Econometricians.

Real GDP measures how much of everything people get in a year, including goods like food and services like haircuts. This is a good start, but how should we compare a year with 3 apples and 5 haircuts to one with 10 apples and 4 haircuts? Apples went up, and haircuts went down.

If we give up here, we’ll be giving up on most years, because rarely do people get more of literally everything. But we can tell that some years have more stuff. Imagine we were comparing 3 apples and 5 haircuts in the first year to a billion apples and 4 haircuts in the second year. That looks like an improvement to me!

Dollars are a measure of how much people value stuff. Statisticians use prices to convert each good into dollars, and then sum them up to get a total GDP. But this approach can mislead. If apples become too cheap to meter, almost no dollars get spent on them, even when people are eating more apples than ever. So, when calculating real GDP, statisticians pick a benchmark year, and then convert the goods using that year’s prices.

But pricing things this way runs into trouble when you try to use the result as a welfare measure.

Imagine that there are only two goods: food and string quartets. People like both, but each additional bit of food or string quartet performance is valued less than the last.

Over time, the inhabitants of this world get better at making both food and music. But, they improve at making food faster than at making string quartets.

As food gets cheaper and cheaper, satisfying your needs costs almost nothing. People move almost all their spending to string quartets. String quartets get cheaper, but not nearly as much as food does. Because almost all spending is now on quartets, real GDP basically tracks how fast the quartet sector grows.

Delete string quartets from the world, and real GDP would, confusingly, grow faster. People would spend all their money on food, and they get better at making food very quickly. So real GDP grows faster without string quartets, but the utility of that world is lower!

Not the best measure. As John Wentworth put it in 2021, real GDP mainly measures the goods which are revolutionized least.

Philip Trammell and Charles Jones have a new paper that suggests a better measure. It’s also the source of the above example. I recommend reading it; it’s shockingly clear!1

Rationality equilibrates

The paper assumes that folks are rational, then leans on a corollary: people get the same bang for their buck everywhere. Spending an extra cent today is just as good as saving it for tomorrow. You might as well spend it on lowering your risk of death or buying more of your favourite tea.

Why does rationality imply this? Cos if it were better to buy tea than save money, you’d already save less and spend more on tea. People keep adjusting their budgets until there are no more wins to be had with that money.

I’ll call this the “rationality equilibrates” argument.

1% of your money or 0.01% of your life

People are actually quantifying the value of their life all the time. The world abounds with options to trade a little danger of dying for a little bit of money. Both working in an oil refinery and buying a cheaper car are a little more dangerous than the alternative, and both make or save you money.

These choices put a price on avoiding death. You could live to see tomorrow, or you could get to spend a bunch more money today. There’s a price at which that equals out. The name for that price is value of statistical life (VSL). I’ll call it “value of life”.

The dollars in that price are not just any dollars. They have the magic property that each dollar is as good as the last. If your value of life is $1 billion, those are dollars that each feel as welcome as a dollar does right now, not dulled by the jaded disgust of a person richer than they can stomach.

This is an example of a “rationality equilibrates” argument: if you take a 1 in a million chance of dying for $20 today, you think the rest of your life is less than a million times as good as that extra $20. To find out how good your life is, in the face of a fickle dollar, we need to know: how good is that extra $20?

To say it another way, the utility of your life, according to you, is its value in dollars, multiplied by the utility of a dollar.

That just leaves finding out how much the next dollar is worth to you. As the authors wryly note, the utility of the next dollar is “rarely observed”. In fact, we can’t observe it!

What you can see instead

As we all know from 2008 MIRI hiring posts, utility functions are unique up to affine transformation. For me, that phrase remained catechistic for years. “Utility functions are unique up to affine transformations, Brother Kave,” I would intone to myself as I waited for my toast. “They preserve relative intervals, frater,” I’d respond.

What does this mean? First, your choices don’t change if we bump up your utility in all situations. If apples are a bit better and bananas are just as much better, you’ll take the same odds when betting my apple against your banana. Second, your choices don’t change if we scale your utilities by some factor. Liking apples more intensely only makes a difference if you don’t like everything else more intensely as well.

We can get rid of the “bump” by asking: how good is a bit more stuff? The difference between four apples and three apples stays the same even as we bump your utility. We can get rid of the “stretch” by looking at how your utility grows. A 3% increase is a 3% increase even if the numbers are all doubled.

The paper looks at how the value of a bit more stuff grows over time: the combination of looking at growth rates and the next bit of stuff means that we’re talking about something objective. It’s value is pinned down by folks’ choices.

Growth mindset

Lifetime utility grows for two reasons. The dollar value of your life can rise. And the value of an extra dollar can rise. Add those two growth rates together and you get the rate at which your lifetime utility grows.

We can use a “rationality equilibrates” argument to find out.

You could spend a dollar today. Or, you could save it for a little later. If you save it for later, you’ll get a bit more money back the next day (because you’ve voted for society to make tomorrow richer at the expense of today). But it’s later, and maybe you’re a bit impatient, and care about later less than now. And also, the opportunity to spend your next dollar might be better or worse later than it is now.

All of these effects matter. But the “rationality equilibrates” argument says it all washes out. You save more money until you’re indifferent between saving the next dollar and spending it today.

We can solve this for a growth rate, and we find it’s remarkably simple. It’s just how quickly you stop caring about the future, minus how fast your money grows when you wait.

To get your growth in lifetime utility, all we have to do is add in the growth in the value of life!

In math:

Where U is lifetime utility, ρ is how fast you stop caring and i is how much interest you get.

Other than soggy bread? Totally. We’ve got ovens, we’ve got baskets, we’ve got trucks. We’ve got everything you need to grow, harvest, bake, store and deliver soggy bread. There’s land and time, and with the time we can get metal out of the land and turn it into machines to get more soggy bread.

A lot of people do spend most of their money on soggy bread, but not everyone. Some folks make groups called firms and those firms spend a lot of their money on machines to bake soggy bread. And machines that help with planting grain and growing it and so on. And they also pay people to work the machines and to do tricky work that the machines don’t. Then the firms sell the soggy bread to people who want it.

The money’s like a vote for how we use people’s time and how we use the objects out here in the world. I mean, not exactly a “vote”, cos if someone owns, like, some land, they get to choose how it’s used. But often they’d rather have some money than the land they’ve got, and so they swap the land for money with whoever offers the most.

Sometimes people just give money to other people. Like, suppose you give all your money to a kid who spends everything on soggy bread. Then we’ll end up figuring out how to get a bit more soggy bread right now. And we’ll do less of everything else we could have been doing. Like, someone won’t plant Friday’s last row of grain so that they can do an extra delivery run.

Suppose you give your money to a firm instead. Well, then we’ll follow its plan a bit more. We’ll plant more seeds and tinker on better machines and stuff like that. People will get a bit less soggy bread today, because we’ll follow the firm’s ideas for how to get more soggy bread in the future.

You don’t just have to give them the money. You can ask for something back. Normally, firms give you a ticket. When they make money, everyone with a ticket gets some. People buy those tickets so their money will grow when they’re not using it. Growing like the blue squidge on the delicacy bread!

You can just keep hold of the money, but then it doesn’t grow. Why not? Well, think about how it changes what everyone does.

If you don’t do anything with the money, then we go about things our normal way. Our money goes a little further, because you’re not voting on how to use what’s scarce: the time and land and materials and stuff. That’s nice! But you do still get to have a vote in the future, and then our money won’t go so far.

If you give the money to the firm, then like I said, we do more of the firm’s plans and less of everything else. Normally that means more soggy bread in the future. So the future will give you some money to say thank you. It’s sort of like you moved soggy bread from now to the future, but it multiplied when you did it. That’s why you end up with more money than you started with.

People don’t actually give the money to the firm, by the way. Not mostly. They trade the tickets. But really, if you buy a ticket from someone, that’s like they sold the ticket back to the firm and you bought a ticket from the firm.

Some people even sell tickets they don’t have! No, it makes sense … I think. Listen. Firms’ plans don’t always work. Sometimes they waste people’s time and metal and fuel, and there’s not any more soggy bread than there would have been if they hadn’t started. And so the tickets don’t sell for as much any more. That firm’s not going to get much money.

Here’s how I think about selling a ticket you don’t have. You get money from the firm, and in return you give them a reverse ticket! A tekcit. The more money the firm makes, the more you’ll owe them later for that tekcit.

Doing this also changes how we all spend our efforts. The firm has less money, so it has less of a “vote” on what everyone does. And you have a bit more, and your money competes with theirs as a vote.

If your vote made sense, you didn’t ask for very much soggy bread from the future, so it didn’t cost you very much. And if you used the money to support plans that are better at making soggy bread, you mean that there’s more soggy bread in the future! And so you can make lots of money in the future selling the tickets you don’t own.

… Anyway, you’ve barely touched the bread! Have it before it dries out!

If the virgoop weren’t so useful for saying sooth, the seiners’ purses wouldn’t hang so heavy. But they’d also be paid less if it weren’t for the danger and skill of their trade.1 After all, it would be easy to pay the weak and scared.

On the outskirts of the palaestrae, the dobbies make their living by kneading the virgoop. The dobbies pound for several days to form the crystals the sooths love. But any drudge can do it.

So do the seiners sell their pricy goop to a crowd of peasants? No, at least in my imagination, they sell it to an even richer broker. Someone who employs a workforce to knead the virgoop.

I wonder if resource gatherers ever sell to poorer refiners, rather than richer ones. I started thinking about this because of millers. In the English manorial system the miller was a step above the peasants. He was richer and more independent. I wondered if there’s an economic law that those who gather resources will always sell to a richer buyer.

Mills and ore refineries are expensive pieces of kit. Big chunks of capital belong to wealthy owners and operators. So I tried making it very easy to refine: maybe you just squeeze out the water. But then the seiners just tamp it themselves.

So perhaps the refining could be tedious, slow and awkward. Then the seiners wouldn’t do it themselves, at least. But I think the seiners will still be as poor as the dobbies if virgoop is cheap.

Expensive virgoop enriches the seiners, but whoever buys it needs cash on hand. In principle, lenders could get the money where it needs to go. They’d loan money to the dobbies, who’d buy the goop, process it, sell it for a small gain, and split that gain between interest and their pay.

But if a dobby had their hands on enough money to buy virgoop, wouldn’t they often take the loan and run? If they could get away with it, they might make years of salary. Frequent thefts would turn off lenders.

A rich person, by contrast, doesn’t need to convince anyone. They can just invest their money. They can hire dobbies to work the goop, and never give them cash they might want to steal. Of course, the dobbies might want to steal the goop itself. So the rich person might set up security, like checking folks when they leave the processing site.

(Why couldn’t the lender do this? Consider how the employer does it. All the employees come to one place, and are easily monitored there. The lender will have a harder time. Each kneader would be in a different place. In other words, the employer gets monitoring economies of scale).

So just making virgoop expensive doesn’t make the gatherer richer than the refiner. If a refiner can get the cash to buy the raw material, they’re rich. At least for expensive materials.

What about splitting the goop into fragments small enough that a dobby can afford one outright?

Then the seiner must find and trade with lots of different buyers. They might prefer to rest, play, or gather more goop. This problem recurs when the dobby is done. Now each dobby must find a buyer, and one large buyer (if any exists) must trade with many dobbies. The transaction costs say: trade the goop in bulk.2

In all these settings, the gatherer sells to a richer refiner. I might be able to tweak things to get them to be about equally rich, but I’m struggling to swing it in favour of the collector. It’s a mystery that we only see cases where there’s either a bundler or a capital-heavy refiner. What unifies the case of the miller, where the refiner is rich, and the dobby, where the refiner is poor?

The cases where the refiner “should” be poor can’t work. The transaction costs are too high. So someone bundles refiners together until the transaction costs are manageable. But for the miller, no bundling is needed. Nothing makes the capital-heavy cases particularly likely. It’s just they don’t get filtered out by transaction costs.

It’s too hard to sell to someone poorer. Imagine all the different Dodonas out there. In some, like ours, the virgooper adds more value than the refiner. So the refiner, our dobby, is poor. In others, the refiner adds more. In all those like ours, someone centralises some of the trading. The cloudseiner doesn’t sell to many dobbies, but one broker. Millers are rich, because if they weren’t, we wouldn’t see independent millers. We’d see grain brokers.

So the law that leaves resource buyers richer than sellers is a selection effect.

Glossary

cloudseiner — from seine fishing (pulling a net with weighted bottom through the water)

Dodona — from the site of the oldest Hellenic oracle

virgoop — from virga (rain that evaporates before reaching the ground) and goop (goop)

maccaboy — from a scented snuff in the 18th C.

palaestra — from ancient wrestling schools

dobby — from dhobi, a washerman. Also, from Dobby, a house elf

The tech has since risen to the challenge. Wispr Flow in particular let me dictate several blog posts during Inkhaven. But, as Beŋ says, “Speech to text has a different ‘texture’ than writing; when I write, I’m forcing structure onto my thoughts as I go. It’s a clarifying act. When I talk, it’s discursive, less sharp, more branching and sprawling.”

Does the sprawl slap or not? When I dictate a post, is the result good or bad? NB: it might be that I tend to dictate posts that would be good or bad, even if the dictation doesn’t have an effect. For example, sometimes I dictate when I’m in a rush. As a guy who read the Sequences but not Toolbox-thinking and Law-thinking, I’ll solve this by asking an LLM to fit a Bayesian model to my posts, and regress their likes and views on whether or not I dictated them.

Of course, whether I dictated something is not completely binary. Yes, for some I just basically sat down, spoke into the microphone, and fixed up transcription errors. Others were written in silence. And some were in-between. Paragraphs written by hand, others spoken. So I’ll give them a score of 0-2 on how dictated they are.

I fit the model … and, the diagnostics suggested some posts were having an outsized influence on the fit. In particular, The Spectre, a dictated post that got linked in a few places.

So I throw in some more variables that might affect the fit. Did I cross post it to twitter? Was it highlighted in the Inkhaven Spotlight? Did taylor.town drop it in his links newsletter? Was it fiction?

And also, this AI didn’t make the best modelling choices IMO. I guess there’ll always be a role for human ingenuity and understanding after all!

So I tweaked those choices, and made promotion effects additive rather than multiplicative. I tried lots of things until the guardrails stopped complaining.

And after all that, we’ve got some numbers! So, do I tend to dictate better or worse posts?

About 10% worse! Though that credible interval is pretty wide. The problem, you see, is that I’ve only written about 30 posts. And the model-fitting machinery wouldn’t mind a few more likes and views, to be honest. So, I’m going to do my part by writing a few more posts for this substack.

I invite you, too, to do your part: read & like!

At my father’s funeral, we played Bob Dylan’s Forever Young. It’s a song from a father to a son. The father blesses his son with a wish in the central refrain “may you remain forever young”: that is happy and brave and true. To be free and grounded in the world. My father succeeded at some of that in his own life, and thinking of that aches sweetly. I want that for me as much as possible, and I want it for each person in the world.

But happiness and courage and freedom are not simply a matter of spiritual strength. We can remain open to possibility, but we would be fools not to notice how plausibilities change with our fading vitality.

I don’t want to just be forever young. I want to be young forever: I want to live forever and be young and free forever.

Inkhaven is ending. Throwing yourself into something is possible at certain times in your life. And those times have a count, a limit. If we were young forever, we could take time and chances and lick our wounds after failures and grow into strange new ways. But as we age, there are projects whose ambition and length will be beyond us. We will weaken and die.

Once I walked past an old woman on the street who had to push down on her leg to straighten it with each step. I hated that.

I know how a criticism goes. If the Beatles had lived longer, they wouldn’t have been the Beatles forever. A thing has its time and place, but its members need not. They could be young and vital and living still. Age’s pumice need not scrub out what is good and true.

The weakness of age is already with us when we’re newborn. We tire, we forget more than we’d wish, we ache at mild strain, we can see and feel few things. I want humanity to be freed from those things too. If I’d known and lost those strengths, these human foibles would sting as much aging; if I could see more clearly how much we could lift and strengthen ourselves, I’d long for that acutely. If I had strengths no human’s ever known, my longing could be more acute yet.

But it’s not just parochialism. Death takes you out of the game, but before the scythe, comes age. It comes to take away your ability to protect yourself. It comes to take your self-sufficiency. As you are age-stricken, good things are plucked from you one by one, until you are left bare and shivering against the sharp of day.

I want to be forever young, and I want to be young forever. And I want that for you too.

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The tree was in the front window of her house. Perhaps in part it was so that people like me could stop and enjoy it. But I didn’t think I was supposed to intrude through the window, to extend my presence through the pane of glass; I’d force her to now be in the same place as eme, looking at her tree, and she’d be uncertain, within her own home, how the interaction would end.

It was good that it was cold. Many of the trees on the street have lights on them. It’s winter, and the harshness of the weather makes each stranger seem a friend. I took a corner onto a larger, darker street.

A college student ran past me. She wasn’t dressed for running, really. More for ambling or shopping. I wondered if she was trying to catch a bus. But no bus routes ran this street, so I wasn’t sure how she’d know she needed to run to catch it.

A friend crossed the intersection as I approached it. I’d just spoken to him about his plan to go back to his accommodations and nap. He was jumpered and beanied against the chill, hunched slightly forward. He reminded me of England, and the pleasing chill of walking a mile from the tube station to the pub, and then entering to warm air and welcomes.

A woman behind me was talking loudly. I wondered if she was mad or not. Eventually she started to overtake me. “Are you serious? Barbara Hamming? The doctor’s wife?” She sounded angry. But, talking about doctor’s wives seemed, frankly, like the wrong socioeconomic class to be someone ranting to yourself on the street. I watched her quizzically as she went by.

She stopped, and turned and looked at me, and said a stream of names, punctuated by expressions of incredulity. Something like, “Really? Sarah Jacob? Are you for real? Barbara Hamming? The doctor’s wife? Are you serious, Joseph?”. She had blonde hair and her cheeks were a bit sunken.

I decided to turn and walk the other way. She followed and stepped in front of me. “Her house doesn’t have electricity. She has to live without electricity, Joseph.” I turned again and she followed me, getting close enough to me to step on my toes, and waving a lit cigarette close to my face.

“I don’t want to talk to you.” I said.

“Call PG&E. Now. Are you serious, Joseph?”

“Listen, I don’t want to talk to you.” I started walking away and she kept up, quite close to me. Now I was quite unsure how or whether the interaction would end.

“Look.” I said, “Which way are you going?”

“Which way are you going?”

“I’m just trying to stop talking to you. Which way are you going?”

“Which way are you going? Barbara Hamming. Are you serious?”

I started to walk and she followed me. “I’m going this way,” she informed me.

“Oh, OK. Then I’m going this way.”

“OK. Sarah Jacob in her house?”

I walked away and she watched me, unhappy, lingering in the middle of the block. I turned the corner. She wasn’t following yet. I decided to run a block, even though I was dressed for ambling.

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Part of the problem is that the government asks for too much certainty or argumentation. Let’s put that aside for this essay. Another part of the problem is that the bureaucracies can be slow at processing things that are going to be approved. They might be slow because they have too few staff or because they’re poorly run. The employees might be lazy or overworked. It’s pretty hard to tell.

If you want to speed things up, you might want to give more money to the bureaucracies so they can hire more and streamline things. But you might also worry you have no guarantee this will help, and that it’s unlikely budgets will go back down. Worse, if you give bureaucrats more slack, they might spend it all on further scrutiny. They are, after all, mostly exposed to the downsides of approving things.

So you’re kind of powerless. You want to give the system resources enough to go fast, but you don’t want to just bloat a bureaucracy, and you can’t tell which you’ll do.

Here are two problems you have.

1. Price. You don’t know how much it should cost to check an application against the rules with a reasonable error rate.

2. Scaling with demand. Your agency receives its funding far in advance. If it needs to hire more staff when demand increases, it has to go through a funding cycle.

The latter is fixed by charging applicants enough to cover costs, but you don’t know what the price should be. And the gatekept activities may have positive externalities, and so you shouldn’t pass on the full approval cost to them.

Before we continue, let’s go back to the 19th century. In Germany, steam boiler operators formed voluntary inspection organisations, because they wanted fewer steam boiler explosions (#relatable). They were successful in this, and so this ended up being a sufficient substitute for a state inspection.

These turned into TÜV. In Germany, you need to get your car periodically inspected, but someone like TÜV will do it, rather than a state entity. They also inspect lifts, medical devices, industrial machinery, wind turbines, and more!

So here’s an option: allow private companies to approve things, and then have a government agency audit them post hoc. They can charge their customers. If you want to subsidise, they can get money from the government for each application processed.

This is how we check big firms’ financial statements. You have one of the big accounting firms check them over, and approve it. This, for example, lets you go public. Then, in the US, the Public Company Accounting Oversight Board samples some of the work the accountants have done in a year, and check that.

It’s also how a lot of building control works in the UK. Since 1985, you can have your building approved by a private “Approved Inspector”. Medical devices in the EU can be approved by a “Notified Body” (of which our friends TÜV are one). Apparently this means devices go to market 3 years earlier in the EU than the US.

This helps with the object-level problem (fast and cost-effective approvals) and, I claim, doesn’t regress too badly to the meta-level (how to have fast and cost-effective audits).

On the object-level: you have multiple firms competing. So if a firm can do it faster and cheaper, it will be preferred by customers. If demand increases, they hire more people from their revenue.

On the meta-level: our problems are that things are slow and expensive. The former matters a lot less for retroactive review, so it’s not as bad if there’s a backlog. For the latter, it shouldn’t be much more expensive to audit an approval than to do the approval in the first place. So the market price gives a handle on how expensive the audit process should be (it also helps with getting a sense for how long it should take).

The obvious worry: will approvers strive to be laxer than the other to get more approvals? We’ll assume for now that’s bad. We should obviously hold the approvers liable for the costs of failures. In principle, that should constrain the race. What about empirically?

One of TÜV’s international divisions, TÜV Süd, certified a dam in Brazil (Brumadinho) 4 months before it collapsed and killed 272 people. Apparently, they initially calculated it as unstable, but retried their structural calcs til they got a friendlier answer.

This is bad. Is it clearly worse than governmental failures? I’ve basically failed to get any good data. There are certainly high profile failures with government approvers. For example, Grenfell Tower, a social housing project in the UK, was approved by a local authority but 72 died in a fire there.

Overall, I find this to be quite promising. The current societal approach to bureaucracy can feel quite traplike. Do you try and cut it, and reduce your dependence? Or do you give it more funding and hope that makes it work better? This seems like a more grounded alternative to either, and, unlike many ideas, it doesn’t seem innately detestable to voters. They’re living with it now!

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It happens to everyone: you stop arguing. You can’t care enough to fight, so you’re left listening to everyone being wrong. Or worse, horrid silence.

This need never happen again!

Arguing can be a great game. The other person is laying out their case, and it’s flawed. You’re tingling and impatient. You can feel the vitality of your argument surging behind you, ready to ride with you.

And it’s a game of roles. Your role is the champion of your side. The champion is noble: he acts with a certain rhetorical largesse. And, crucially, he is chosen by fate to win.

Wisdom status: I do this sometimes, and I think it’s fun and fine. Not sure it rises to the level of recommendation tho.

Stay mad

Remember, you don’t agree with the person you’re arguing with.

Probe at that disagreement like a canker sore. They’re over there, being wrong. Think about the character flaws behind their wrongness: their tribalism, their laziness, their self-satisfaction, their cynicism, their gullibility. And think of the consequences! They’re probably going to tell other people — convince them!

Why anger? Because in disagreement, there’s a risk of becoming sullen. Of thinking: “God, they’re so wrong. It’s not even worth my time to correct them”. If you’re angry, the paralysis lifts. Now, you won’t keep your disagreement bottled up, because you can’t; the fire burns away your boredom and indolence. Let the rage agitate you.

If you can’t sit still, you’re on the right track.

Aside

If you’re having trouble detecting initial disagreements, imagine that all of their claims are about to become broadly accepted, that everyone will accept them and plan around them. That should get the juices flowing.

Play high

Remember your champion’s role. Your service to the truth elevates you. Their incorrectness implies that they’re somewhat befuddled. It can be easy to censor that sense, and lapse back into paralysis. Don’t censor! This is easier if you can sense that it’s play. Their character is befuddled. Yeah, that character may be part of them. But they’re leaning into it.

Some modes of truthseeking together are like a forest walk together. You point out a toadstool of evidence; they marvel at a consideration pinecone. You choose your path together.

Argument’s not that. You have a job: finding good arguments for your side. This is your duty. If you were in court, you’d be mad if your lawyer spent a bunch of time presenting arguments against you. So too, the spirit of your position is mad if you get distracted from defending it.

Unlike in court, that doesn’t mean you have to conceal arguments for the other side that occur to you. If they come up, mention them. But focus on your duty: finding where reality tilts in your favour.

Sort of like this inspirational post of words in front of a sunset, but about being kind of cocky:

Wondering if the other person is right is destabilising to this duty. Your correctness implies that they’re missing something. Connect with that; to me a little arrogance enters the character. And then it’s easier to notice the flaws in their argument, and you’ll be sure you have something to say in response. Sometimes it’s easier to solve a puzzle when you already know it can be solved.

If your opponent’s points seem bad, pursue the badness. You can be polite about it. But if it’s hard to come up with a steelman, still press the point. Just say “I don’t think you think this, but are you saying: [strawman]?”. If they agree with the strawman, knock it down. If you’re losing too much steam, knock down the strawman and then let them respond.

Don’t assume they’ve considered the obvious. Feel free to bring up the basics. If they have a sophisticated answer, hound them til they say it. Often, they don’t.

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Give up on arguments, not your point

Though rare (given that you’re right), your opponent may someday soundly defeat one of your arguments. Honour the soldier by prosecuting the campaign.

Outside of argument, I sometimes identify as someone who says their “true rejections” (that is, my real reasons for thinking or not thinking something). But this can be an epistemic trap. My irrelevant argument is defeated, but I don’t want to accept its irrelevance, so I try and change my conclusion. This is dumb.

But in the argument game, you’re not even required to bring up your true rejections. Tempo is king in an argument. If you chose to keep the argument going, you played it right.

The argument might have knocked down one of their subpoints, that’s progress. Some sallies are worth attempting, even if their defeat won’t change your position. Often, this is the part of arguing that feels most bridge-building to me. I’m mapping the other person’s position, and pointing out where it seems weak.

So you were wrong. Concede the point, and reverse up the argument tree to the furthest subpoint you still feel confident in. Be graceful about this, and then carry on from there. If necessary, check if you’re convinced on the main topic. Don’t let yourself be forced into consistency with your previous points. Check whether you’re really convinced. And if necessary, hit a random restart in argument space.

Don’t worry about following their points

To keep the heat up in the argument, you shouldn’t be spending time letting an opponents points sink in. That’s not to say that you can’t cede ground, or even change your overall mind. But this should come from an exhausted checkmate. You and your opponent are dancing together, and you’re trying to waltz through every consideration before the end.

They might make an argument about something you don’t find interesting or that you didn’t fully follow. Respond to whatever they said that seems most central to you. If they really care about something, they can bring it up again. If they bring something up several times, but you don’t understand the relevance, put some heat on them to clarify. If they’re monologuing abstractly, mention when it’s not making sense to you.

Don’t be a dick

You’re trying to keep up the rally, but you’re not trying to hurt the person, nor to win at all costs. Concede lost points clearly and cleanly.

But don’t fold if losing the point didn’t actually change your mind. Sometimes the bottleneck to thinking together is keeping going. Argument is a form of play that keeps things going. Constraints offer creativity, and championing a side is no different.

Stay in the game.

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Sarah: … The police scanner transcriptionists.

Matt: Right! So, given all this sophistication, how did they eventually shut down the Juice Factory?

Sarah: OK, well are you ready for this? Cos this is maybe my favourite part of the story.

Matt: I’m ready; I’m buckled in; let’s go!

Sarah: So, as we just talked about, they had people inside the police department who were dropping hints about planned raids in the area. And in case that fell through, they had compromised some of the law enforcement officials’ phones …

Matt: Including inspectors, captains, even a bureau chief.

Sarah: They were getting up, really up the ladder. And if all that failed, they had someone listening to the police scanner for some immediate warning.

Matt: And they needed this because their operation was pretty noticeable when it was underway.

Sarah: Yep, according to court documents, during peak production, there was over a gallon of water being used a minute, there would have been substantial vapour exhaust, there were delivery trucks. It stuck out if you were a bobby on the beat.

Matt: So impressive with that tiny crew. If I remember correctly, they would shut down when they knew there was police activity in the area.

Sarah: And reopen when …?

Matt: Huh, I guess I never thought about it. I guess they have the schedule for how long the police would be around … except I guess it’s hard to know when a drug bust would end.

Sarah: Yeah, they’re not exactly known for their cooperative counterparties.

Matt: Haha!

Sarah: Haha!

Matt: OK, so how did they know?

Sarah: They would have a guy sit out in a car, and watch the whole thing. Once everyone shipped out, he’d give the all clear, and they’d get started again.

Matt: Pretty smart.

Sarah: That’s what I thought … until I found out they always had the same guy watching.

Matt: They didn’t rotate?

Sarah: Nope. The same guy. And his car had a bumper sticker on the back that said “Panty Dropper”

Matt: No way!

Sarah: Yep. So the police started to notice a pattern. Every raid in that neighbourhood of town, the Panty Dropper would be watching.

Matt: Wow! I mean, if you’re going to go through all the effort of watching these busts, at least rotate the driver. These guys just didn’t think to …?

Sarah: Nope. Nope. It’s one thing I can’t wait to ask Uri Levin himself about, after this short break …

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Matt: Welcome back! We’re going through the wins and the epic fails of the Levin Drug Cartel, and from USP Victorville, we’re joined by Uri Levin himself. Hi Uri! Are we connected?

Uri: We’re connected.

Sarah: So, Uri —

Uri: We tried rotating the drivers by the way.

Matt: Oh yeah? It didn’t stick?

Uri: Listen. How many guys with cars do you think we had? You think we’ve just got an infinite pool of them? Remember, we hadn’t made it to profitability. People were driving their own cars, and some of them were pooling. So we had like 5. And half of those cars, the crew had painted gang symbols on. Anti-police bumper stickers. Shit like that. Do you think that’d work as a lookout car?

Sarah: Might stand out as much as the Panty Dropper!

Matt: Ha ha!

Sarah: Ha ha!

Uri: Ha ha. So we had a couple of cars, right. We tried switching the guy out once. One of the guys who I could talk to a bit. Not all of them are like that. Things get lost in the rapport, y’know? So I talked to this guy, tried to explain a bit. Halfway through the bust, he gets out of his car, wanders over to our place. “What the fuck are you doing? Drawing a straight line to this fucking place?”

“Oh don’t worry about it,” he tells me. “They’re getting started. I waved to the crew when they arrived.”

Sarah: Matt, cover your ears, but I’ve got to ask. What did you do to him?

Uri: Do to him? Nothing. He was the only guy who could work the condensers. It’s hard to get a guy like that. So we kept him around. I couldn’t even chew him out. Didn’t want to seem like I was going soft on a guy who was pissing me off.

OK, so rotating to that guy didn’t work. Who else could we try? My lieutenant? I need him keeping shit on lock on site. We’ve got to keep working on the quiet stuff while they’re around.

Matt: Well there’s your mistake! Just close up.

Uri: Close up? I’ve got guys in from Honduras. I’ve got distributors waiting for material. I’ve got a specialist in from China. Cash is pouring out of me. I’m moving product or I’m dying. You can taste the competitor coming for your customers. Those fickle kids will switch on a dime. This isn’t a business where you keep people waiting.

We’re not sitting on some fountain of endless cash that can just do the sure thing whenever a problem rolls along! We’ve got to try and make it actually work. And then, whichever risk blows up, the people scoff and say “can you believe?”. But what should we have done instead? Where does the Pareto-juice come from motherf—

Noether’s theorem is a wonderful result in mathematical physics. Like Euler’s identity, it connects several fundamental things.

One is conservation principles. Let’s say you look at a really short video of a physical system. It’s almost a snapshot, but there’s just enough extra information that you can see how things are changing. From that little video, you can calculate many properties for it:

1. Leftishness. How much is it, overall, on the left?

2. Yellowishness. Is it rather yellow, or not so much?

3. Energy. What is the sum of (a) the square of the momenta, divided through by twice the mass and (b) the integrals of the forces that would have had to be exerted to move the particles inro place.

4. Cakeishness. A Battenberg? A Jaffa? Twice cooked, or just once?

Some of these properties are conserved. That is, they don’t change over time. Of the list above, only energy is a conserved quantity, though the marzipan does give Battenberg a surprising longevity. A law that says some quantity of a system is conserved is called a “conservation principle”. As well as energy, both linear and angular momentum are conserved properties.

The next fundamental thing: principles of least action. These are a bit further from everyday experience. Here’s how I would think of it.

Let’s go back to our little videos of the system, and the properties we calculate from them. To calculate an action, we take all the little videos, for each we do a calculation to get a property amount, and then we add them all up across all the videos.

It turns out, if you pick your properties right, then in a real physical system, the action will always be minimised. This can be quite a mind-expanding way of looking at that system. You can calculate how it evolves over time by demanding something about a property of its whole trajectory, and not just how each step follows from the last. This viewpoint inspired Ted Chiang’s most famous story (the basis of the film Arrival).

And the final fundamental thing: symmetries. Symmetries are the changes an object is unchanged by. For example, you can reflect something in a mirror. For many objects, they will look different afterwards. But for some objects, their shapes mean that they are unchanged by being rotated in a mirror. Similarly, take a classic five-pointed star. If you rotate it one-fifth of a turn, the object is unchanged. These immunities are called symmetries.

So, what does Noether’s theorem say? Basically, for every symmetry of the action, there is a conserved quantity (and vice versa).

The problem with this theorem … is that it’s rather high-falutin’. I was raised in a universe with forces, and those forces accelerated objects around. Fancy cosmopolitan timeless heptapod universes with minimised actions are not how we do things! To properly understand it, I say, we need to bring the force laws back into the picture.

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Shift symmetry

So, the first symmetry we’ll consider is moving things around. Imagine the whole universe hanging against the velvety backdrop of space. Then you realise the velvety backdrop of space is not covering the end of your kitchen table, so you hold the universe in place with your hand, and yank the backdrop to the side.

Nothing changes about the evolution of the universe as a result of this. If you later decide to pull that velvet in the opposite direction, then it will be as if you did nothing. It could have been that the universe does different stuff depending on where it is in space. But it doesn’t. That’s a symmetry.

Noether’s theorem gives us a conservation law from this symmetry: the momentum of a system is conserved. But what does this mean in terms of the forces in our universe?

Well first: the forces don’t depend on position with respect to space. That one’s kind of a gimme.

The other is that the net force on the universe is 0. If we were born in the 17th century and didn’t have Noether’s machinery, we might say it as: every force has an equal and opposite reaction. That is, it gives us Newton’s third law.

This checks out: conservation of momentum follows pretty directly from Newton’s third law. The change in momentum of each particle is proportional to the force on it. You add up all the forces and get 0 (that’s Newton’s third). Therefore you add up all the changes in momentum, and you also get 0.

Turn symmetry.

The next symmetry is twisting. You decide you want to lay your tablecloth velvety backdrop of space in a different direction. You once again hold your universe in place with one hand, and shimmy space around with the other. You make sure not to put any twists in it. Yes, it would be quicker to just take everything off and start again, but you just spent a morning putting the universe just where you wanted it so you’re going to figure out how to do it this way.

Again, if you turn it first one way, wait a bit, and turn it back again, it’s the same as not turning it at all. The evolution of the universe doesn’t depend on how it’s turned with respect to space.

Here’s the classic Noether theorem conservation law: angular momentum. Once again we want to see what it says for forces.

It means that if two particles are interacting, then the force between them is directed along the spoke between them. That is, it pulls them together, or pushes them apart. Again, you can prove the standard Noether result (of conservation of angular momentum) from this.

Time symmetry

The final symmetry we’ll consider. Again, the universe is on your kitchen table. You’ve been using a stopwatch to map how it changes over time. You reset that stopwatch to zero, but keep it running. The universe doesn’t care. It doesn’t matter what the time on the stopwatch is, only that it’s changing.

Noether maps this to conservation of energy. For force laws, one consequence is that the force laws don’t change over time. If you arrange stuff in the same way at a different time, the forces will be the same.

It also means that the forces can’t have a kind of swirly shape, like this. To be clear, it’s also ruled out by the rotational symmetry rule, so it’s not that exciting. But it’s nice to know that time symmetry also rules it out. (If it weren’t ruled out, you could go round and round in a loop, always getting faster).

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What is comparative advantage? Suppose, and it shouldn’t be too hard to suppose, you are better than me at everything. You are a better baker, a superior speaker, a handier haberdasher and a cooler cucumber. But we can still gain from working together. Maybe, of my meager skills, I am best at baking. So when we work together, it is best for you to handle haberdashery and for me to bunglingly bake. It turns out this is surprisingly general.

Each thing that we do, speaking speeches and cueing cumbers, comes at the cost of other things we could do. Comparative advantage says that whoever gives up the least to do something should do it (for they can get back what they gave up more efficiently through trade).

This comes up in real life sometimes. If you’re running an event, often there’ll be a bottleneck person. They’re the person with all the context and all the relationships. Even if they’re very efficient at folding maps, probably someone else should do it, as that doesn’t need any context.

But it comes up a lot less than people think. Comparative advantage is a theorem: it’s always true. But not every situation has an interesting comparative advantage dynamic. In the event running case, you might think the key person should do nothing but interface with the external relationships and spread information around. If they do anything else, they’re paying a big opportunity cost in those things, and the cost can’t be cancelled by anyone else’s labour.

Yet, it often turns out they should spend some of their last hours directing furniture movers how to layout a space. I claim this will turn out to be their comparative advantage, but thinking in comparative advantage won’t help you arrive at this realisation. You need to know what the project needs.

The vision for a project inflects everything. What is the crucial thing people need to do, and how can space support that? What is the feeling people should get when they walk in the room? How will people connect with each other, and if meals are a big part of that, how should meal serving work?

Often, when you think about some task, it will have a genre, and someone will be tagged with that genre in your head. “Oh, this is a ‘making things pretty’ task. John’s the man for that” or “Ah, someone needs to organise something. Better call Jane” or even “Ah, videos. Right up the alley of those folks at VidCo”. We shall need a word to describe these “genre people”. I shall call them “schmexperts”.

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You might think that schmexperts should do all their genre tasks, and you would be wrong. Projects can only be done by those who are muse-stricken with them. There is some agent who has some particular taste that they’ve built for a project, and will be guided by their yearnings and repulsed by the hot bile of dissatisfaction. In my experience, that can’t be transferred. That agency must be one to steer the project; probably, they will do a substantial amount of it themselves. In my experience, that agent is normally an individual human person, but perhaps it could be a team or other group.

And exactly which project gets done makes all the difference. Value is not smeared evenly across the endless expanse of project-space. It would be an understatement to describe it as lumpy. Rather the value runs in dense rivulets, stopping suddenly and then appearing again in distant origami folds. Suppose two people want to make similar films, but have slightly different ideas of the main topic, its framing, what things have to be kept; those will be the soul of the film.

Of course, if schmexperts are far better at choosing which projects are worth doing, then the problem disappears and comparative advantage (or its brutish cousin, absolute advantage) are relevant again. But the schmexperts aren’t. I’m not really sure why. Maybe just because project choice is very hard, and there’s no real skill there? Or, perhaps because project choice is very domain general, and specific skills don’t help you?

Comparative advantage is true, but only the agent who has an idea for a project can lead it. Ideas do not fall along the lines of schmexpertise. And so the comparative advantage question becomes, “who has a good idea that they care about and will make happen?”

We actually had some committed funding, but we weren’t sure when it would come in. I had been reading a bit about cashflow, and had always felt that I’d not gotten a chance to show off my grasp of gambler’s ruin. The fact that we might hit 0 in a bank account magnetised me.

Maybe we needed different rules of thumb for how we’d spend money this month. We could go around pestering people to speed up our transfers! Perhaps a contractor is happy to consolidate their billing to a later month.

“We can take out a loan,” said my boss. “The money’s coming. It’ll probably be in before we hit zero. But if it doesn’t, we’ll be able to find a loan. We’ll probably pay like 1% for a one month loan. That means money is like 0.2% more expensive this month. It’s not worth breaking the org over.”

This funny little detail of grand strategic import, the magic of the ruinous 0, shimmered and the mirage was gone.

This November, another story. Sometimes I wish to write blog posts; I want to express myself, and have my friends read what I write and talk to me about it; I want to say something that’s of interest and use to people. Or that warms them a little. But once I start typing, the trouble begins.

“Is this too abstract? Is there anything of interest to someone yet? Will they follow what I’m saying and want to talk to me about it?” I sour on my keys. “Should I start the post over? Is blogging even a good way to get what I’m looking for?”

I came up with a fix. I gathered some friends, and proposed a simple plan. We’d write for a few minutes, and then read each other’s works, and leave notes on what we responded to and questions we had and so on. And then we’d write for a slightly longer block, and read again. And we’d build up the length of time we wrote for. From here, the plan got a little bit more complicated and my friends could not be cajoled to pursue the promised land.

But the first part, in which we got some clues of feedback earlier, worked quite well. I wrote drafts of several blog posts in an hour, and I felt that each had something a friend might like to read.

There’s a pattern here: a threshold becomes a slope. The hard line of the zero becomes smoothed out. It is different below zero dollars; you have to organise a loan and pay interest. But it’s not a dramatic cutoff when the money is coming. Publishing a blog post isn’t the only step in a conversation. You can find a way to move some of the conversation earlier.

Here are two other quick examples of a threshold becoming a gradient.

One, gig work. Without that, you have to hire an employee (or get a full-time job). With gig work you don’t. You can pay for the part of the work you need. Imagine if you had to have a full-time plumber in order to get help with a leak in your apartment.

Two, renting a car. Rather than owning one, you can pay for the time you need.

Both of these cost more per minute than the full-time or full-ownership arrangement, just like going below zero costs more. But now it’s a slope; you have the choice of stopping part of the way. I call these ramp-making phenomena “smoothers”.

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When I was a teenager, I would see people sitting on grassy hill sides along a public path. But while the path was public, the hill wasn’t; there was even a small sign to that effect! And I would be agitated. Does ownership even mean anything if people are doing this? It might be one thing if they were ne’erdowells, breaking the law with spite on their lips. But, as far as I could tell, people thought this was just the proper order of things.

I can understand that a little better now. My understanding of property rights has enough flexibility to enable a young family to sit on the side of the hill. Maybe I think the owner should be able to kick them off, but I think it’s fine for the family to assume it’s OK until actively told otherwise. They don’t want people tramping off the path and up onto their hill, but a toddler having a snack on a liminal tuft of soil might be OK.

There’s another case lurking in expected utility theory. Suppose you have three choices to pick between: apples, bananas, and carrots. There are no gambles that sometimes pay out in apples, sometimes in bananas. Just these choices. Then, even if you prefer apples to bananas to carrots to apples, the worst that will happen is you go in a circle. You start with carrots, and then you switch to bananas, from there to apples and back to carrots. A bit silly, but no big problem.

But once you add in probability, things change. If I can add in lotteries (a 40% chance of apples, a 60% chance of bananas, and so on), and I can create all kinds of in-between options. You prefer apples to bananas, and you prefer slightly sour apples to bananas. I can make things a little worse every trade, and the cycle spirals downwards.

Being consistent in the face of all the choices that probability adds means I’ve got to be able to represent you as having a utility function. When I can make an option a bit better (a sweetening) or a bit worse (a souring) there’s a lot of structure you have to have to your preferring. And that structure means I can represent you as having a utility function. This is one of the ways probability can be a smoother.

Smoothers, of course, are leaky abstractions. It is in fact more costly to get your employee time in high-optionality piece meal chunks. Breadcrumbs of feedback on one’s first sentences are nice, but the experience of reading the final blog post will be different in kind and not just degree. If the chooser is consistent, and the choice set is very complete, the utility function is an accurate representation. But even granting that, it might not be an illuminating representation. The cost of cashflow is a bit different below zero than above, even if the balance sheet looks good.

But perhaps there is an easier motivation for schlepping than the desire for greatness, something that flows almost without limit, spite, bitterness, and the desire for revenge.

Curtis Sliwa was vigilante. He was, naturally, also a radio show host. He had founded a group called the Guardian Angels. They would patrol the New York subways, and try and dissuade crimedoers with their scarlet berets (with matching jackets). They would let people sit next to them if they were scared. And, because it was the 80s, they were trained in karate.

So, with the fame from founding this group, he had a radio show. On it, he had a section called “Mob Talk”, regarding the activities of the Mafia in New York. In this segment, he called members of the Gotti (allegedly Crime) Family “criminals” and “knuckle-draggers”. John Gotti, the head of the Gotti Family, found these remarks to be very disrespectful. And, it seems, felt somebody should “talk this over” with Gotti.

In April 1992, 3 men with baseball bats attacked Sliwa outside his home. They hit him with the bats dozens of times. But Sliwa survived.

Think about this: Imagine you’re John Gotti. Imagine someone has publicly disrespected you. You try to put him back in his place by attacking him, but he survived. The good old ambush with baseball bats method. What do you do? If you answered “spend months constructing a fake taxi that you will trick your victim into entering, having modified the door handles so it was impossible for him to exit, and then your son pops out from the passenger foot well, where he was hiding, and shoots him,” you are correct.

Sliwa had a pretty regular schedule. He had to get from his apartment to the radio studio in order to make his radio show in the morning. He left around 5am. Every day he would take a yellow New York taxi cab. The Gottis observed this and figured this out and hatched their plan.

They made a special taxi; some sources say they modified a stolen taxi, others say that they more-or-less built it from scratch. But they made it so that the handles in the back of the door didn’t work. So once Sliwa was in, he wouldn’t be able to get out.

Of course, as any cabby will tell you, you can be in the right place, the right time, right in front of the punter’s nose, and still not get the fare. It took multiple attempts before he got in the car. Once he was in, John A. Gotti, the son of John Gotti, emerged from where he was hiding and shot Sliwa. Sliwa would have tried to escape when he saw the gunman, but he couldn’t, because the handles didn’t work (some say they ripped off, others just that they didn’t work).

I would say this is a pretty impressive commitment to the bit. Building out a faked car is a substantial amount of effort. Staking out your enemy so you know their whole routine is a substantial amount of effort. Trying multiple times to entice them into your rigged car that you’ve already presumably spent days or weeks modifying is a lot of effort. It takes mental fortitude when, after you’ve created your special fake car, and hidden your son in the footwell, not to lose heart when the person you’re trying to assassinate just wanders past your taxi cab.

This is an impressive amount of shlep to push through. Most people wouldn’t do that to make a lot of money, but defending one’s good name? Now that’s worth a shlep.

(Sliwa survived. He jumped out of the moving car. Through the front window. He ran for mayor of New York in 2021 & 2025)

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“Mr Imbersley,” said Mr Ammy.

“Mr Avvy” said Mr Imbersley.

“Mr Imbersley,” said Mr Avvy.

There was a moment’s pause.

“Mr Avvy,” said Mr Ammy.

Mr Avvy, who had been sat next to Mr Ammy in the same room for the last couple of hours, didn’t know what to say. After a moment, he ventured: “Hello”.

That business concluded, Mr Imbersley launched into a little speech. “Well, Mr Ammy and Mr Avvy, I don’t know if you have been down to the garden recently, but by every one of my 212 legs, it’s in quite a mess at the moment. The gnomes are all topsy turvy.”

“Yes, by every one of my six legs,” said Mr Ammy, who was very impressed by Mr Imbersley. (Mr Avvy only has two legs, though he did have hands on the ends).

“I thought you two gentlemen,” said Mr Imbersley, “would be the perfect folks to try and get that cleaned up.”

“Yes, Mr Imbersley,” said Mr Ammy vaguely honoured.

“Yes, Mr Imbersley,” said Mr Avvy, copying his friend.

“When the gnomes get topsy-turvy,” explained Mr Ammy, who was wearing a hard hat to protect himself from the gnomes tumbling through the air, “it’s because the air has gotten very dusty. Look at that pile of rugs!” In the middle of the garden was a pile of very old, very dusty rugs. “So we need to suck all of the dust out of the air, and then things will be right as rain.”

“Very good,” said Mr Avvy. “Let me get something to help,” and off he went waddling on his hands and came back a few minutes later with a pair of bellows.

“This will do fantastically good work, Mr Avvy” announced Mr Ammy. With a flourish he opened the handles and sucked in a bellowsful of air and then blew it into the bottom of the stream.

“When it bubbles back up,” said Mr Ammy, “it will be clean and dust-free.”

Mr Ammy labored at this for some time.

“I don’t think it’s working,” worried Mr Avvy.

“Have a little bit of patience,” said Mr Ammy. He kept sucking up the air and blowing it into the stream until the sun had over-crested its zenith.

“Look,” cried Mr Ammy. “That little fellow is sitting down!” And it was true. One of the gnomes was sat on the grass, looking for all the world just like a statue.

“It’s working!” cried Mr Avvy.

“Yes,” said Mr Ammy. “It’s working.” Mr Ammy kept at it for the next several hours, sweating and heaving as he tried to suck the dust out of the air. And, slowly but surely, more and more of the gnomes started to sit on the grass. Mr Avvy only had to wipe their little footprints off his goggles every ten minutes or so by the time Mr Imbersley arrived.

“Well, what’s this? What’s this?” cried Mr Imbersley. “I set the two of you to a task, and you spend all day lollygagging and have barley made a dent in it!”

“That’s not fair!” said Mr Ammy who had spent all afternoon toiling under the sun.

“Yes, that is not fair!” said Mr Avvy, who had not. “We’ve been sucking the dust out and putting it in the stream. It’s the dust that makes the gnomes go all topsie-turvy, you know.”

“Yes, I do know,” said Mr Imbersley. “But the air will stay dustly as long as that pile of old rugs is here!” The pile of rugs was twice as tall as Mr Avvy and 5 times as wide as Mr Ammy. “Why didn’t you just clean the rugs? Or even move them?”

Mr Ammy looked at Mr Avvy, Mr Avvy looked at Mr Ammy. No one had anything to say.

“Never mind,” said Mr Imbersley. “Why don’t the two of you go home? I’ll clean up the rugs, and I’ll see you tomorrow.”

The next day, Mr Imbersley came and found Mr Ammy and Mr Avvy. He was wearing rather splendid slippers on each of his 212 feet.

“Good morning, Mr Ammy and Mr Avvy!” he crowed. With a flourish, each of the slippers flew off his feet and landed in a neat pile. On the bottom of each slipper, explained Mr Imbersley, is one of the tasks that must needs be done to prepare their part of the shipment to Go-Up-And-Get-Over Land.

“It only sails on the new moon,” explained Mr Avvy to Mr Ammy.

“Yes, so I had heard,” said Mr Ammy, who had not.

“I trust the two of you to get things ready for the shipment.” With that, Mr Imbersley crossed over one part of his body and under another, and then was gone.

“Oh no,” cried Mr Ammy, “there’s far too much to do. How are we ever to get through this stack of slippers?”

“Well said,” Mr Avvy, “there’s no point complaining. If we have to do it all, we have to do it all. Talking about it will just make it take longer.”

“How right you are,” said Mr Ammy, who was very glad to have a wise friend like Mr Avvy.

Mr Avvy was a big believer in esprit de corps, so with a little smirk and a wink, he shoved his fist into the middle of the pile of slippers and yanked one out, causing a glittering cascade of chaos.

“Right,” he said, “we’re to make a cake. Let’s get started on that.” So Mr Ammy and Mr Avvy pulled down the big recipe book from the shelf and opened it up, leafing through its sticky pages until they got to the best spread of all: The Cake.

“Alright, Mr Ammy, let’s write down some ingredients,” said Mr Avvy. “Right you are,” said Mr Ammy.

And the list of ingredients was like this:

• three sarapangs

• two welches

• five spoonfuls of gritty ha-ha’s

• a wind in a bottle

• and a big gulp

They took that list to the grocer who, thank goodness, had everything in stock. “What are you making this cake for?” asked the grocer.

“Can’t talk now!” said Mr Avvy! And off Mr Ammy and Mr Avvy hurried. They followed all the steps in the recipe book, checking each one twice to make sure they got it right. After all, if they’d had to start over, they’d have had no chance in getting through the slippers in time.

“You can lick the bowl if you like,” said Mr Avvy with saint-like generosity.

“No, no,” said Mr Ammy. “I’m quite happy for you to lick the bowl.”

“If you say so,” said Mr Avvy. And in a flick, all of his tongues had licked the bowl clean.

They put the mixture they had made in the HumMaker and there it stayed until it was golden brown. While they waited, they were busy making icing.

Out came the cake, on went the icing. “What a wonderful cake!” said Mr Ammy.

“Yes, we’ve done a great job,” said Mr Avvy.

“What’s this?” cried Mr Imbersley, who had just at that moment poked his head and front eight legs in through the window.

“It’s dawn time. The shipment has already left. We missed it, and you didn’t do anything that mattered!” said Mr Imbersley.

“Well, we made a cake,” pointed out Mr Avvy. And, we must grant, he was quite to rights on this point.

“The cake!” said Mr Imbersley. “Why would you work on the cake gefore you worked on the jewel-studded tiaras or the handpressed flower books?” despaired Mr Imbersley.

“Well …” began Mr Ammy “We thought we had to get it all done!”

“Of course you had to get it all done!” said Mr Imbersley, “But if you weren’t going to get it all done, you should have at last done the important things.”

“I’m sorry, Mr Imbersley,” said Mr Avvy.

“Oh well,” Mr Imbersley sighed. “Mistakes do happen. I’ll see you tomorrow.”

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“Today did not go right at all!” said Mr Ammy.

“And nor did yesterday,” agreed Mr Avvy gloomily.

“I don’t understand why,” said Mr Ammy.

“I do,” said Mr Avvy. “I’m just having a hard time putting words to it.” Mr Avvy was having just as hard a time putting words to it as he would if he didn’t understand why at all.

“Aha!” said Mr Ammy. “The days went wrong because we did the wrong things.”

“Yes, yes!” said Mr Avvy.

“Well, that’s a relief,” said Mr Ammy. “Let’s not do that tomorrow.”

To be continued

I think about this concept a lot, and wish you could too, if you chose. Then we could talk about it, or I could use it in essays like Pareto Juice II. Even if you know quite a lot of math, you might have happened not to know this one. Partly, that’s because it suffers from one of the worst pedagogical mistakes I know of in math teaching. And partly that’s because it naturally has a bunch of prerequisites that aren’t on the normal course of learning.

I think I can explain it to you without having to go through all of the mathematical prerequisites.

The first thing I want you to think about is hills. Here’s a picture of a hill.

We want to go as high up this hill as possible. But we’re fixed to be on a particular path on that hill. We’re trying to find the highest point on that path. The path might go up and down as it goes round the hill, but somewhere it’s at its highest.

Here’s a second hill.

Imagine that the hill are overlapping with each other; this is a ghost hill, that overlaps with the other one. This hill represents the value of some resource. The higher the point on the hill, the more of the resource we expend. And the lower we are, the less.

We might call the first hill the objective hill, cos it represents a thing where we want to get as high as possible. The second hill is the resource or constraint hill.

For example, suppose we’re at a grocery store, trying to decide how many apples and how much bread to buy. Those things both have some costs associated with them. Then we can imagine the ground underneath the hill as like a map of how much bread and how many apples we’re buying. As you move north, you’re saying you buy more apples. As you move east, you’re saying you buy more bread. The height of the hill is the total cost. If we have $20 to spend, that will mean we have to end up on those points that are exactly north enough and east enough that the total cost is $20.

(This is a pretty weird “hill”; it just slopes up and up as you go further north and further east).

So, when have to expend some fixed amount of a resource, this represents a path around this second hill that’s at a constant height the whole way round. We call paths round the hill that are at a constant height “contour lines” or “level sets”. Here I’ve illustrated some.

There’s a constant height contour line on the second hill, and that contour line is sitting above some path on the ground. When we go back to the first hill and pull that path from the ground back up, it will describe a path on the first hill. That path might not be constant height instead it might go up and down in a wiggly way. This is the path that we’re constrained on. Here I’ve shown what the paths we drew on the second hill look like on the first hill.

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Now, I’m going to tell you some specific things about the kinds of hills we’re going to think about. Each of these hills is only going to have one peak. As you move away from that peak, you’re always going down. You could be going down at different rates. You could move slowly along a shoulder that’s flat or more or less flat, but you’re never going to go back up again. That’s one of the rules for our hills.

The second special thing about these hills: if you zoom in very, very close to the side of the hill, it looks perfectly flat. There are no points where there’s a sharp turn where it’s going up and then suddenly flattens out or anything like that. Everything is smooth enough that when you get in very close it is completely flat. You can imagine that we’re approximating the hill with little flat hexagons (though we’re choosing the hexagons so you’re never looking at an edge of one).

Let’s think about the character of contour lines on hills. In particular, if you’re on one of them, and you ask, “What is the steepest direction from here? If my step is a fixed size (ignoring the height change), where should I turn so that the height changes the most?” Well, let’s see. Let’s pick a random direction you could go.

Because the hill is locally flat, the amount up you go when you take a small step can be broken up into parts. I can ask “how much would you go up if, starting from the beginning, you went a little bit north?” and “how much would you go up if, starting from the beginning, you went a little bit east?” and add them up. If the ground was curvy, this might give you the wrong answer. It would always give the right answer, even in the curvy case, if I asked second “how much would you go up if, starting from a little bit north of the starting point, you went a little bit east?”. But here we get to ask a simpler question.

North and east aren’t special. You could break the vector up into all sorts of directions. In particular, we could break it up into its part parallel to the contour line, and its part perpendicular to the contour line.

The part parallel to the contour line doesn’t go up at all: that’s what it means to be a contour line!

The part perpendicular to the contour line is where all the change in height is going. And so, if we don’t want to waste any of our motion in changing the height, we should step directly in the perpendicular direction. This is generally true.

On a contour line, the direction of steepest ascent is perpendicular to the contour line.

But actually, this argument generalises. Suppose we’re back on the first hill, on one of the bumpy wiggly lines around that hill that corresponds to the contour line on the second hill. Now, we want to know, on this path, what’s the direction of steepest ascent? We’re not talking about how the resource function changes, like we were a second ago. We’re talking about how the objective function changes. And actually, this can change as we go around the path. Sometimes, moving along the path will get us higher. But at the highest point, neither moving forwards along the path, nor backwards, will get us higher.

At the highest point on a constraint, the direction of steepest ascent is perpendicular to the the constraint curve.

And from these two things it follows:

At the highest point on a constraint, the direction of steepest ascent of the constraint is parallel to the direction of steepest ascent of the objective.

(This is exactly the condition encoded by the Lagrange multiplier equation ∇f = λ∇g)

That’s the core idea behind Lagrange multipliers! You might ask, “what’s the multiplier part?”. The multiplier part is the ratio between how first the objective function changes and how fast the constraint function changes, when you’ve gotten to the constrained optimum. It’s a pretty useful number: it tells you how much relaxing the constraint a little bit helps. Can you have a much better shopping trip if you get a bit more money, or does it not really matter much?

I care a lot about Lagrange multipliers, but I’ve not been able to put the why that clearly into words yet. But hopefully this helps with the what.

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Let’s take a turn into the Forbidden Section, and crack open the LessWrong samizdat:

A recent comment I wrote on another forum described how to convince people of the value of a technique. Read the comment for details, but the short version is: display something which you made by using the technique. If the thing is clearly cool, then the technique recommends itself—“by their fruits ye shall know them”.

But what if the technique is a meta-technique? That is, what if the things you make with it are themselves techniques? A technique is not obviously cool, that being our original problem…

Again the solution is simple: go down another level. Display some cool thing you have made or done, using a technique which you have made by using the meta-technique. Thus the first-order technique recommends itself by its product; and the second-order technique recommends itself by its product, which is the first-order technique.

— Said Achmiz, Key lime pie and the methods of rationality

In my gloss, Said is talking about this problem. As goodness lives at the object level, if something is good, it ultimately pays off there. Either directly, or because it enables something that pays off in the object level, or it enables something that enables something that pays off there, and so on.

I think this is true. But you can end up with a mountain of indirection, where it’s unclear whether anything at a given level is responsible for anything at a level below. Credit assignment is hard and the world is big and tangled. This post is about a way of designing systems of abstraction in a way that helps them remain tethered to what ultimately matters. This particular recipe for system design has the advantage of being somewhat systematic.

Skip connections

This is the example that I have in mind, which I use as a metaphor for thinking about this general pattern. It’s helpful but not essential for the post, so you can skip it if you want.

Neural networks are basically stacks of simple functions. Exactly the details of the simple functions is what you learn in the course of training them, and the simple shape is something you decide up-front.

In order to have that training go well, it turns out it’s helpful to add some shortcuts to the stack of functions. That is, take the input to some of the simple functions and add it to its output.

Without these shortcuts, the connection between the feedback signal and the early layers is super distant, and often numerically translates to very subtle signals. And it makes it harder to stop and not change something: if, at some point, the neural network has some state that should be passed on unchanged for a while, it’s tricky for the optimiser to find the function that doesn’t mess things up. With the skip connections, it’s easy. The undistorted signal is already there, just with some noise on top that can be quietened.

I mostly think about the case when the input from every function is added to its own output. That does a lot of interesting things to the structure of the neural network. For example, the input of every function also flows all the way to the output unaltered.

So the initial input flows all the way to the output unaltered. Then the output of the first function (which is the input to the second) flows all the way to the output unaltered and so also for the output of the second function, and so on.

That means that the output of early functions are directly represented in the output of the overall function. They’re just combined with other outputs directly via addition.

This apparently massively increases the depth and complication of the neural networks you can train. I don’t know whether anyone knows exactly why this happens. One story: the early layers are being trained to predict the output directly from the input. They’re only very simple functions. So they basically learn linear regressions and things like that from the input. In transformers, they might learn to be n-gram models for small n.

I think it should be clear that this phenomenon can be metaphorically extended to explain everything about society, life, philosophy, organizations, and epistemology.

The Skip Connection Theory of Everything.

The Skip Connection Theory of Everything (SCToE, pronounced “skoe toe”, so as to rhyme) has two tenets.

1. You should strive to maintain a brute tethering to unintermediated (and unorganised) data about reality

2. More complicated abstractions should be built on top of abstractions that already work by their own lights, like how later layers are built using the simple models of earlier layers.

The first corresponds to the way skip connections create direct flows from early input to later layers. The second corresponds to how earlier layers are incentivized to be good direct predictors, even ignoring the later layers that will make use of them.

Here is a mere sampling of the domains over which the SCToE (remember, “skoe toe”) grants absolute mastery.

Epistemology

Epistemic spot checks are where you take a work, you find a place where it makes a clear checkable claim, and then you go and check it. You can think of the work you’re spot checking as an edifice built on top of observations and inferences and inferences from those inferences. You’re trying to assess whether these final inferences are correct, and to do so, you’re descending all the way done to a checkable piece of reality and making sure that checks out.

A related idea: when I’ve heard a claim from someone and might pass it on, I often try to do a little due diligence on the claim before doing so. I certainly don’t always do that, especially not doing all the reference-chasing down to the original source. But I hope that this has good effects if it is universalised. If at each point, people go back a little along the chain of evidence, it becomes harder for claims to become completely garbled through a game of telephone.

Math & computing

Interesting mathematics is often built as a generalisation of some math that was already useful and interesting to explore. An obvious example is the tower from numbers through vectors to matrices and tensors and differential geometry.

Now these things have been worked out, I like to look at some of them through different lenses than of increasing dimensionality or other abstractions. For example, it’s nice to think about matrices as linear maps. But I think a reason this stack of mathematics has worked so well is because each stage stretches from something that worked out before.

Here’s another case: escape hatches in programming frameworks. Sometimes, when you’re doing programming, you need to work with a system that is powerful and flexible, but it has a lot of sharp edges. It might not mesh well with systems you’re already using. So people often use a framework that wraps up the sharp edges and makes it play more nicely with what they’re doing. For example, it might make it easier for automated systems to keep track of if the shape of data going out of one place is what another system expects to be coming in.

Classic examples here are web development frameworks, ORMs, parser combinator libraries, and so on.

But all abstractions are leaky. If you want to do something unusual, you might need to dig into the implementation details to build your custom solution. The nice soft wrapping around the outside might stop you from interfacing with the cutting edge when it’s time to get into the nitty gritty.

So wisely designed systems often provide some way of bursting through the wrapping, and getting to the raw material underneath.

Work

In some workplaces, there are hierarchies. Someone reports to a manager who is in turn another manager’s report, and so on. And, in some of those workplaces, people will have one-on-one meetings with their manager. This is a high-fidelity feedback signal between the report and the manager.

But if you have a towering layer of delegation, things can slip. The leader has some clear intention for an outcome and strategy. The people on the frontlines have detailed understanding about what’s happening, which should shape both the goal and the plan. There is in principle a channel of information that can flow all the way up the hierarchy. But there’s plenty of space for distortion at each level. Like in the neural network, it’s hard to learn the identity function from a leader’s intention to object-level action, or indeed from object-level observation to a leader’s vision.

Skip level one-on-ones are where someone meets with their manager’s manager. This provides another layer of more direct feedback throughout the organisation. I envision extra cables pulling a tensegrity up from the floor.

Another example: suppose you have some ambitious plan. At the end, the plan is supposed to have done something good. You have a thesis: do X, achieve Y. Consider trying to find a version of your plan where a smaller version of X achieves a smaller version of Y. This can stop your plans drifting from the actual mechanisms of the world.

Also

Aggro is the foundation

Citations should cite the ultimate source of a claim, either instead of or in parallel to the proximate source

I’m interested in what future surgery might look like. This is a quick off-the-cuff attempt to babble from first principles about it. I don’t look stuff up or come to many answers; I mostly try and think about the problem a bit myself before I hopefully go on to look into it.

Questions

Will we need to cut people open with big slices, or will it be small pinholes, or will we not need to cut them at all? If it’s pinholes, will we be able to worm through the inside of the body without cutting or dicing it, or will we have to still make some internal? Will we always need general anaesthesia, or anaesthesia in general, or can we be precise enough that it doesn’t really hurt? Will we be able to make the wound healing from surgery faster? Or will we just avoid infliciting wounds on people?

To think about this, it seems like there’s a lot of stuff it would be helpful to know. For example, what kinds of things do we currently do with surgery? Here are some that I know about: sometimes we remove things (like tumors), sometimes we sew things together, sometimes we just abrade something a bit, sometimes we add some support to something that’s already there.

On removing

If you take something out, does it strictly have to come out, or is that just worth doing because we already have a big opening? Could we just break it up internally? Or, can we take it out in bits? I understand that warts are sometimes treated by removing their blood supply. How generalisable is that? If we cut off a tumors blood supply, will it simply die.

If you just cut something loose, my guess is that it rots inside the body in a potentially bad way; there might be a way for bacteria to find it to grow on. If you just cut off its blood supply, maybe it’s not as bad? Because, I suppose, the cells sort of metabolise a bunch of their contents and starve, and there’s not an easy rupture for bacteria to get in.

On sealing

If you start cutting into something, how bad is it for the blood to spread around inside? If it’s quite bad, then we really need to sew or cauterise as we go, but if it’s not too much of a big deal then maybe we can, for example, cut something up into chunks and funnel it out through a small hole.

Suppose you’re putting a tube inside somebody to do some surgery. If you want it to snake around between their organs, how much machinery do you need to put inside of it. You could put tendons inside of it that you tension, but maybe you only get one curve per tendon. You could also put little motors that bend the tube along its length, so its more like its articulated at joints.

You need to see the space where the surgery is happening. Even if a robot is doing it autonomously, it needs to understand its environment. It could have cameras, or maybe we could do sensing from outside with ultrasound. It might also need something to clean the cameras.

On swarms

I’ve talked a bunch about having a flexible tube entering the body through a small incision. But an alternative would be to have many little remote controlled, autonomous robots flooding the body. It seems that the venous system is widespread and easy to (relatively) non-invasively access. Could we deploy robots that way? How much work could they do and where would they go when they’d finished the job?

On healing

Can we make the healing process after surgery much easier, perhaps by depositing pre-cloned, pre-grown replacement tissue? How does tissue get integrated into existing tissue? I normally imagine it growing out from damaged tissue, but if I had a bit taken out of my arm, and then recovered the missing flesh and put it back, it seems like that might be easier on my body than having to grow the flesh anew.

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They look normal, but they’re slightly unfair. And they’re unfair in a clever, subtle way. If you roll them enough times, you’ll find that snake eyes — two ones — comes up 1 time in 35. All the rest seems almost normal, just a hair less probable. But snake eyes: it comes up slightly too often.

Now, I can smuggle these dice into the casino where they work, and make sure they end up at the same craps table as you. And if we put our chips on snake eyes, we’ll be raking in the expected dollars. No guarantees, of course, but bring your bankroll, and we’ll get away laughing.

… Ah man! Good work at the table, but we didn’t get any snake eyes. That’s the way it runs sometimes. I mean, we only have a 1 extra hit in 1260 rolls here. The EV stays positive, even if we’ve had a losing streak.

… Sorry you’re so down, bro. Ah, you borrowed some money? I mean, it was positive EV, but I’m not sure I’d have done that. Anyway, I’ll buy you lunch.

VCs lionise plans with a lot of upside potential

A lifetime of taking bets that have a small probability of a huge upside might lead to way more meaningful change than a lifetime of taking sure things. But, if you’re open to being pitched on things that are unlikely to work, it makes you pretty attractive to will-o-wisps, who can lead you down damned paths, where there’s not really any value to be scrounged.

Ah, you’re willing to take the long shot? Very wise, my dear, very wise. There are few with the clarity of foresight that you have to do so. And I have just the longshot for you. No guaranteed payoffs, of course! That would be a scammy get-rich-quick scheme, or worse, a dull grind. But for a thoughtful creature like you, I have just the thing.

It will take a while to pay off, so you must stay the course. Some become worried or dejected along the course. But if you stick it out, then the rewards can be great. It is not guaranteed to work at any particular point, so you must keep trying. Or I may come up with another path for us to try and take. And many of the benefits will not even fall to us, for we are noble of mind and heart, and we give to others who we will never see.

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Being open to taking longshots, being open to plans that take a long time to pay off and being open to distant or diffuse benefits you can’t observe, are all things that make you vulnerable to will-o-the-wisps.

Also, these could be valuable plans! If you can help a lot of people a little, that can be a huge deal, and may be the main kind of leverage available to you. Not all plans pay off quickly, and many positive EV gambles are not that likely to pan out.

I want to avoid being led astray by wisps. And I also want to be able to think and plan, and not just do what I can already see working. I’m not sure how to sail between this Scylla and Charybdis. Here are some options:

1. Just cut off the risk of following wisps. Avoid plans with uncertain, diffuse, distant, delayed benefits

2. Find contexts where it’s safe to do those plans because there aren’t any will-o-wisps around. But this can be tricky, because wisps are not always malefactors. I think wispiness can creep in among friends, when a plan doesn’t really make sense but offers something everyone wants.

3. Refactor plans so that they express some of their value in certain, observable, immediate benefits. That value should be at least enough to pay back the effort they’ve demanded, even if most of the hoped for value is in the future.

I think (3) is more doable than my intuitions credit. I don’t know of any simple argument for why this must be so. The best I have: there are a lot of degrees of freedom to acting in the real world; plans are rarely constrained enough that there’s only one path forward.

Here’s an example of refactoring a plan. Sometimes, I get invited to parties. And some of my best experiences have been at parties. But generally, I don’t like them. I often have a bit of a back-and-forth. I tell myself: parties are good for seeing your friends, for meeting new & interesting people, for laughing and making jokes, for dancing. I respond: they’re often a horrid wall of pain and boredom.

But I don’t just need to eat my party vegetables. I don’t know what specific things I like at parties, or what specific moods I have to be in for them to go well, but I expect there are some regularities there. It’s a false dichotomy to suppose my options are either to stay home or follow a wisp to the party and hope for a good experience. There is value in events, and I could try and structure things so I get that more explicitly. I could think about whether I’ll get what I want at a given party, and then try and pursue it. Or I could run my own events, that will structurally provide the things I’m looking for.

Here’s another example: sometimes I think we should impose a 100% land value tax. Yes, it’d be a shame that it’d destroy the value of many people’s retirement assets. But c’mon! Don’t they know that we have to do this in the name of resource efficiency? Or, maybe we could figure out some other way around this situation. Maybe the land value tax could go up slowly, so people have time to react, and the NPV isn’t destroyed in a single blow. Maybe the land value and the property value could become unbundled, so fewer people are holding their retirement in land. Rather than demanding we all walk through the desert to the promised land, I could try and bring pieces of the value earlier, or even just shorten the desert.

I don’t know that it’s always possible to do this. But I think there are biases against doing it. Some of these might be structural to cognition: fear of weighing down a plan with too many constraints, or a belief that sacrificing certainty might be magic enough to achieve ambitions. Some might be unhelpful memes: the wisps like it when people are prone to follow their lights. For now, I intend to try and tread on surer ground, and see how far I can get.

Compounding Resource X can also eat your freedom and pursue its own intrinsic ends.

Imagine you have a small apple orchard. You pick the apples and sell them at market. With the money you make, you can more than pay for fertiliser and utilities for your home, your clothes and food. So you have some extra money to spend. And you use it to buy more land and more rootstock and scions. You make even more money with each harvest. And you keep reinvesting, and eventually you have a great empire of orchards across the state, with 1,000s of full-time employees and 10s of thousands of seasonal ones.

What resource compounded here? In our simple story, many resources grew exponentially. Your land, your trees, your money, your farming equipment and irrigation. I’m tempted to say that money is your compounding resource here, but, if you’re trying to get market-beating returns, then it’s worth noting that all the rest of the resources are necessary. You have one specific money-compounding machine (and indeed, tree-compounding and land-compounding machine): your fruit business. The resource doesn’t just compound on its own, but requires a machine to be carefully maintained and expanded as you work.

As the farmer, your life will be completely different from when you started. It will not involve apple-picking or travelling to a farmer’s market. You will manage people, you will look at spreadsheets, you will have long calls with lawyers and potential buyers. Potentially quite fun stuff! But different from where you started.

This is generally true. If you have a resource X that compounds a lot, your efforts will become largely about maintaining and managing it That’s where you’ll invest your skills, your habits, the ways you know to organise your time, the places you get meaning from, the things people that you talk to.

And not only that, if it compounds enough, it will just be impossible for you to handle it yourself anymore. There’ll be other people, there’ll be organizations that are investing in it even though they don’t directly have control over it. Even if you try and lop the head of the machine off, even if you leave and no longer tend to resource, it will continue on its own for a while. Perhaps you were the secret sauce that helped enable the compounding, and the resource will be spent down slowly. But there’s still big bundle of resource, likely trying to preserve itself, and perhaps committed to things that you would rather not see done.

Compounding resource X is not necessarily flexible. It might enable something unusual, but you might not be able to change or stop what unusual thing it does once you’ve started.

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I shifted a little on the red PVC sofa in his front room. “Well,” I said. “I’d really like a better job. Maybe something in tech. And it could sound cool at parties. That’d be good! But …”

“But what?” asked the sorcerer.

“I don’t really know how to. I don’t know what I’d do really. I’ve looked for jobs a bit, but it’s hard. I’m … scared. My current job gives me enough money to live. I don’t have that many savings … I’m not sure if I could manage without it.”

“Good,” said the sorcerer. “We can use that. You must sacrifice your job and your safety and hand in your notice at once, and then as soon as feasible after you have done so, cut open the pad of your finger. That is all. Once you have done that, return to continue your instruction.”

“Do I just use, like, a kitchen knife or something to cut my finger or …? Sorry, I’ve just not really done bloodletting before.”

“Buy a scalpel off Amazon. It’s what they’re for after all. Now go! The F1 is on!” And he swiveled his lazy boy away from me and clicked the television on.

“I’m sorry, Greg. It’s just time for something new.”

“Well, I’m sorry to hear that. Sorry for us anyway! I’m excited for you though, mate. What’s the new thing?”

“Um. There are a few things. There’s like one thing with some blokes … some friends from uni, actually, where we might start a thing with … pictures. Anyway, I’ve got to go!”

“Been good working with you, mate.”

“Yeah”

“We’ll do a send-off for you next week.”

“Yeah, yeah, sure. Okay.”

I headed straight for the bathroom. Even the embarrassment and shame of having made up what I was going to do next didn’t mask the thrill of embarking on my first sorcerous rite. I fished the scalpel out of my jeans pocket, as well as the single-use alcohol wipe I’d prepared. The sorcerer hadn’t mentioned that, but after talking to ChatGPT a little it had seemed wise. I wiped down the blade and pressed it against the pad of my forefinger. Was the forefinger the right finger? Had he said finger or thumb? Hopefully, either one would work. I didn’t know what I’d do if I’d just quit my job and I didn’t manage to even get a spell out of it. Bracing myself, I split the skin.

The pain wasn’t as bad as I’d feared. I washed my finger under the tap and waited for the bleeding to stop, but it didn’t seem like it was going to any time soon. I wadded a bunch of toilet paper round the finger and hurried out. Next time, I thought, I’ll bring plasters.

I was back on that red sofa again.

“Good,” said the sorcerer. “It sounds like the pieces are all in place.”

“Is that it? Was that the whole spell? It didn’t feel very... mystical,” I said. The sorcerer sucked air through his teeth and looked round the apartment. Eventually, he saw a chunk of amethyst on the coffee table.

“Pick that up,” he said, “Look into it. Fill it with your intention, with your desire for a new job, see your security that you sacrificed burning to give your future fuel.” I did as he said, feeling a bit sheepish as I buried my brows and tried very hard to put my intention into the amethyst. I was about to mention that I wasn’t sure I had a good grasp of how to move intentions from the realm of thoughts out into the physical world when a melodious gong rang out.

“It is done,” intoned the sorcerer. I couldn’t see a gong anywhere. Noticing my confusion, the sorcerer tapped his phone again, and the melodious gong rang out again. He raised his eyebrows at me, inviting me to compliment his setup.

“Compact!” I said.

“Yes,” said the sorcerer.

Nothing happened immediately with the new job. I was just unemployed for a while. I wasn’t sure how to tell that the spell was working, or if there was anything else I needed to do to activate it. I couldn’t get hold of my sorcerer. According to his answering machine, he appeared to be perpetually out at a recording of Blankety Blank.

But eventually something happened. In a fit of desperation, I attended a “startup speed dating event”. An excitable fellow and his sullen partner seemed almost magnetised towards me, and took me out for drinks. They offered me a job!

It was a bit awkward wandering into the office that Monday, my Guinness-soaked memories not entirely clear on what the role was or what the company did.

“Hey!” I asked my new fiery friend/boss, after the introductions had been made. “Can you give me a one sentence version of the elevator pitch that I can tell people,”

“At Amethyst we’re productising onboarding knowledge in high-touch high-churn verticals!”

“Oh.” I said. “Excellent.”

I wonder whether one day I’ll just know it’s time for my next lesson through some sort of divinatory prowess.

“That could happen,” said the sorcerer. Had I said that out loud or just thought it? “But for now, Monzo request works, yeah?”

“Yeah,” I said, a little crestfallen.

“Alright, good job on the last spell, mate! What’s next?”

“I suppose I’d like a new car maybe.”

“Money problems again, is it?” said the sorcerer.

“No, not this time,” I said. “The issue is, I’ve got the money, but I promised my childhood friend that one day, our next car would be together, and it’d be like a really sporty one.”

“Right, OK. So are you gonna buy it?”

“I don’t really want a sporty car. I find them a bit scary.”

“Alright then, just buy a different car.”

“Yeah, but I just think it’s one of the things that he’s really holding on to at the moment. It’s not been a great couple of years for him.”

“Ah,” said the sorcerer. “We can use that. Tell him to fuck off and that you’re not going to hold out for a silly dream car with him. How would a shared car even work? Do you guys live together?”

“No, he still lives at home in Basildon.”

“You don’t even live in the same county! Yeah, tell him to fuck off and that you’re getting your own car.”

“Do I have to say ‘fuck off’?”

“No, you can say ‘I’m really sorry sweetheart but I’m not going to get a tandem car with you and we’ll never go tulip-picking’ if you like. Now, fuck off and don’t forget to cut your finger afterwards.”

And so I (nicely) told Danny to fuck off. I think he took it pretty well, though I wish he wouldn’t have worn his Jaguar shirt. We’ve not texted in the month since; I expect I’ll hear from him soon. I do have a car now, which is quite convenient.

“Good, you’re walking the path of the blood magician,” said the sorcerer. “What else do you want?”

We’d met this time in London Fields. He was wearing a black romper with a red spider web pattern on it. “I was thinking,” I said, “maybe I could start going to pub quiz nights.”

“Listen, mate,” said the sorcerer, “I don’t think showing up to the Wands and Wankers on a Tuesday night requires eldritch rituals.”

“Yeah, the thing is,” I said, “I could go with my friends, but I’m worried that I won’t be as useful as they are. I think of myself as a pretty smart bloke, but what if I’m not the smartest? What if I don’t help the most?”

“Ah,” said the sorcerer, “we can use that.

Every time in the next month you don’t know something, tell whoever you’re with your best guess — you don’t have to say that you’re sure that’s the answer,” The sorcerer was used to my questions by now. “You just have to say that that’s your best guess, and then you’ll be wrong a lot of the time. Keep doing that until everyone knows the depths of your stupidity.”

“Feared stupidity,” I corrected.

“Okay, mate,” said the sorcerer kindly. “When someone remarks on how their view of you has changed, that is the time to cut your finger.”

“Listen,” I said.

“What?” said the sorcerer.

“I’m not sure that this is magic at all; I think this is just therapy.”

“It’s not fucking therapy,” said the sorcerer. “This is fucking blood magic.”

“Yeah, I just feel like mostly you’ve been encouraging me to let go of my security blankets and stop getting in my own way. Now you’re just encouraging me to change my self-identity. It feels like there’s not really anything occult going on.”

“Not anything occult going on? Listen, mate: it’s not my fault if you’re so catastrophically insensitive to subtle forces that you think that when you cut your fucking finger to change your life or when you sacrifice some of your blood to un-stitch the world, that’s just you getting over your psychological hang-ups, mate. But believe me, it would take something a bit more potent to get over those big fucking hang-ups.”

I punched the sorcerer in the face and he fell over. The couple near us yelped.

“Someone call the police. He’s punched him!”

“Who has?” asked a nearby dog-walker.

The sorcerer looked up, gazing near but not at me.

“Oh for fuck’s sake,” he said, “he’s gone invisible.”

I made my escape, not sure how long my undetectability would last.

When I was sure I was clear, I stopped at a rubbish bin. I fished my scalpel out of my pocket and I tipped it into the bin. I was wearing a plaster this time.

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