On Writing

It’s almost tautological to say that you can make something better by removing the bad or unnecessary parts. When we apply this advice to writing it means crossing things out with a red pen, or pressing the delete key, hoping that we’ve properly identified the pieces of text that aren’t essential to the whole. I used to try to improve my writing by combing over each sentence in search of “needless words” to remove. I came to realize that apparently needless words can serve a purpose that’s easy to overlook: they can improve the rhythm and pacing of a sentence and can contribute to subtle changes in inflection. I also came to realize that if my goal is to use the reader’s attention well, it’s more valuable to cut out entire paragraphs, pages, or chapters that are unnecessary than it is to worry about individual words. So how can a writer go for the really big prize, eliminating whole paragraphs, pages, and chapters as opposed to a few words here and there? Every piece of writing is different but there are common causes of bloat. I’ll venture to say that the biggest cause of bloat is anxiety – specifically, the writer’s anxiety manifested on the page. Basically, if you can cut the anxiety out of your writing you can make it shorter by, I don’t know, thirty, fifty, ninety percent without sacrificing your message.

When one sits down to write, it’s common to feel a swirl of emotions, and many of these are negative. Writing is hard! The thing you want to discuss might be very complicated. You might not even be sure what you want to say or fully convinced of the point you hope to make. Perhaps you’ve missed something important? You might not feel worthy of writing about your chosen topic, considering that you don’t have credentials X, Y, and Z. Perhaps your point is very serious and you worry that you won’t do it justice. Any time you write something, you expose yourself to criticism. People might misunderstand you. They might question you. They might think you’re naive or stupid. They might think your message is obvious, or that it’s unoriginal, or that you’re wasting their time, or that you haven’t done your homework, or that you’re an imposter.

You want to guard against imagined criticism and ridicule, so you start hedging, making disclaimers, trying to anticipate and preemptively respond to all possible lines of attack. You talk about how dauntingly complex it is to broach this particular topic. You move to establish your authority on the topic while also making sure that no one could accuse you of inflating your credentials. You move to defend your position while also making clear that you’ve considered all other sides of the matter and that you’re aware that nothing can be known for sure. Writing becomes an adversarial project where your goal is to score some points without losing more than you’ve gained. Writing becomes more about you than it is about subject at hand. You think you’re writing about your topic but really you’re manifesting your own personal anxiety with the topic as a vehicle.

If you can eliminate the anxiety, and the gunk it creates in your writing, you’ll be left with something that really shines… or maybe something that doesn’t shine… but you won’t know until you try. Imagine the reader likes you, respects you, trusts you, and is ready to understand your point. Imagine you’re a good writer and you have unfettered access to the truth. Now tell it as simply and vividly as you can. That’s your mission.

What I’m saying here is the product of my own quest as a writer and the insights I’ve gained from one remarkable book: Clear and simple as the truth by Francis-Noël Thomas and Mark Turner.

I’ll give an example from my own recent experience. Over the past four years, I’ve done a lot of thinking about how America has gotten so polarized and I’ve wanted to summarize my observations in an essay. But I’m not a social scientist, I don’t have a degree that’s applicable to this topic, and I haven’t done any formal research. I’m just a guy who’s spent some time reading, watching, and thinking. I could have started my essay by making disclaimers and explaining why the reader should still take me – a layperson, an average citizen – seriously as a commentator on the nation’s affairs. But I realized that no reader stands to benefit from my justification for why I should be taken seriously. That justification contributes nothing of value to their lives or their knowledge. If they’ve stumbled upon my essay, they’re ready to spend a few seconds or minutes trying to ascertain my point and decide if it’s interesting enough to pursue, so I better make the point efficiently and let them judge it for themselves. The more I hedge and defend and qualify what I’m saying, the harder that’s going to be for them. Expressing my own doubts about what I’m saying doesn’t help the reader either. It’s better that I speak with full confidence and let them decide if I’m right or wrong.

I make one particular assertion in my Polarization essay: I say that people tend to ascribe good intentions to those who share their gut reactions and bad intentions to those who don’t. This is something I happen to believe. Of course I’m aware that it’s the kind of claim that researchers in psychology and sociology might study and write papers about and gather data to support or refute. Because I respect expertise, I feel that I should either find references to support this claim or let the reader know that it’s just a hunch that I can’t support in any formal way. Maybe I encountered the claim sometime in the past and forgot the source — I had better look it up. If I were writing a paper for a college class I’d indeed have to do that. But an academic mindset is actually my enemy when it comes to writing effective personal essays. If I get quickly to saying what I really think, without the justification, the hedging, the pugilistic citations, the defenses, the reader will sooner be able to make their own judgement, and guess what… so will I! If I manage to get my point down on paper without the gunk of self-defense and reified anxiety, I’ll be able to discover what I actually think and then I’ll be able to decide whether I really believe it. Cut the fear, keep the meat. In this way, the goal of “Writing to learn,” named by William Zinsser, might come to fruition.



What causes polarization in society?

If this seems like an intractably complex question, let’s approach it by asking why polarization surprises us in the first place. Since it’s easier to stoke enmity than empathy, easier to start a war than to end one, why shouldn’t polarization be the norm? Why shouldn’t all societies be divided all the time?

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Language, Society

Don’t lead with lies, even quoted ones

To anyone in the media who might ever read this, I beg you to stop spreading propaganda through your well-meaning but counterproductive efforts at “fact checking.”

When a politician releases propaganda, they want the propaganda to spread. They’re hoping for people to repeat it as often as possible. They’re trying to exploit the illusory truth effect — the way familiarity breeds belief.

Whether the propaganda is repeated approvingly or disapprovingly doesn’t matter. As long as the repetition – the transmission – occurs, the goal is achieved. If you, as a member of the media, repeat the propaganda and then explain why it’s false, you’ve still repeated it and served the goal of the politician who wanted precisely that to happen. This applies especially to the genre of fact checking.

When you fact-check a statement by a politician, you often do it in two steps. First, you recite the statement: “Politician X said ‘Pigs can fly.’” Second, you address the veracity of the statement: “There is no evidence that pigs can fly.”

It matters what you lead with.

Leading with a falsehood – even a quoted one – is a terrible approach because it gives the falsehood the spotlight. Wouldn’t it be great if pigs could fly? You should give the truth the spotlight instead. The truth is at a disadvantage because it’s less titillating than the lie. Pigs are earthbound – how boring! If your goal is to promote the truth, you need to work extra-hard to compensate for its inherent disadvantage. Showcase the truth by introducing it first. Explain why it matters. Only then, once the truth has been firmly established, quote the lie. Then repeat the truth. “Pigs definitely can’t fly. But Politician X claimed today that they can. But we know they certainly can’t.”

After this “truth sandwich” has been presented – truth-lie-truth – you should then examine the motivations behind the lie. “Given that pigs can’t fly, why would a politician want citizens to believe the falsehood that pigs can fly? What is at stake?”

Realize that your audience consists of some people who trust you more than they trust Politician X, and some people who trust Politician X more than they trust you. If an audience member is in that first category – if they’re already suspicious of Politician X – then your fact-checking probably doesn’t tell them anything they didn’t already assume. You’re only asking them to dedicate more of their mental energy to considering a falsehood that they’ve already rightly dismissed. But if an audience member loves Politician X, they’re going to cling to what Politician X said. When you quote Politician X they’re going to concentrate on the quote itself, ignoring the analysis that you offer next. They’ll forget your quibbling assertion that Politician X’s statement is false because what you’re saying isn’t as exciting and they don’t really trust you to begin with.

The only way to make fact-checking effective as a tool for promoting the truth is to make it about the truth. The truth is the story. The truth is the main character. The truth gets the spotlight. The propaganda – the false statements that are being fact-checked – should be given a minor role. They should only be allowed an appearance after the truth has had its initial say. And once the propaganda gets its turn, the truth should get another turn, the final say.

When I started writing this post, I assumed I was developing the material on my own. Indeed, fact-checking has been a pet peeve of mine for some time and I had written about it back in 2016. But when I searched for the term “truth sandwich,” I came across an NPR article from 2018 citing the linguist George Lakoff. I vaguely remembered reading it back then. I must have internalized the idea and forgotten the source — not unlike someone who remembers a claim they heard during a “fact check” session and then forgets the fact-checking part. So… the “truth sandwich” idea isn’t mine – the credit goes to Lakoff. Back in 2018, Lakoff’s proposal got a few mentions. A few members of the media discussed it and published articles on it. I fear that two years later, the lesson has not been widely learned and propaganda maintains the upper hand, happily co-opting the efforts of those who attempt to fact-check it out of existence. So I will do what I can to promote Lakoff’s truth sandwich. I hope you will too.


Only Twelve Notes

How is it possible that all of music… uh… make that all of Western music… uh… make that much of Western music is formed from only twelve notes? How is it possible that some of the greatest music takes flight with fewer than twelve notes — only seven, or only five? This is a question that often occurs to people taking their very first steps in learning about music theory. If you knew absolutely nothing about the technical side of music, but you only knew of the infinite variety of musical experience – the way music can make you feel ecstatic and depressed and every shade in between, the way music can keep you entertained for hours on end – you might be shocked to learn that all of these diverse and brilliant riches are constructed from at most twelve elements. It seems unbelievable that you’d never get bored of those same twelve elements repeated over and over. But then you get used to the idea. As you learn more about music theory, you may feel that you understand how it all works, but the question “Only twelve?” might still cross your mind from time to time. I myself was thinking about it the other day and imagining how I might respond to a beginning student who insisted that there simply must be more than twelve notes. I imagined several responses I’d give the student, and I’ll record them here.

The first response is a cheeky one: asking more questions. So you’re surprised that there are only twelve notes? Then how is it possible that everything we taste is built from five basic flavor sensations: bitter, salty, sweet, sour, and umami? How is it possible that everything we see is based on three primary colors: red, blue, yellow? How is it possible that all of Shakespeare, no, all of English literature – everything we’ve ever read or written, and everything we will ever read or write – is formed from 26 letters and some punctuation marks? How is it possible that all of the content we’ve ever seen on the Internet – every video, every news article, every comment, every social media post – is represented using only two elements: ones and zeroes?

The second response is to dispute the premise. Yes, Western music has twelve named note but each named note may occur in many different ranges. The note A0 at the bottom of the piano’s range is a very different sonic experience from A7 near the top of its range, but they are both called A. A piano actually has 88 keys, not 12, and each of those 88 sounds different. If someone endeavors to sing the note A at 440hz, their voice may wobble slightly, or they may deliberately employ vibrato, in which case we hear a range of frequencies hovering around the 440hz mark. And in fact, a piano can be tuned in different ways – equal temperament is only one option. The use of twelve named notes is a simplification that conceals a much wider variety of sonic material that music can and does exploit. Music has cymbal crashes and washboard scratches and whispered words and other sounds that don’t have a specific pitch. And there is some Western microtonal music that uses 19 named notes, or 22, or 48….

A third response is to point out that twelve notes actually give rise to a very wide variety of permutations and combinations, which each have their own distinctive qualities. Lets say I want to make a sound combining four of the twelve named notes, and I want to pick one note to be the lowest, another (possibly the same) note to go above it, a third note to go above that, and finally a fourth note to go on top. I can do this in 12^4 = 20736 different ways. Now what if I want to create sequences of note combinations? The possibilities explode.

A fourth response is that notes can be delivered in an infinite variety of ways. A note can be loud or soft. It can be long or short. It can be played by a piccolo or a tuba or a guitar… or an entire ensemble. You can attack a note directly or you can slide up to it, or down to it. On each instrument there are countless articulations. There may be only one named note A, but that A can take countless forms.

A fifth response, perhaps the most interesting to me, is that notes can give different meanings to each other and can renew themselves in our perception. A sequence of notes can put a listener in a certain state of mind, and that state of mind then determines how the listener hears further notes in the sequence. If I play the note C a few times, it may come to sound familiar to you. If I play a C chord, followed by a G7 chord, followed by a C chord again, then the note C will sound like “home.” Even though you may have heard the F# chord millions of times in your life before, the F# chord would sound strange and unexpected if you heard it at this particular moment. Your perception of a note or a chord is not governed as much by your history of hearing it over your lifetime as it is by the context that’s been created by the notes and chords you’ve heard just moments ago. If I had played a different chord sequence – F# followed by C#7 and then F# again – it would be the note F# that you’d experience as “home” while the note C and its chord would sound alien and unexpected.

Music uses gesture and pattern to make certain notes and chords sound familiar while others sound foreign. Once a perceptual frame is established, music can shift it around, making the now-foreign sound familiar and the now-familiar sound foreign. In this way, you can listen to a four-hour concert that uses only twelve named notes, never getting bored with any of those twelve, because the context in which you’re hearing those notes – and thus the meaning those notes acquire – is constantly changing. A C that you hear at the beginning of the concert may not sound the same to you, may not mean the same thing to you, as a C that you hear in the middle or at the end. That C and in fact all of the twelve named notes are only vessels that assume different meanings and affects according to the infinite variety of contexts that they create for each other and the infinite variety of moods or perceptual frames that they put us in. Music uses notes to give meaning to other notes, and as the music continues, the meanings change. While the meaning of C can change over the course of a concert, it can also change from one moment to the next: C might serve as the root or anchor of the chord you’re hearing now — it might be a stable note in this instant — but it might become the tension-giving seventh of the chord you’ll hear next.

A sixth response is that we don’t only hear notes — and the melodies and harmonies they create — when we listen to music. We hear rhythm too, of course. (Another question: How is it possible that most of the rhythms in Western music are made from whole notes, half notes, quarter notes, sixteenth notes, thirty-second notes and their dotted and triplet varieties?) Beyond that, we hear texture. We hear performers, we hear composers, we hear the people the music is about, or the people it’s for; we hear something of the history of when it was written or performed; we hear the memory of when we heard it first or heard it last; we hear the way we feel right now as it relates to the sounds that confront us. We may be something of a different person each time we listen, and listen again, to the same piece. There’s that.


Food Shopping

Going to the supermarket is part of the rhythm of life. A long time ago, we might have hunted or foraged for our food; now we visit stores. At least it’s form of going out, leaving home, braving a wilderness of sorts.

When the pandemic hit in March, I stopped going to supermarkets. I knew they were open and full of shoppers, but I felt that if had the option of staying home, I should take it: I’d be safer, and so would all the people I might otherwise encounter and exchange air with. So I figured out how to get all my groceries delivered.

As unnatural as it might have felt for a person of times past to think of buying food in stores, so it felt unnatural and deflating to me to avoid stores and have food magically arrive at my door. But the whole thing worked out in a way that – to my surprise – moved me closer to some of my goals. To reduce packaging waste and possibly save some money, I had been wanting to buy my food in bulk more often. And to prevent Amazon from taking over my entire life, I had been wanting to reduce my dependence on the grocery chain it acquired in 2017, Whole Foods.

When the pandemic hit, I placed my first few grocery orders through – you guessed it – Whole Foods a.k.a. Amazon. These orders arrived at my door unreasonably fast. But then, for a while, it became impossible to get a delivery slot. So I looked at my other options.

I had been a longtime customer of a produce delivery service called Boston Organics. It’s a small business local to me, and it’s a certified B corporation. I had been getting a box of fruit from them every two weeks. Now I realized I could also get my veggies from them, as well as bread, yogurt, tofu, and basic condiments. I updated my order contents and changed my delivery schedule to once a week. This part was really easy.

With my perishables taken care of, the next things to consider were all the shelf-stable items I wanted to buy in bulk: grains, lentils, nuts, pasta, dried fruit, oil, tinned fish, soymilk.

For grains and lentils, I remembered that I often bought the Bob’s Red Mill brand when I shopped at Whole Foods. So I went to the Bob’s Red Mill website and found I could order directly from them. For many items, there’s an option of ordering a case of small packages that’s eligible for free shipping, or a 20-30 lb. bulk bag that costs $30 shipping. The bulk bag is often cheap enough that you end up saving money over what you’d pay for the equivalent amount of small containers at a supermarket, even with the added shipping cost. I ordered bulk bags of quinoa and bulgur wheat from Bob’s Red Mill. I found another company, Pleasant Hill Grain, that ships grain in large plastic pails. I ordered teff and oatmeal from them. All of a sudden, I had enough grain in my house to last a year.

I ordered at least six months worth of beans from Rancho Gordo in California.

When I had shopped at Whole Foods, I often bought the Eden brand of soymilk, along with some of Eden’s Japanese condiments (rice vinegar, mirin). I went to the Eden website and found I could order a case of soymilk from them directly, free shipping, along with any of their other products.

There was an inexpensive variety of whole wheat Orecchiette pasta that I sometimes bought at Shaw’s. I went to the De Lallo website and found I could easily order a case.

For nuts and dried fruit, my friends recommended Tierra Farm (a B corporation that focuses on organic items) and I also knew about Superior Nut Company because it’s local to me. Between these three companies I ordered enough nuts to last a year or more (I’m freezing them).

I ordered many month’s worth of prunes from a prune company called Sowden Bros. I ordered tinned fish (which I eat occasionally) from Cole’s Trout. I ordered some cooking oils from a small company in the Finger Lakes of NY, Stonybrook WholeHeartedFoods. And I ordered more oil and a bunch of Portuguese specialties from a Portuguese importer that’s located just south of me, Portugalia Marketplace.

What did I discover? I discovered that I could purchase all my non-perishable items in bulk, directly from many of the brands I used to buy at Whole Foods and other stores. Coupled with a delivery service like Boston Organics for my perishable items (fruits, veggies, dairy, etc.) I had a complete solution. I literally never needed to go to the store. And none of this involved Amazon. If you don’t have a company like Boston Organics near you, there might still be CSAs in your area — arguably an even better option as it means buying directly from the farmer.

Of course, a lot of packages are being shipped to me – that’s a lot of cardboard, and a lot of fuel spent bringing the boxes to my door, and a lot of work by couriers who may be putting their own health at risk. I’m not saying this is a perfect solution.

Still, I’ve been pleasantly surprised by how easy it is to buy in bulk, directly from companies I like, eliminating Amazon and Whole Foods almost entirely from my food shopping routine.

The whole solution was only possible because I’m privileged enough to be able to afford these bulk purchases, often from brands that charge an organic premium. Still, I think I’m saving money over what I would have spent going to the store every week or two. And while each box that arrives at my door means fossil fuel was spent on delivery, the contents of the box are going to last me a really long time.

Will I ever step foot in Whole Foods after the pandemic is finally under control? I might. But I won’t need to. And unless they’re willing to sell me a 30 lb. bag of oatmeal at a bulk rate, I’ll be buying that directly from the supplier from now on, thank you very much.


Heavenly Toast

I’ve never posted a recipe before, so for fun, here’s a simple one that I came up with during the pandemic lockdown. I call it Heavenly Toast because it uses what I call the Heavenly Combination, which is 1) avocado plus 2) sweet potato. I typically use the Heavenly Combination as the basis for a thick salad dressing: I mash the avocado and sweet potato together with garlic, olive oil, lemon juice, and spices. But the Heavenly Combination also works fantastically well on toast. I’m not going to practice false modesty here. I believe this recipe to be the most delicious version of “avocado toast” one could hope for. It’s possibly one of the most delicious things one could hope for. It does depend on a secret ingredient though.

You’ll need bread to toast, an avocado, a sweet potato, an onion, salt, and the secret ingredient (more on that below).

First, cook the sweet potato. I find that the fastest way to do this is simply to put it in the microwave on high for 5 to 7 minutes. It will cook nicely in its skin. I don’t love using a microwave for everything, but I would keep a microwave just for the convenience of cooking sweet potatoes.

When the sweet potato is nearly done cooking, put the bread in the toaster and toast it.

Now mash and spread a layer of the sweet potato over the toasted bread.

Next, slice open the avocado and mash a layer of it over the sweet potato. You definitely want to do things in this order — sweet potato first, then avocado. If you do the avocado first, it’s going to be displaced when you try to spread the sweet potato.

Now chop an onion into very small cubes and sprinkle some of it over the avocado. Be more generous with the onion than you otherwise might. The raw onion adds texture to the dish and the sharpness of its taste is well absorbed by the Heavenly Combination, so fear not. You might consider using an onion variety that’s on the sweeter and milder side — crunchiness is also a virtue here — but any onion will do. If you really don’t like raw onion, you could try sauteing it lightly. Whatever you do, don’t leave it out.

Now sprinkle some salt over the onion layer. This is really important.

Finally, drizzle some of the secret ingredient over the whole thing. The secret ingredient is butternut squash seed oil. I’m only aware of one company that presses this oil: Stony Brook WholeHeartedFoods in the Finger Lakes region of NY. (I have no connection to this company.) The oil can be described as nutty, buttery, and very rich. To be honest, this oil was not “love at first taste” for me and I tried it in a few other dishes without great success. But when I drizzled it on an earlier version of this recipe, something magical happened. The taste went from very good to otherworldly. I would strongly suggest getting butternut squash seed oil if you want make this recipe; however, you could also experiment with other finishing oils like truffle oil, pine nut oil, walnut oil, etc. A basic olive oil is not going to do the trick here. You need something that’s intense enough to cut through the other flavors and also unify them in a delightful harmony. Somehow, butternut squash seed oil does that here.

Time: 10 to 15 minutes.

One thing I love about this recipe is that nothing I’ve tried to add to it so far has made it any better. I’ve tried adding garlic, tomato, fresh basil, fresh tarragon, fresh oregano, sesame seeds, and the like. These wonderful things don’t make it worse, but they don’t make it better either. With just the six core ingredients, you’ve got something optimal, and… heavenly.



Let’s be candid: there are few things more infuriating than other people’s stupid beliefs. What is an example of a stupid belief? Take the idea that the coronavirus is a hoax. I call this idea stupid because the virus has caused 640,601 worldwide deaths as I type, and I call this idea infuriating because it leads to behavior that increases transmission, making the situation worse for all of us. When I hear someone fiercely advocate for such a stupid belief, even saying that masks are bad for our health, I feel a sense of shock. How could a person possibly believe a thing so wrong? To answer the how question, I must examine why I am shocked in the first place.

My working theory of belief, I confess, is a simplistic one. I tend to think that every person is on a search for truth. Beliefs are the outcome of a search for truth. We all search for truth in our own ways, and it turns out that some people are quite bad at conducting this search, so they end up with beliefs that don’t make any sense. When I am confronted with such ludicrous beliefs, I tend to give the believer the benefit of the doubt. They are on a quest, just like I am on a quest, but they took a wrong turn in this particular case, just like I have certainly done in other cases. The outcome of their failed search for truth may be an outlandish and toxic belief, but nevertheless it arose from a desire that’s noble and universal: the desire to understand the world.

When I am shocked by a ludicrous belief, my shock comes from not understanding how anyone could be so ignorant of the facts in front of them, so incapable of simple reasoning, so inept at the most basic things we do when we search for truth. You would think that a person who believes the coronavirus is a hoax wouldn’t survive a day on this planet. Forget about their catching the virus. Surely they’d burn themselves on a stove, thinking the flame was a hoax, and promptly get hit by a bus, thinking physics is a hoax. But they don’t. It turns out that lots of people who believe horribly stupid things are actually great at surviving in the world. Not only do they not get hit by buses especially often, but they sometimes achieve great popularity and wealth despite their believing – or perhaps because of their believing the equivalent of 2+2=5. The fact that this surprises me tells me that my working theory of belief needs revision.

After years of watching American politics, observing the American response to climate change, and now the American response to the coronavirus, I’m forced into a sad conclusion: people, for the most part, aren’t on a search for truth, and beliefs are not best conceived as the outcome of a search for truth. Beliefs are simply stories that people adopt because there is a payoff of some sort. When we are shocked that someone holds a particularly irrational belief, our shock arises because the payoff is not apparent to us. If we were to identify the payoff, then we would find it clear why the person holds the belief.

A belief is an investment. If you are to make a financial investment, like purchasing a mutual fund or a piece of real estate, you first need to encounter it. You might find it on your own, or someone might actively pitch it to you. You might resist at first, but a skilled salesperson might overcome your objections. When you buy it, there might be a transaction cost. As you hold it, there will be ongoing maintenance costs, but you will accept these because there is a hopefully larger return. The investment might have some “intrinsic” value, but this intrinsic value might be totally disconnected from the returns you experience. If market conditions work in your favor, you might experience a great return on something that is intrinsically worthless.

When you adopt a belief, there is a transaction cost too. You might have to abandon something else you currently believe, and there might be something unpleasant in the new belief that you have to come to terms with. You might have to admit you were wrong in the past. As you hold the new belief, there will be an ongoing maintenance cost. Your own mind might periodically challenge the belief, finding gaps and contradictions within it. Your friends and family might challenge the belief, arguing with you, and even ceasing to associate with you. If you keep holding the belief in light of these costs, that’s likely because the returns are greater. If the belief happens to be true, then perhaps it helps you solve problems or navigate situations that require an accurate model of reality. But even if the belief is false, it may have other, more attractive returns. The belief might make you feel good. The belief might place you in a community of other believers whose company you enjoy, or distinguish you from those whose company you hate. The belief might make you feel superior to those who make you afraid. The belief might win you the attention you want. The belief might get you a job. The belief might serve as a social bonding mechanism, a calling card, or a salve.

The cost of maintaining a belief may depend somewhat on its veracity, but only somewhat. One would hope that it is harder to maintain a false belief than a true one, since the false belief would conflict with observed reality or contain logical inconsistencies that trouble the mind. But this is only a problem if the believer constantly searches for logical inconsistencies among his or her many beliefs and constantly tests those beliefs against observed reality. If the believer isn’t in the habit of doing these things, the maintenance costs go down considerably.

I used to imagine that a person’s many beliefs existed in some vast common space in their mind – mingling with each other as if in a great ballroom – and that if two beliefs contradicted each other, the host would inevitably notice this and feel disturbed enough to seek a resolution. I don’t see it this way anymore. The space of belief is more like a forest at night, filled with hiding places. Denizens of the forest who might antagonize or kill each other if they met in daylight hide quietly in their own nests.

A person might hold two contradictory beliefs without those beliefs ever meeting and doing battle. And a person who valiantly endeavors to rid their beliefs of contradictions will have a hard time of it, because that person has no way of acquiring a complete inventory of their beliefs, no better chance than a naturalist might have of cataloguing every living being in a vast and dark forest. The mind harbors no unified list of beliefs that can be printed out. You can try to write all your beliefs on paper but I would wager that there are dozens of beliefs you will not know about and dozens that you may be too uncomfortable to write. There may be some that you begin to write and promptly deny. There are beliefs that only become apparent through one’s actions, in situations where one is too distracted to articulate them as beliefs.

When I look at the news and hear that throngs of people still think the coronavirus is a hoax, or still think climate change a hoax, I am astonished because I think of how painful it would be for me to hold those same beliefs. These beliefs would clash with my confidence in science and my faith in the scientific establishment. My friends, all of whom accept the coronavirus and climate change as real, would laugh at me. I would have to reconsider all the efforts I am making in my own life to try to reduce my carbon footprint. I would have to change my news sources and my idea of who is a trusted authority. When I imagine holding these beliefs, I am so caught up in the pain I would feel that I find it difficult to conceive there could be a payoff of any sort.

To understand people who call coronavirus or climate change a hoax I must imagine that the economics are different for them. For me, the transaction cost and ongoing maintenance cost of these conspiratorial beliefs might be very high; for them it might be very low. Their friends might already agree that the virus is hoax and cheer them on for saying the same. Announcing the belief might bring them love. They may not feel any great allegiance with the project of science, no matter that they use its products (computer, cellphone, modern medicine), so they would feel no hesitation in disputing scientific authorities. As they assert these beliefs, they may feel a sense of pride and power in challenging an establishment they consider oppressive. Believing the virus is a hoax may mean, for them, that they get to share more laughs and have more beers with friends. For them, the experience of holding the belief might be entirely pleasant. Why wouldn’t they believe it?

We might wish that it couldn’t be so pleasant to believe in something so dangerous, that it couldn’t be so lucrative to invest in something so wrong, but it can. A person’s beliefs may be more a record of what rewarded them than of what brought them closer to truth. Perhaps the dynamics of belief share the same skewed outcomes as market-based capitalism: beliefs are adopted, just like financial investments are made based on the immediate payoff, without accounting for externalities or hidden social costs. One can easily believe something, or invest in something that damages the common good, without ever realizing or paying for the damage, and so the damage accumulates, compounding until there is a collapse.


Canon #88, Carminite

Announcing Canon #88, “Carminite.”

The essence of a canon is imitation: the follower copies the leader. In some canons, imitation is exact: the follower plays the same notes that the leader played moments before. In other canons, imitation involves some kind of transformation. There might be a chromatic or diatonic transposition. There might be an inversion, where an upward movement is imitated as a downward movement and vice versa. There might be a stretching or shrinking of note durations. There might even be a reversal or retrograde statement of the material. In all of these cases, imitation is deterministic: once the leader plays a note, it’s clear what note the follower must play – there’s no choice. Of course, during the composition process, liberties may be taken. The composer might decide that even though the follower is supposed to play a certain note to stay faithful to the leader’s example, the required note doesn’t sound good and a different note will be chosen. These exceptions to the imitation scheme are precisely that: exceptions and not the norm. When I write canons I often agonize over these exceptions: is it better to keep the canon strict or to make alterations that diminish the formal purity of the piece while making it more musically engaging?

For a long time I’ve wanted to write a canon with a different concept of imitation: one that would be approximate or flexible instead of prescriptive or fully determined. There are lots of ways you could flesh out what “approximate imitation” means. The idea I had in mind was that interval direction would be preserved while interval size could be changed arbitrarily; meanwhile, rhythm would be preserved exactly. That’s to say, if the leader plays two quarter notes that move up by a major third, the follower would have to play two quarter notes as well, and they would have to move up as well, but they could move up by a minor second or a perfect fifth or any other interval.

Writing a piece like this, I hoped, would help me address a question I’ve been thinking about for years: what makes a canon sound like a canon? What formal elements are essential to creating the experience that we seek when we listen to a canon? Is the strictness of the imitation important, or is it dispensable? Is rhythmic imitation more important, or is the replication of melodic contour more important? To shed any light on this, a piece employing approximate imitation would have to be more than a canon that takes liberties here and there — many canons already do this. It would have to be a canon where the leader’s intervals are very frequently changed by the follower, not in a predictable way, like always cutting them in half (see Interval Compression), but in a free and unpredictable way.

One might expect that the idea of approximate imitation would make a canon much easier to write: more flexibility, fewer constraints. So, after months of attempting it, I was perplexed at my inability to get such a canon working. The project, in fact, seemed much harder than writing a strict canon. Why should this be so? The reason is what I alluded to above: approximate imitation introduces a new burden. To really showcase this concept, you have make the follower regularly – not just occasionally – vary the leader’s intervals. So it’s like you’re writing two melodies at once. You do all the work to make the leader’s line sound good, and then, instead of having the follower copy the leader’s already-good-sounding line, you have to make the follower do something different, but still similar, and this different-but-similar thing also has to sound good. That’s hard.

In Canon 88, I’ve finally been able to create an example of approximate imitation. What made it possible this time around? I’m not sure there was any particular trick, although I did make the early decision that this would be a dissonant canon without a clear tonal center. I spent more than a week working on possible outlines, and then another week trying to develop them: two false starts before something finally came together. The false starts were interesting in their own way. I think what went wrong with both is that my melodic developments on top of the non-tonal outline started to become too tonally suggestive. I was beginning to turn a non-tonal skeleton into a tonal piece, but this was a lost cause. Each possible tonal focus was hinted but not maintained long enough to give any satisfaction. As one possible tonal center was abandoned and another suggested, it created the disappointing, sloppy variety of chaos, rather than that very different variety I seek: the one that is intriguing, potent, and structured. In the final attempt, the one that worked, I managed to create lines that were less tonally binding, so they played better with the non-tonal outline, not constantly working up an expectation and then disappointing it.

This canon also explores a V-shaped registral contour I had been wanting to execute in a canon for some time. Both voices start very high and gradually descend until they’re both very low. At the midpoint, they turn around and begin ascending till they return to their high starting range.

In the first section, the lower voice leads. At the midpoint, the upper voice takes over as leader.

The two sections of the piece have different characters: the first is more whimsical and skittish; the second is more patterned and goal-oriented.

The second part of the piece is built from a retrograde or reversed version of the outline I used for the first part. So, the bones of the piece exhibit a kind of mirror structure around the midpoint, but the details in each half are completely different.

As the canon uses approximate imitation, of course, there’s no specific “interval of imitation” used here.

Subjectively, the piece brings to my mind a kind of cartoon dance or chase: fast, erratic, and maybe a bit comical.

The choice of name, “Carminite,” is not particularly significant in this case, though I liked its sound and I noted that Carminite is a red mineral. Sometimes pieces bring to mind certain colors. Red seemed like a good match in this case but to try to explain why, I’d have to be more inventive than I’m feeling right now.

So, does this piece answer any of my questions about the nature of canons? It leads me closer to the conclusion that strictness is non-essential. Approximate imitation sounds, or can be made to sound, very much like classic, strict imitation. Perhaps proving this was my unstated intention when writing the piece. While I set out to showcase approximate imitation as something distinct from strict imitation, my impulse was to reign it in and apply it in a very controlled way. The ear can be guided into ignoring countless discrepancies between leader and follower when more important similarities call for its attention. It’s possible that as I wrote the piece, I tended to put the discrepancies in places that didn’t draw focus.

What also may have happened is that the more glaring discrepancies in my outline got smoothed over by later melodic elaboration. For example, the outline might have had a minor third leap in one voice imitated as, say, a tritone leap in the other — a difference that would be easily noticed. But these leaps might have been filled in as a run of three semitones in one voice versus a run of three whole steps in the other voice. Of course, a semitone run is different from a whole-tone run, but if the ear is more interested in the destination, these paths may sound quite similar: they are both sequences of “small” steps. So while there are many discrepancies between leader and follower situated all throughout the piece, they’re not as glaring as they could have been made to be.

For me, the experience of listening to Canon 88 is much the same as what I get when I listen to my previous canons, barring aesthetic differences from piece to piece. It doesn’t sound like an outlier to me. But this experiment yields no final or general conclusion about approximate imitation because the idea can be realized in so many different ways; only one of them is explored here. It’s perhaps a tame application of the concept, and yet it gave rise to what I feel is one of my freer-sounding pieces. At the moment, it’s one of my favorites. My goal now is to try using approximate imitation again, in a way that makes the discrepancies even more apparent.


Canon #87, Barite

Announcing Canon #87 — “Barite.”

Work on this piece started in a typical way for me. I spent a week exploring various ideas from my canon to-do list, but I couldn’t get any of my sketches to take flight. I kept working through Memorial Day weekend; still nothing. It was hard not to think the long weekend would have been better spent on something else entirely – maybe I should have given up and tried again later? – but I know that every day that seems fruitless is an investment in what’s to come. In a sense, you can’t get something done unless you’re willing to accept the feeling that you’re getting nothing done, and keep going anyway. Finally on Monday evening, I noticed a simple technical option that I hadn’t yet explored in any of my canons. I’ve written a few canons in 3/4 time where the lag is one beat, but I hadn’t written a canon in 3/4 where the lag is two beats (leader starts on the first beat, follower starts on the third beat). Why not? Although Max Reger isn’t my model for canon writing, I notice he used this construct in a good number of his 111 Kanons durch alle Dur und Molltonarten. Ready for something new to work on, I abandoned the other sketches I had been struggling with and started a canon in 3/4 with a two-beat lag.

As with most of my canons, the first step is to create an outline, not one that I like, but one that I love. Why is this step so important? After all, the quality of the outline doesn’t necessarily dictate the quality of the finished piece. It’s totally possible to transform a lackluster outline into a great piece because as you’re working, you can revise the outline or simply throw it away when it stops serving you. The problem for me is that when I don’t start with an outline I absolutely love, it’s hard to find the motivation to keep struggling to reveal its potential. If I do love the outline, then that love propels me: I feel an overwhelming resolve to do whatever it takes to transform the outline into a full piece of music. So while I could probably start with cursory outlines that take a few minutes to throw together, and maybe I’d produce more pieces that way, I’m more inclined to spend hours or days creating an outline that totally captivates me, because once I’m hooked, I’ll never abandon the piece even when the going is rough. You could say I have a kind of perfectionism about my outlines, but I take the view that perfectionism itself isn’t evil: one just needs to be realistic about what one chooses to be a perfectionist about. Outlines are the good things to be a perfectionist about because they’re simple enough that you actually can make them perfect.

So I started making an outline for Canon 87, and managed to get something I loved. During the outlining stage, I don’t really know what style the piece is going to land in. My outline for Canon 87 was full of unprepared and unresolved dissonances, suggesting it would take on a modern style, but the melodic material was firmly tonal and full of diatonic sequences, and the implied harmonies all seemed to fall within the realm of “common practice.” As I developed the piece, this duality persisted: in a melodic or “horizontal” sense, the piece started sounding like something from the 18th century but in a “vertical” sense it seemed much more modern. Towards the end of the piece, the interval palette becomes more consonant, with more thirds and sixths on measure onsets; the sound is less conflicted in spirit and style. I considered revising the latter part of the piece to keep the style more consistent with the dissonant opening, but I decided instead to embrace the piece’s progression from a dissonant to a more consonant palette, and from a severe to a lighter mood.

To bring the piece to a satisfying conclusion, I knew I’d have to break out of the canon and write some free counterpoint. I was ready for ending to be a struggle as it often is. But then I came upon the idea of having the voices move mostly in parallel at the end (after all, they had established their independence by now, right? What more did they have to prove?). I brought them closer together and had them converge into a unison at the final beat, and that worked.

A few details: the piece uses diatonic imitation at the fourth above. It opens in D minor, progresses to G minor, moves back to D minor, and finally progresses to B-flat major. The imitation is fairly strict, but the bottom line takes various ornaments that the top doesn’t repeat. I chose the name Barite because, for whatever reason, the piece brought the color yellow to mind, and Barite is a mineral that can look yellow when cut as a gemstone (all of the other more familiar yellow gemstone names are taken by now). Unlike many of my pieces, Canon 87 has only one section and doesn’t go through an inversion. (It’s probably possible to get this material to work in an inverted form, but it would take some rewriting, and although I always wish my pieces were just a little bit longer, I think this one reaches a natural stopping point and doesn’t call for an extension.) The piece is based on the simplest of melodic figures: on almost every measure onset, in the bass, you can hear a note, followed by its lower neighbor, and then the note again. I like working with simple figures such as this — I like seeing how much they can do.