Two post-election gripes

Donald Trump has been elected the next President of the United States, so I’ve been channeling my disappointment into irritation that people are responding negatively in ways that I don’t quite approve of. Two complaints follow.

1. The Electoral College

The calls to have electoral college delegates select Clinton because she won the popular vote set off a lot of alarm bells for me.

First, if you are advocating for this but wouldn’t make the same appeal in the event that Clinton won the EC while losing the popular vote, then your position is not principled; it’s just some thin excuse to win despite the clear rules of our democratic process. We had a fair election under conditions that everyone knew applied from the beginning. If your policy is to deny the outcome in the event that you don’t like it, then I honestly wish you would just come out and say so.

If you do believe that the delegates should choose the popular vote winner in any case, then the main point I would make is that the election isn’t a poll of public opinion happening in a vacuum. Both campaigns plan stump speeches, allocate advertising money, and craft their messages based on the electoral college. The campaigns do their best to win based on the rules, and the distribution of votes would not be the same if they valued each vote equally. We can’t just treat the ballots on November 8th as a survey of the popular will after each side had the chance to give their broadest pitches. They didn’t have the chance because they were funneling most of their resources toward winning according to the rules. For that matter, we don’t know how many dissenting voters just stayed home in states that were obviously in the bag for one party.

Whether the electoral college SHOULD be the system we use is another question. If I were writing the Constitution today, without considering the political reality of 1787 America, then I would do something else. But honestly, the electoral college doesn’t offend me that much.

The founders were terrified of a tyranny of the majority. Smaller states get more delegates in part so that rural citizens, who have less economic influence and would otherwise have less political power, receive a voice on par with those in metropolitan centers. To that extent, the EC did exactly the job it’s supposed to do this year.

The delegates were also supposed to be selected by state governments so that the candidates for the highest office in the country would be vetted by people more politically active and knowledgeable than average citizens — a provision that has been, perhaps unfortunately, done away with for all practical purposes and will never come back. If I’m not mistaken, the fact that state governments select delegates was also intended to help keep the power of the federal government in check, because it would be in the states’ interests not to elect an autocrat who would seize power from more local levels of government. Obviously, we’ve moved away from this federalist model in many ways.

(One of the reasons I’m such a stickler about federalism is the same reason so many people are afraid of Republicans controlling the presidency, both houses of Congress, and soon the Supreme Court. If you insist that people shouldn’t decide matters on the most local level of government where it’s reasonable to do so, then sooner or later you’ll be represented at the more global levels by people who are antithetical to your values. But neither party seems to respect this very much when it’s their turn to take power, so I’m not sure where to turn for a defense of federalism in practice.)

The point of all this is, I’m not so sure the EC is outrageous. If anything, it’s probably the deviations from its original vision that allowed Trump to become President-elect as much as the College itself. Political elites would never have put him in office; while I’m not sure that selection by elites would produce a better average President, I do suspect that it would produce a higher competency floor than popular election.

The primary remaining function of the Electoral College is to give disproportionate influence to people who are basically not represented in the economic and cultural powerhouses of the country (prestigious newspapers like the New York Times and the Washington Post, universities like Harvard and Stanford, economic centers like New York City and Silicon Valley, etc.). If there’s one thing that I think can’t be contested about this election, it’s that the people who speak for op-ed writers and established politicians are not the people who speak for the ~50% of Americans living in the majority of the country’s geographic expanse. While our system doesn’t do enough to give a voice to others, such as the large population of urban poor, this attempt to level the playing field is not entirely without merit.

Finally, the “will of the people” is not such an easy thing to clearly identify. Should we really assume that third party voters are utterly indifferent between the major candidates? Maybe we should have a runoff election? Problems with constructing “fair” election rules multiply like the heads of Hydra, and at the end of the day all we can really do is pick a system and stick by it.

2. The American Physical Society

The American Physical Society issued a press release congratulating Trump on his election, which included the text:

“APS urges President-elect Trump to incorporate the necessary policies that will enable our great nation to reclaim its scientific leadership, which it has lost during the past decade. APS believes that such policies will help the Trump administration achieve its goal captured by its slogan, ‘Make America Great Again.’

According to the Information Technology and Innovation Foundation, the United States ranks just 10th overall in innovation, ‘largely because its innovation-supporting policies, such as funding scientific research, are lower than those of other countries.'”

Predictably, there was outrage and the APS retracted the statement. Nothing was issued in its place except an apology.

Is the American Physical Society supposed to pretend like Trump isn’t going to be the President? Should it also pretend that Republicans aren’t going to control both houses of Congress?

Science funding in the years to come is not going to be dirtied by Trump’s signature to the federal budget; it will be payed for by taxes as it always has been. Nor is it virtuous to shut out lines of communication with people on whom the continued existence of scientific progress depends (whether we like that or not).

Appealing to common interests does not denote an endorsement of Trump’s statements about climate change or vaccines. The mission of the Trump administration need not be antithetical to the mission of the scientific community down to every last detail.

The APS is nominally a non-partisan organization. That doesn’t mean it should look the other way about things that harm science, scientists, or the broader society. It does mean that it should put political grandstanding aside when that does not advance its advocacy.

I hope the APS issues statements about Trump’s science advisor, his public comments about scientific issues, his proposals to immigration reform as they might significantly impact researchers, and so on. I don’t want them to pander, because then they couldn’t do any good! At the same time, in order to fill the important role of positive advocacy (rather than condemnations only), they have to be committed to finding some common goals with the people who control 75% of science funding. (Note that “control 75% of science funding” ~ “control 75% of science.” We may not be happy about it, but I can guarantee you I wouldn’t show up for work if I didn’t get payed and couldn’t buy equipment, and I bet my colleagues wouldn’t, either.)

The common thread

What riles me up about these two cases is seeing people whom I would like to be allied with giving up on basic principles in favor of denial and anger. To suggest changing the rules of a fair election after the fact is horrifying, as many on the left observed when Trump was the one talking about it. And to silence ourselves in order to avoid addressing Republicans will only allow them to achieve their most wrong-headed goals without compromise. We can neither bypass nor ignore the system. There is no better world; there’s only a better version of the one we’ve got.

How big can it be?

Eliezer Yudkowsky presents a thought experiment: is it better for 3^^^3 people to get a dust speck in their eye — a nearly undetectable annoyance for each of them — or is it better that one person be tortured for fifty years? Within a utilitarian framework, this is designed to highlight the question of whether utility aggregates forever. (If you reject a more fundamental premise, for instance that it’s meaningful to compare the suffering of different people, then this isn’t the most useful thought experiment to dwell on.) In other words, would an enormous number of occurrences of an almost infinitesimally bad thing be far worse than one occurrence of the worst thing that can occur on the scale of a single human life?

Someone* wanted to mock rationalists and they decided to pick this thought experiment as a target. The blogger “rubegoldbergsaciddreams” presents an illuminating critique of their misrepresentation. I’ve cut out a lot of the content to focus just on the parts pertaining to how big 3^^^3 is.

Paraphrasing the dust speck thought experiment as “torturing one person for five years is indisputably, literally, MATHEMATICALLY better than letting a billion people get a dust speck in their eyes” is misrepresenting the original claim on a literally unthinkable level. 3^^^3 is so much larger than a billion that the words “scope insensitivity” fail to describe the depth of the error being made here. If you were to scale the original question to “a billion people having dust specks in their eyes”, the amount of time the individual would be tortured for is literally undetectable. It’s less than amount of time it takes light to travel the Planck length. It’s so much less than the Planck time that I actually cannot give any analogy sufficient to explain it. If it were not physically impossible to construct a machine capable of torturing someone for such a period of time, they would never feel it. Their neurons would not be able to fire, their body would not be able to react to the stimuli. The actual comparison would be “One person experiencing literally no adverse effects is better than a billion people getting a dust speck in their eyes”, which isn’t actually fair because WE LIVE IN A WORLD WHERE TIME AND SPACE ARE DISCRETE AND I HAVE TO ROUND EPSILON DOWN TO ZERO.The volume of the known universe, measured in planck lengths cubed (8.711375 * 10^187), is less than 3^^^3.

If you recorded every thing ever spoken by a human to an audio file (estimated to take up about 42 Zettabytes) and then flipped 336000000000000000000000 coins, one for each bit of data, the probability that your coin flips would perfectly correspond to the data is greater than 1/3^^^3.

Actually, I can do better than that. There are ~ 10^82 atoms in the universe. If you assigned each of those atoms a random location anywhere in the universe (8.711375 * 10^187), the probability that each of those atoms ends up exactly where it started is greater than 1/3^^^3.If you see a number like 3^^^3, you should conceptualize it as being about the same size as infinity. You’ll still be wrong about it, you’ll still think of it as much, much smaller than it actually is, but you might at least avoid making the kind of mistake that [blogger] did here.

The reason such a huge number was used in this case was because it was needed to get the point across: the counterfactual to EY’s claim (that 3^^^3 dust specks in eyes is better than 1 person being tortured for 50 years) implies that there’s a discontinuity in utility aggregation, and if we really believe that such a thing exists, than it’s very important to discuss where that line should be drawn and why. EY believes that no such discontinuity exists, and that’s a perfectly defendable position: others disagree, and there are merits to their beliefs as well.

Okay, so 3^^^3 is bigger than some puny number like how many ways there are to rearrange every atom in the visible universe, but can’t we do better?

Before I launch into calculations, let’s give a primer on the up arrow notation. We’ll want to start with more familiar arithmetic operators. Multiplication is:

a*b = a+a+\cdots+a (b appearances of a)

Exponentiation is:

a^b = a*a*\cdots*a (b appearances of a)

Double-arrow operation (“tetration”) is:

a^^b = a^a^\cdots^a (b appearances of a in a “power tower”)

Triple-arrow operation (“pentation”) is:

a^^^b = a^^a^^\cdots^^a (b appearances of a)

Hopefully the generalization to more arrows is straightforward, but we won’t need more than three arrows in this post. One important point is that although addition and multiplication are commutative, meaning the right-hand sides of their equations above can be executed in any order, exponentiation and subsequent operations are not. For example,

3^3^3 = 3^(3^3) = 3^27 = 7,625,597,484,987
\neq (3^3)^3 = 27^3 = 19,683

By convention, we evaluate exponents and subsequent operators from right to left if parentheses don’t explicitly call for another order. Also, numbers like 3^3^3 are more commonly written as 3^{3^{3}}, but since this gets unwieldy with more than one superscript, I’m going to stick to the caret notation.

It’s harder for me to think about triple-arrow notation than double-arrow notation, so let’s start by reducing 3^^^3. By definition, 3^^^3 = 3^^(3^^3), so this is a tower of exponentiated 3’s that is 3^^3 = 3^3^3 = 7,625,597,484,987 digits high.

So that’s our target: 3^^7,625,597,484,987.

There are about 10^80 electrons, protons, and neutrons in the observable universe, and about a billion photons (mostly in the cosmic microwave background) for each of those. Let’s shuffle all of them, for about 10^89 particles total. The smallest physically meaningful region is thought to be a Planck volume; there are about 10^185 of these volumes in the visible universe. So the total number of ways to shuffle all these particles among all these positions is

(10^185)^(10^89) = 10^(185 * 10^89) ~ 10^91 < 10^10^2.

 Compare this with a base-3 double-arrow number, 3^^4 = 10^10^12. Indeed, we’re not doing so well.

What if we re-shuffle everything at every moment, in increments of the Planck time, since the Big Bang up to the present? There have been about 10^61 Planck times, so the total number of possible outcomes is

((10^185)^(10^89))^(10^61) = 10^10^(2+89+61)
= 10^10^152 ~ 10^10^10^2.

We found a number bigger than 3^^4! But 3^^5 is approximately 10^10^10^12, already unimaginably larger than 10^10^152.

So far, we’ve been proceeding as follows: imagine a bunch of conditions with many independent outcomes, compound them, and look at the total number of outcomes. In that spirit, suppose we have a N conditions each of which has the same huge number of outcomes A — let’s imagine A = 3^^4 = 10^10^12, for instance. When we compound them, we get a total number of outcomes equal to (((\cdotsA)^A)^A)\cdots^A, with N appearances of A. Pulling the exponents down, we see that this is A^(A^(N-1)).

Now consider one final scenario. Suppose there are A = 3^^4 ~ 10^10^12 different combinations of fundamental particle types that might be present at any point in space. (This is far, far larger than we have any reason to think.) Further, suppose a universe is 10^10^12 Planck volumes and has existed for 10^10^12 Planck times (again, both far larger than in our universe). If we randomly pick a combination of particles to be present at every point and at every time, and repeat this for 10^10^12 universes, then N=4 because we have conditions over particle types, positions, times, and universes. The total number of possible evolutions of all these universes is then

(3^3^3^3)^((3^3^3^3)^3) ~ 10^10^10^10^12
~ 3^^6.

If I had managed to compound this process over a preposterous number of conditions — not just particle types, positions, times, and universes, but over 10^10^12 different things — then the result would have been the same up to a rounding error — namely about 10^10^10^10^12 ~ 3^^6.

Stated in terms of probabilities: if you populated every point in space with a random sample of particles drawn from an unimaginably large collection of options, in each of an unimaginably large number of universes, independently at every moment, then the chance that every one of them retraced exactly the history of our universe (with its apparently smooth trajectories of particles and simple laws of physics that don’t at all suggest “every point in space is occupied by something totally random at each moment independently) would be unfathomably more favorable than winning a bet at odds of 1:(3^^^3), even if our universe were unimaginably bigger and older than it actually is.

Let’s revisit the recommendation of rubegoldbergsaciddreams: “If you see a number like 3^^^3, you should conceptualize it as being about the same size as infinity. You’ll still be wrong about it, you’ll still think of it as much, much smaller than it actually is, but you might at least avoid making the kind of mistake that [blogger] did here.”

I tried to follow this advice; I really did. I took a number, 10^10^12, that is — let’s face it — about the same size as infinity. I rose it to a power of itself, then rose the result to 10^10^12 again, and repeated 10^10^12 times just for good measure. Even this near-infinite compounding of near-infinities doesn’t come close to reaching 3^^^3.

At this point, I’m out of ideas; I can’t describe a scenario in words, even a completely preposterous one, that gives me a number significantly bigger than 3^^6. And 3^^7,625,597,484,987 is so sickeningly larger than 3^^6 that I don’t know what to make of it. I knew it would be big, but I’m still flabbergasted.

*I don’t know anything about the blogger who made the original critique of Yudkowsky’s thought experiment, so I’ll assume they don’t want to be highlighted negatively by a complete stranger who has not even bothered to read their relevant post. Anyone who cares to find the original author can always do so.

Against verbal substitution

When I was in middle and high school, my friends and I used the word “gay” a lot. (Actually, I tended to use cleaner language than most of my peers and I don’t recall saying it myself. But it’s a near-certainty that I did on occasion.) Playing Garou, Mark of the Wolves: “that combo is so gay.” Complaining about homework: “This assignment is gay.” The considered opinion about a friend having to stay in on a school night: “That’s gay.”

I’m glad that we grew out of this phase. It’s just so boring. Of course it is, because it’s adolescent, and adolescent sensibilities are unsophisticated. But there was something irreplaceable about our use of that word. It’s not an overstatement to say that the character of my childhood would have been different without it.

What I could never quite explain to those who objected to this was that “gay” meant something unique. You cannot eliminate that word without forbidding someone from expressing a certain sentiment.

People have suggested saying “lame” or “stupid” instead, but those do not mean the same thing. My facility with language isn’t sufficient to explain the nuances here, but I believe the difference between “gay” and “lame” is that the latter is usually out of touch, while the former is closer to “unfair”. Dad jokes are lame, but not gay. (Example dad joke found by quick googling: “On all of my medical forms growing up my dad wrote ‘red’ for my blood type. To this day, no one knows my actual blood type.”) A 10:00 PM park curfew is gay, but not lame. There are cases where either could apply, but like almost any pair of words, they do not have full overlap. The important point is that replacing a word necessarily means forbidding the meaning that someone originally intended to express.

If this isn’t convincing, consider that people also object to “lame” on similar grounds. If we replace “gay” by “lame,” and “lame” by “stupid,” and “stupid” by “silly” — all transcriptions that people have written impassioned articles to advocate for — then can you still really believe that we’re saying the same thing in the end?

It’s a perfectly respectable position that the costs of people using “gay” in a derogatory sense outweigh the benefit of being able to express that particular adolescent dismissal. But we ought to be clear on what we’re doing, and that is not just language policing. It’s meaning policing, because language is how we convey meaning. And the the cost-benefit case for disallowing people to express certain meanings should require a very high burden of proof.

(That said, I wholly endorse “tabooing” words so that people have to clarify their meaning during a discussion. One of my book groups has tabooed “interesting” because that word was allowing us to be too non-specific about what engages us. I’ve found the same trick helpful for discussions about religion and morality, among other things. This should not be confused with a claim that no one should ever say “interesting,” or “God,” or “right.”)

I’ll give one example where this kind of language seems particularly indispensable. When discussing physics education research with Starburst, he proposed that social factors are too neglected by some pedagogy theory. His example pertains to the “clicker” fad from around the time we started college. These are devices that allow you to register multiple choice answers during a lecture. The professor might put up a slide, for example, that says “The acceleration of a freely falling body: (a) increases with mass, (b) decreases with mass, (c) is independent of mass.” You click a button on a remote for (a), (b), or (c), and the distribution of student responses updates on the projector in real time. This is supposed to keep students actively engaged and tick some other ticky boxes that teaching research has found ought to be ticked. But in both our experiences, it doesn’t work because clicking those buttons…well, it’s just so lame. You can dress that up in more mature language, but doing so will obscure the experience of the 17- and 18-year-old students in those classes, which could have significant consequences.

[Starburst does not necessarily endorse any of this post, including my interpretation of this conversation from probably three years ago.]

So do we say “gay” in a derogatory manner or not? Personally, I haven’t had the slightest temptation to do so for many years. It’s not very useful to me because I don’t want to express what it means, and that’s because I don’t have the unserious, cynical disposition of a teenage boy. But if someone does feel compelled to say it, my recommendation is that we help them understand all of its meanings first. They should know that it can be hurtful. They should know that it is rarely beneficial to express what it means. They should know how to use more specific words when they have something more specific to say. They should know these things just like they should know them about “fuck.” Then if they decide that it’s what they mean to say and they feel the need to say it, we should hear them out in the language where they can most naturally express their perspective.

Getting the most out of your tannins

The crafting system in Elder Scrolls Online uses an upgrade system where you can apply “tannins” (or stitchings, depending on the crafting skill) to your items for a chance to improve them. The more tannins you try to use in a given attempt, the higher your success probability.

Because it was a lot more fun than actually playing Elder Scrolls Online, I worked out the optimal tannin-applying strategy for different models of marginal upgrade utility. The details are written up here. Continue reading

We are all single-issue voters

One of the things I love about social choice theory is the radical perspective on politics afforded when you regard democracy not as a moral duty or pragmatic arrangement, but as a map from a set of votes to a set of winners. We can then ask, what properties might we like this map to have, and what additional constraints are imposed on the map by those properties? If the map cannot simultaneously have every property we would like to impose, which should we regard as the most important to preserve? Is some map preferable in a special case than the one we prefer for the general case? All the psychology and morality are taken out, but the questions still feel so human. Continue reading

A score or more scores for…er…video games

In this post, I review the following games:

Child of Light – 2/5
Valiant Hearts – 1/5
LIMBO – 3/5
Gone Home – 1/5
Super Puzzle Platformer Deluxe – 4/5
Depression Quest – 2/5
Gravitation – 3/5
Passage – 3/5
Krypteia – 3/5
The Banner Saga – 1/5
To the Moon – 1/5
Minecraft – 5/5
Patterns – 1/5
Long Live the Queen – 1/5
The Binding of Isaac – 3/5
Gunpoint – 4/5
Assassin’s Creed – 1/5
Papers, Please – 2/5
400 Years – 4/5
Dys4ia – 1/5
Nothing to Hide – 1/5
Machinarium – 3/5
Heroes of Sokoban – 4/5
Braid – 5/5
Starseed Pilgrim – 3/5 Continue reading

Book review: Enough Magic in the World [2/5]

[Note: I like to write reviews as a way of unpacking how I respond to art, but I don’t presume to have any aesthetic authority. Since this book was written by a personal friend who holds my opinion in high regard, it seems worth reiterating that I’m doing nothing different here. Anyone looking for considered guidance to editing is much better off consulting an editor.]


A few months ago, I attended an “open studios” event in my community, where local artists open their homes or work spaces to the public. There was a little bit of everything you’d expect, and a few things you wouldn’t. The artists were all happy to talk about their work or more casual topics, enthusiasm about local art was everywhere, and I saw parts of my city that I never bothered going to before. It was a lot of fun.

The thing that most stood out to me, though, was how unmoved I was by the majority of the work. My sense of artistic quality is calibrated primarily by museums, so what I’m used to judging has been refined and vetted and often valued at millions of dollars. While there was art on display for Open Studios that I enjoyed, none of it impacted me as much as my favorite piece at any famous museum, and most pieces hardly made an impression on me at all. It’s easy to forget how extraordinarily good museum pieces are when one only views pieces in museums.

This was a bit how I felt reading Enough Magic in the World, a coming-of-age novel about a young woman named Alice who graduates from college and subsequently discovers that she has untapped magical abilities. She is enrolled in an academic institute for magic, a bit behind many of her peers but able to catch up after a while. Through some fault of her own and a great deal of random happenstance, she and her friends become entangled in critically important political machinations. To say the least, this seems unlikely. To say the most, I will use Bayes’ theorem in the next section.

There were some things in the book that I liked, even if they weren’t represented with the density that I’ve come to expect from the novels that I read. For example, I love this paragraph:

Sida considered this for a few seconds, tilting her head to the side so her hair fell onto her thin shoulder. She was dressed almost as simply as I was, yet somehow better, as if she held jeans and t-shirts in high regard and felt everyone else should do the same.

Even though everything in this description is nominally pretty ordinary, there’s a touch of perception that reveals something unique and intimate. That touch is superficially nonsensical, but immediately opens up into an impression that we know exactly what is meant. Because it is slightly bizarre, it resists any familiar pattern of cliché, lending itself credibility.

I’m honestly not sure whether I’ve ever written a sentence of prose that I like as much as the second one above. If a book consisted entirely of paragraphs like that, then it would have a good shot of being a great novel. I would hope to see EMitW move toward a denser population of passages like this as it evolves. Continue reading

Book review: The Book of Imaginary Beings [4/5]

The Book of Imaginary Beings is a medieval-style bestiary written in a self-consciously inconsistent style, encyclopedic at times and humorous at others. Some entries evidently report the facts about their subjects, while some cast explicit doubt about not only their own veracity but even about the possibility that anyone could have believed in such creatures. This initially seemed like strange territory for Jorge Luis Borges, if anything can qualify for that description, but by the end that impression had vanished: it’s imaginative, far-reaching, observant of the human psyche, and serious about its own absurdity, consistent with Borges’ vision that I’d become familiar with elsewhere. However, one gets the feeling that unlike his more challenging work, he wrote this book simply for the fun and freedom of it. Continue reading

Isn’t it time?

[Content note: one-year retrospective on a breakup. If you are any of the people who broke up with me a year ago, you’re still welcome to read this as long as you know what you’re getting into. I also discuss facts about my relationship with sexuality (respecting others’ privacy, of course) that some people might conceivably be embarrassed for me upon reading. On second thought, everything in this post might be pretty embarrassing.]


It’s said that you can’t logic yourself out of something that you didn’t logic yourself into, and that is indeed the case. For people with my temperament, it’s an observation that deserves forceful and frequent repetition. Even more so—and this is the ultimate tragedy of the human condition, in case you were wondering—it must be said that you can’t logic yourself into something that another person didn’t logic themselves out of. Continue reading

Reflections on a brief span of giving


A few minutes ago, a woman approached me for donations to a charity that supports the local deaf community. Such events in life are always awkward, but this had the potential to be doubly, nay, triply so. For at that very moment, I was staring at the confirmation page to donate to Captain Awkward herself.

My choice was between giving money to a woman who writes a funny advice column on the Internet so she can buy some fancy cheese, on the one hand, and giving to people whose fundamental quality of life could perhaps be substantially improved with my contribution on the other. I had chosen the former, and I knew it.

The woman in front of me only brought that knowledge into the open. She didn’t need to see my browser window to challenge my priorities. I’m happy to say that I faced the challenge with resolve: I told her that I couldn’t help, and then I sent some of my hard-earned money to a lady I don’t know in Chicago. Continue reading