the numbers would be great for opponents of meat-eating, but they’d be orders of magnitude better than when we included fish.
It might be reasonable to assign a very, very high probability to $AV$ . Biting the bullet is not too hard. Maybe we do have enough reason to believe $\mathbb{P}(AV)$ is really, really high, so $\mathbb{P}(AV\mid IH)$ is big even when $V/H$ is too.
We have to consider not just the probability that meat-eating is okay, but also the consequences of our being mistaken. If I turn out to be a sucker for going vegetarian, then I’ve missed out a bit, but I didn’t really do anything wrong. It might be better to play it safe.

Book Review: China’s New Red Guards by Jude D. Blanchette

Screenshot from http://www.maoflag.cc/ (14/5/2023)

“I didn’t see many people starve [during the Great Leap Forward],” says maoflag.net co-founder Li Dingkai, one of the neo-Maoist reactionaries in Jude D. Blanchette’s 2019 monograph China’s New Red Guards, “just a few old people and some children.” The short book (161 pages) is an informative introduction to the intellectual backlash against reform-and-opening. I also highly recommend Blanchette’s interviews on the Sinica podcast.

China’s New Red Guards is a revisionist history of a famous mistake. In 1999, presidential candidate George W. Bush declared, “Our greatest export to the world has been, is, and always will be the incredible freedom we understand in America … If the Internet were to take hold in China, freedom’s genie will be out of the bottle.”

In his notorious 2000 ‘Jell-O’ speech, Bush’s predecessor Bill Clinton made the same prediction, “By joining the W.T.O., China is … agreeing to import one of democracy’s most cherished values, economic freedom. … The genie of freedom will not go back into the bottle.”

The explanations I have heard for why Bush and Clinton were wrong take one of two forms: 1. the bottle was empty, genies don’t exist, there is no appetite for freedom in China; 2. the CCP successfully shoved the genie back in the bottle. Blanchette makes us wonder if the presidents were essentially right. Freedom’s genie is loose in China. But it’s dressed in a Mao-suit.

2001 was a bad year for China’s old-school leftists. In July, President Jiang Zemin announced the “Three Represents”, a change to the Communist Party constitution which allowed capitalists into the Party. In December, China became a member of the World Trade Organization.

These compromises touched a nerve. Jaded party-members attacked the entire post-Mao reform agenda in magazines like Pursuit of Truth and Midstream. Jiang Zemin cracked down, cancelling the magazines. “Had Jiang taken this action just a few years earlier,” Blanchette remarks, “it’s quite likely that the journal’s brand of orthodox leftism could have withered … But in the early 2000s, there were new options.” In 2003, Pursuit of Truth was reborn online as maoflag.net. It shared the web with sites like Peasant-Worker World and Patriots’ Alliance.

The neo-Maoists influence took off as China’s relationship with the USA soured. But they were more than glorified bots. The movement sent costly signals of ideological integrity. In 2006, the websites Land of Utopia, Workers Online and Left Bank were shut down for campaigning on behalf of Wang Bingyu, a worker who had murdered an exploitative boss. Land of Utopia also joined the brutally suppressed unionisation at Shenzhen Jasic Technology factory. One of the unionizers described his awakening reading “Utopia, Maoflag, Red Song Union, Red Flag, etc.”

The movement is emancipationist in form. A valuable option (living in a crime-free, incorrupt, egalitarian, unified society) is inhibited by a small elite (think-tankers, intellectuals, industrialists, turncoat communists). The presidents failed to realise that the most obvious instrument to restore this option, at least for children of the ‘60’s, is not liberal democracy but a renascent one-party nation-state. The rhetorical world of the Cultural Revolution was more able to grab attention on the Chinese web than the Western liberal dream.

What the book lacks is a sense of scale. I am left unsure of how much ordinary people cared about the scandals, speeches and petitions which make up the book’s narrative. I also don’t know whether there were alternative populist ideologies in the early Chinese internet. Blanchette is clear that the Neo-Maoists’ authoritarian communism gave them an advantage in the censors’ eye, unavailable to more heterodox emancipationist projects. But what is the best explanation for the impotence of other radical anti-elite projects on the internet? Lack of interest or suppression? The near-impossibility of understanding Chinese popular opinion make these questions difficult, but some comparative analysis would help.