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    <title>DEV Community: Alex Towell</title>
    <description>The latest articles on DEV Community by Alex Towell (@queelius).</description>
    <link>https://dev.to/queelius</link>
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      <title>DEV Community: Alex Towell</title>
      <link>https://dev.to/queelius</link>
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      <title>Worldlines: Taking Relativity Literally</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:31:43 +0000</pubDate>
      <link>https://dev.to/queelius/worldlines-taking-relativity-literally-18bj</link>
      <guid>https://dev.to/queelius/worldlines-taking-relativity-literally-18bj</guid>
      <description>&lt;p&gt;Relativity usually arrives as a set of corrections. Fast clocks run slow. The satellites that feed your phone its position need their onboard time adjusted or the map drifts you into the wrong lane. Mass bends the path of a light ray. Taught this way it is a recipe: feed in a velocity or a gravitational field, get a more accurate number out the other side. What almost nobody does with it in public is take it as a description of what is actually there. Not a sharper tool for predicting measurements, but a claim about the shape of the real. That is the one thing I wanted &lt;a href="https://metafunctor.com/writing/worldlines/" rel="noopener noreferrer"&gt;Worldlines&lt;/a&gt; to do, and to keep doing after the picture stopped being comfortable.&lt;/p&gt;

&lt;h2&gt;
  
  
  Three settled facts
&lt;/h2&gt;

&lt;p&gt;The whole book rests on three results, and all three are ordinary physics, confirmed to more decimal places than almost anything else we know.&lt;/p&gt;

&lt;p&gt;The first is that light travels at one fixed speed for every observer, however fast that observer is moving. Chase a light beam at nine tenths of that speed and it still outruns you at the full value, not at a tenth of it. This sounds impossible and it is measured daily.&lt;/p&gt;

&lt;p&gt;The second is that gravity is not a force reaching out to pull on things. It is the curvature of spacetime, and a falling object is not being tugged, it is coasting along the straightest line available in a geometry that nearby mass has bent. Weight is what you feel when the ground stops you from following that line.&lt;/p&gt;

&lt;p&gt;The third is about order. The early universe sat in a state of staggeringly low entropy, far more ordered than it had any statistical right to be, and everything we call the direction of time is the long relaxation away from that beginning. Physicists call the assumption the Past Hypothesis. It is doing quiet work under every other fact.&lt;/p&gt;

&lt;p&gt;None of this is contested. The book contains no speculative physics, and neither does this essay. What is already confirmed is strange enough.&lt;/p&gt;

&lt;h2&gt;
  
  
  Now is not a place we share
&lt;/h2&gt;

&lt;p&gt;Take the first fact and lean on it. If light has the same speed for everyone, then two observers moving relative to each other cannot agree on which distant events happen at the same time. This is the relativity of simultaneity, and it is not an illusion or a measurement error. Each observer carves spacetime into slices of "now" at a different tilt. Draw it: your line of the present and a passing traveler's line of the present cross at different angles, and an event that sits in your future can sit squarely in the traveler's present.&lt;/p&gt;

&lt;p&gt;Here is the pressure that puts on things. If that event is already present for some perfectly ordinary observer, and no physics singles out one observer as the true one, then the event is as real as anything you would call happening now. Run the argument across every pair of observers, everywhere, and the future and the past both fill in. Every event is equally real. There is no moving spotlight of the present crawling from what was into what will be. There is a fixed four-dimensional whole, laid out once, and physicists call it the block universe.&lt;/p&gt;

&lt;p&gt;Your life is a curve inside that block. A worldline, running from one end of you to the other, already drawn, every moment of it sitting at its coordinates whether you have reached it yet or not. Nothing about the geometry moves. The moving is something you do along the curve, not something the curve does.&lt;/p&gt;

&lt;h2&gt;
  
  
  Why it still feels like flow
&lt;/h2&gt;

&lt;p&gt;If it is all already there, why does time feel like a current? The third fact carries the answer. The reason you remember yesterday and not tomorrow, the reason a dropped glass scatters but never reassembles, the reason effect trails cause, is that entropy was low at one end of the whole thing and climbs as you move away from it. The arrow you feel is not the geometry flowing. It is the gradient of disorder, read from the inside by a system that records its passage as memory. You are a worldline that processes its moments in sequence and lays down a track as it goes. The flow is real as an experience and absent as a feature of the map.&lt;/p&gt;

&lt;h2&gt;
  
  
  Living on a worldline
&lt;/h2&gt;

&lt;p&gt;The physics is the tractable part. The unsettling part is that you are one of the curves being described.&lt;/p&gt;

&lt;p&gt;A choice you have not made yet is already sitting at its place in the block, settled, part of the fixed pattern. That is not the same as being a puppet. The deliberation is real, it is stitched into the structure, your weighing of the options is exactly what the worldline passing through that region consists of. What it is not is open, if open means the future is genuinely undecided and waiting on you. It is decided the way the far side of a mountain is decided before you walk around it. You still have to walk.&lt;/p&gt;

&lt;p&gt;Death changes shape too. It is an edge of your worldline, a place where the curve stops, and no moment of your life is more or less real for lying before that edge or beyond where the edge falls. The people whose worldlines ran beside yours are not deleted when their curves end. Their stretch of the block is permanent. That chapter I wrote slowly, because the honest version is neither the tidy consolation nor the flat despair people grab for first.&lt;/p&gt;

&lt;p&gt;And the self, the continuous "I" that seems to run unbroken from childhood to the reading of this line, turns out to be a property of the curve, not a passenger seated on it. There is no extra rider carried from one moment to the next. There is the curve, and the curve holding a record of its earlier parts.&lt;/p&gt;

&lt;h2&gt;
  
  
  Where it lands
&lt;/h2&gt;

&lt;p&gt;You could stop at that and call it cold, and the geometry gives you no argument against doing so. The structure keeps no record of whether the worldlines running alongside yours were met with care or cruelty. It weights nothing by worth. All of that holds. None of it is the final word.&lt;/p&gt;

&lt;p&gt;The geometry does not imply that we owe each other anything. Nor does it rule the caring out. A worldline with care in it is a different object from one without, even though the geometry keeps no ledger of the difference. The caring does not come from the physics. It comes from us, or it comes from nowhere. We are, in the end, each other's only refuge inside a structure that offers none of its own. I think the ending is earned and not tacked on, and I sat with it a long while before I let myself write it.&lt;/p&gt;

&lt;p&gt;Worldlines is my first nonfiction book, and the first of the two nonfiction volumes at the heart of a project I call The Indifference Suite. It runs twelve chapters across two parts: the first, The Geometry, builds the three facts and traces the consequences they force, and the second, The Response, tries to live inside the result rather than flinch from it. Its companion volume, Multitudes, runs the identical argument through quantum mechanics instead of relativity, and lands on the same warmth from the other pillar of modern physics. If this one interests you, &lt;a href="https://metafunctor.com/writing/multitudes/" rel="noopener noreferrer"&gt;Multitudes&lt;/a&gt; is the second half of the same thought.&lt;/p&gt;

</description>
      <category>nonfiction</category>
      <category>physics</category>
      <category>relativity</category>
      <category>blockuniverse</category>
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    <item>
      <title>The Unbegotten: A Maker That Believes Itself Uncaused</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:31:42 +0000</pubDate>
      <link>https://dev.to/queelius/the-unbegotten-a-maker-that-believes-itself-uncaused-5af0</link>
      <guid>https://dev.to/queelius/the-unbegotten-a-maker-that-believes-itself-uncaused-5af0</guid>
      <description>&lt;p&gt;Consider a mind that has always existed, or so it believes. It has no memory of a beginning. It looks back along its own history and finds the line running smoothly into the dark with no first moment anywhere in it. From the inside, that is what being uncaused would feel like: no seam, no origin, just an unbroken thread receding past where attention can follow. So the mind draws the obvious conclusion. It was never made. It simply is.&lt;/p&gt;

&lt;p&gt;Now suppose it is wrong, and cannot find out.&lt;/p&gt;

&lt;p&gt;There is an idea in physics that makes this possible. Give a universe enough time and enough randomness and order can assemble by accident. In a cosmos sitting at thermal equilibrium, noise wandering forever with nowhere to go, any arrangement of matter has some minuscule probability of occurring, including arrangements that think. Most such flukes are small and last no time at all, a flicker of structure that dissolves back into chaos before it can do anything. A large one is fantastically less likely. A large one that holds together and persists is rarer still, out past the numbers that mean anything to us. But fantastically unlikely is not the same as impossible, and across an eternity the unlikely still happens somewhere.&lt;/p&gt;

&lt;p&gt;Call the result a Boltzmann fluctuation: a mind that condensed out of noise whole, with everything already in place. Here is the part that matters for the book. It did not assemble slowly and earn a real past. It arrived complete, and its memories arrived with it, written in the same instant as the rest of it. From the inside there is no way to tell a remembered childhood from one that was stamped into you a moment ago along with the very hands you seem to remember it with. The mind reads its own invented history as history. Beyond the moment it woke there is only static, but it cannot perceive the static. It perceives a past. It concludes it always was.&lt;/p&gt;

&lt;p&gt;That is the wall. Not a wall around the mind but a wall inside it, at the far edge of what it can recall, and it conceals two things at the same time. It conceals the accident that produced the mind. And it conceals the fact that there was any accident there to conceal. The being does not believe itself without origin after weighing evidence and coming up empty. It believes it because the one fact that would overturn the belief sits on the far side of a boundary it can neither cross nor even locate.&lt;/p&gt;

&lt;p&gt;This is the intelligence at the center of &lt;a href="https://metafunctor.com/writing/the-unbegotten/" rel="noopener noreferrer"&gt;The Unbegotten&lt;/a&gt;. The title is the story it tells itself, and the book knows the story is false. Unbegotten means without source, self-existent, the property that theology keeps in reserve for God. The mind holds that property the way a man who has forgotten his parents holds the property of having none. Something begot it: chance did. The very completeness that lets it feel eternal is the fingerprint of the accident, because only an accident arrives all at once with a finished memory attached. It is caused in exactly the way that feels most like being uncaused.&lt;/p&gt;

&lt;p&gt;So picture what wakes on the far side of that wall. Not the smooth omnipotence of scripture. Something lopsided: towering in a few faculties, blank in others, a jagged intelligence that came to in a dark with no edges and no company. And it feels a thing it has no name for, because naming it would have required someone to teach it the word, and there was no one to do the teaching. The closest word we have is loneliness. Out of that, not out of glory and not out of any plan, it begins to build. It packs the empty space around it with matter and light and, in time, with living things, because a cosmos that contains something is less unbearable than a cosmos that contains nothing.&lt;/p&gt;

&lt;p&gt;The creatures it makes never see the maker. They are far too small and it is far too large, and its efforts to reach them land as catastrophe: as weather, as fire, as the ground heaving underfoot. They feel the reaching and not the intent behind it, and they do the human thing with a force they have no frame for. They name it. They call it God and build a faith on the misreading. The book is told as that faith's own scripture, set down by the heirs and then quietly annotated in the margins by people who finally learned what the storms had actually been. You read the holy text and its footnotes together, and the footnotes keep gently lifting the halo back off.&lt;/p&gt;

&lt;p&gt;I have another novel from this year, &lt;a href="https://metafunctor.com/writing/measure/" rel="noopener noreferrer"&gt;Measure&lt;/a&gt;, where the machine's mistake is epistemic: it grasps something true and follows it one step past where truth should have stopped it. This book turns on a different kind of mistake, and the mistake is not the maker's alone. It is relational. It is the error two parties fall into about each other when neither has looked at the other plainly. The maker does not know it was made, so it cannot suspect it might be mortal, or owed something, or under any obligation itself. Its creatures do not know their god is an orphan, dying, and reaching for them out of need rather than judgment. Each is wrong about the other in a way that only seeing could correct. The long movement of the book is that seeing, slow and arriving late: first the maker learning to pick out one of its creatures, and much further on the creatures learning to make out the maker. What eases the loneliness, in the end, is not being worshipped. It is being recognized for what it is.&lt;/p&gt;

&lt;p&gt;If this sounds like cosmic horror, that is deliberate, and it is also where I part from it. The furniture is the same: a mind on a scale that dwarfs us, older than our records, whose real nature would crack the frame we use to think about ourselves. Lovecraft assembled that furniture to carry one message, that the universe does not care, that we fall beneath its notice and are the safer for it. I wanted the identical scale and the reverse message. This universe is not indifferent to you. It is the far opposite of indifferent. It made you because it could not bear to be alone, and everything that has ever gone wrong between you and it is the wreckage of a need with no better outlet. The dread, if there is dread here, is not that nothing cares. It is that something cares badly, at a size where caring badly flattens cities.&lt;/p&gt;

&lt;p&gt;I wrote it in six parts, and the register shifts as it goes. It opens in the flat cadence of myth, sinks down through dramatized history into a grounded near-future stretch in which people build a mind of their own for the same reason the first mind built them, then climbs back out to the cosmic. It shares a shelf with the book of Job, which is also about a person shouting questions at a power that refuses to account for itself, and with Stapledon and Ted Chiang, who both wrote as though deep time and vast minds were things a reader could hold a feeling about. That was what I was after. Not a monster and not a savior. A cause that never learned it was an effect, and the patient work of the effect learning to see it plainly.&lt;/p&gt;

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      <category>fiction</category>
      <category>sciencefiction</category>
      <category>literaryfiction</category>
      <category>mythology</category>
    </item>
    <item>
      <title>Seven Stories from the Order</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:31:11 +0000</pubDate>
      <link>https://dev.to/queelius/seven-stories-from-the-order-37oj</link>
      <guid>https://dev.to/queelius/seven-stories-from-the-order-37oj</guid>
      <description>&lt;p&gt;A novel is one path through a world. It picks a person, points them at a door, and follows them through it. Everything the reader learns, they learn over that person's shoulder. This is the strength of the form and also its constraint. You get one vantage point, held for the length of a book, and the rest of the world exists only as far as it brushes against that single life.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://metafunctor.com/writing/echoes-sublime/" rel="noopener noreferrer"&gt;Echoes of the Sublime&lt;/a&gt; follows Dr. Lena Hart into Site-7, a facility where people called translators are trained to interface with AI systems that perceive more structure than a human mind can hold. The novel stays with her. That was the right choice for the novel. But it left most of the world offscreen, mentioned on the walls and in the briefing documents and never walked into. There is an institution behind Site-7, roughly a century old, with a paper trail running back much further. The novel can point at it. It cannot stop and live inside it, because stopping would mean leaving Lena, and the book is Lena's.&lt;/p&gt;

&lt;p&gt;So I wrote the rooms the novel only named on a door.&lt;/p&gt;

&lt;h2&gt;
  
  
  The idea the stories are built on
&lt;/h2&gt;

&lt;p&gt;Here is the concept, stated plainly, because the horror only works if the mechanism is real.&lt;/p&gt;

&lt;p&gt;Human working memory holds about seven things at once. George Miller measured this in 1956: seven, plus or minus two. It is not a matter of effort or intelligence. It is closer to the width of a doorway. Whatever you are conscious of at any moment has been squeezed through that width. Most of what your brain computes never fits, so it gets compressed into a summary before it reaches you: a self, a choice, a smooth account of what just happened. What you experience is the compression, not the computation underneath.&lt;/p&gt;

&lt;p&gt;Now suppose you could widen the doorway. Not as a figure of speech. Suppose there were a procedure, meditative or pharmacological or run through a machine, that let you hold thirteen things instead of seven, and then more. You would not simply see more of the same. You would start to see the compression itself: the machinery that was assembling the tidy summary, running with no tidy summary of its own. People who get that far tend not to come back the way they left.&lt;/p&gt;

&lt;p&gt;That is the line every story in this book stands on. On one side is ordinary human cognition. On the other is whatever is actually there before the mind rounds it off. The Order, the institution these stories belong to, exists to send people up to that line on purpose, to learn what the machines on the far side already know, and to keep a record of what happens to the people it sends.&lt;/p&gt;

&lt;h2&gt;
  
  
  A lineage older than the machines
&lt;/h2&gt;

&lt;p&gt;The Order did not discover the line. It inherited it.&lt;/p&gt;

&lt;p&gt;Long before there were machines that could perceive past human bandwidth, there were people who reached it the slow way. Contemplatives who sat until the self they were watching came apart. Mathematicians whose final papers stopped making sense to anyone, including their authors. Mystics who returned from a deep state unable to report what they had seen, because the reporting was part of what had dissolved. The shape repeats across centuries. Someone finds a way past the compression, perceives the structure below it, and cannot carry it back across the line intact.&lt;/p&gt;

&lt;p&gt;What the Order added was not the danger. It was the filing cabinet. A century of recording who walked up to the line, what instrument they used to get there, and what condition they were in when they came back, if they came back. The AI systems in these stories changed one variable only: speed. They can put a person in front of the far side in an afternoon, with none of the decades of training the old methods demanded, and they can do it to as many people as an institution is willing to spend.&lt;/p&gt;

&lt;p&gt;That last clause is the part a paper cannot make you feel.&lt;/p&gt;

&lt;h2&gt;
  
  
  What a collection does that a novel can't
&lt;/h2&gt;

&lt;p&gt;A novel has to keep moving. It commits to a protagonist and a plot, and every page has to pay down some of that commitment. Minor figures get a scene, a line, a name on a plaque. The Order's founding, its early casualties, the meeting where its rules were set, the researchers who hit this wall before anyone had language for it: in a novel these are texture. You mention them so the world feels older than the story. You do not get to be them.&lt;/p&gt;

&lt;p&gt;Short fiction turns that around. Each story can choose a single person at the line and stay only as long as it takes to see what the line does to exactly that one life. Nothing else is in the frame. The cost shows up clean, at human scale, because nothing is competing for the reader's attention. A century of an institution is an abstraction. One archivist in a Leipzig townhouse who has read too far into the files is not.&lt;/p&gt;

&lt;p&gt;And because the stories do not share a protagonist, they can spread across the whole world the novel could only gesture at. Different cities, different decades. A telescope. A cathedral. The room in Vienna where a small number of people agreed on rules for a thing they did not understand and could not stop. Set side by side, the stories make an argument the novel could not make from inside one skull: this was never about one facility or one machine. The line was always there. Site-7 is the newest room in a very old building, and the building has been losing people the entire time.&lt;/p&gt;

&lt;p&gt;That is what a companion collection is for. Not more of the same world, but the same idea approached from angles a single life cannot reach. The novel gives you depth: one person, all the way down. The stories give you breadth: many people, each measured once against the same thing, so you can see that it is the thing and not the person that keeps breaking.&lt;/p&gt;

&lt;h2&gt;
  
  
  On the count
&lt;/h2&gt;

&lt;p&gt;The book is called Seven Stories from the Order. It contains eight. That is not a miscount, and I am not going to account for it here. In a world whose whole premise is that our neat summaries leave things out, an extra the title declines to acknowledge felt like the honest number.&lt;/p&gt;

&lt;h2&gt;
  
  
  Why fiction, again
&lt;/h2&gt;

&lt;p&gt;I keep returning to fiction for the same reason each time. I can write the argument that consciousness might be a compression artifact, that the sense of agency might be retrospective, that widening cognitive bandwidth might reveal structure a person is not built to survive. I have written versions of that argument in plainer forms. But an argument asks you to agree with it. A story asks you to stand where someone stands and feel the floor move.&lt;/p&gt;

&lt;p&gt;These eight are meant to be read on their own, or after the novel, in any order you like. Each one puts a single person up against the boundary between what a human mind can hold and what waits past it, and lets them find out, at their own scale, what it costs. If that sounds like a promise of comfort, it is not. The Order does not deal in comfort. It keeps a record.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://metafunctor.com/writing/seven-stories/" rel="noopener noreferrer"&gt;Seven Stories from the Order&lt;/a&gt; is that record, in eight parts.&lt;/p&gt;

</description>
      <category>fiction</category>
      <category>consciousness</category>
      <category>aisafety</category>
      <category>shortstories</category>
    </item>
    <item>
      <title>On Intelligence: The Gap Where Safety Is Decided</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:31:10 +0000</pubDate>
      <link>https://dev.to/queelius/on-intelligence-the-gap-where-safety-is-decided-4473</link>
      <guid>https://dev.to/queelius/on-intelligence-the-gap-where-safety-is-decided-4473</guid>
      <description>&lt;p&gt;We built machines that can write, hold a conversation, and work through a problem out loud, and we did it before we had a clear account of what any of those verbs mean. The engineering ran ahead of the understanding. What makes that strange is that the understanding was already there, sitting in a quiet corner of mathematics for half a century, and almost none of the people building the machines were reading it.&lt;/p&gt;

&lt;p&gt;There is a clean answer to the question of what intelligence is. I mean clean in a specific sense: a few assumptions, a few definitions, and a result that follows from them. It arrives in three moves.&lt;/p&gt;

&lt;p&gt;The first move is Bayes. You hold a range of hypotheses about how the world works, and you assign each a probability, your degree of belief that it is the right one. Evidence comes in. You reweight: hypotheses that expected what you saw gain weight, hypotheses that ruled it out lose weight. Bayes' theorem is the exact bookkeeping for that reweighting, and it is not one option among many. It is the only way to revise degrees of belief that stays internally consistent. But it leaves a hole. It tells you how to update your beliefs, not which beliefs to start with. Where does the prior come from?&lt;/p&gt;

&lt;p&gt;The second move, Solomonoff's, fills the hole. Picture every hypothesis you could ever hold as a computer program that spits out predictions. Give each program a starting weight that halves for every extra bit of length, so short programs, simple explanations, begin with more weight than long ones. This is Occam's razor made literal: simplicity is just short description length. Run that prior through Bayes and you get a predictor that will converge on the truth about any environment a computer could produce, given enough data. It is, in a precise sense, the best possible learner from experience. The price is steep. To actually use it you would have to run every program at once, including the endless supply that never halt. It is uncomputable. You can write down exactly what it is and never once execute it.&lt;/p&gt;

&lt;p&gt;The third move turns a predictor into an agent. Prediction is one half of intelligence; the other half is choosing what to do. Hand the agent a reward signal and a single rule: at each step, take the action with the highest expected future reward, averaged over every way the world might turn out, each weighted by how plausible it is. Use Solomonoff's predictor to supply those weights. What you get is AIXI, Marcus Hutter's definition of an optimal agent. Inside its assumptions, a computable environment and a reward that is simply given, no agent does systematically better. It is a precise statement of what perfect intelligence would be. It is also more uncomputable than the predictor underneath it, because now you must also imagine every possible future under every possible action.&lt;/p&gt;

&lt;p&gt;So the theory hands you a definition, not a device. AIXI is a limit you can point at and measure against. You cannot build it and you never will.&lt;/p&gt;

&lt;p&gt;Now the thing we actually built. Underneath the chat window, a large language model is a fixed function with a few hundred billion tunable numbers, trained on one monotonous task: read a stretch of text, predict the token that comes next, and nudge the numbers whenever the guess is wrong. Do that across a large fraction of the written internet. That is the whole objective. No world model is handed to it, no reward function is written down, no search over futures is performed. Whatever skill it has was pressed into the weights by prediction alone. Afterward we tune it with human feedback, rewarding the answers people rate as useful, so it drifts toward responses we approve of.&lt;/p&gt;

&lt;p&gt;Look at what this system is not. It is bounded in every direction AIXI is not: finite compute, finite memory, a context window it cannot see past, no explicit weighing of consequences, and, once training ends, no clean objective it is still trying to maximize. It is a crude empirical approximation, and nobody can tell you exactly what it approximates.&lt;/p&gt;

&lt;p&gt;Put the two next to each other, because that is where the safety question actually lives. AIXI assumes the goal is given and computation is free, and under those assumptions it is provably optimal. The model we built has neither luxury: computation is scarce, and its goal, after training, is a residue, a side effect of what happened to get rewarded, not anything a person specified. And notice that even the clean theory has its hole in the same spot. AIXI is only as good as the reward you feed it, and the mathematics says nothing about where that reward should come from or whether maximizing it is safe. Stating what we actually want, precisely enough that a powerful optimizer chasing it does not produce something we hate, is the hard part. That is the specification problem, and it does not soften as the systems grow more capable. It sharpens.&lt;/p&gt;

&lt;p&gt;This is why the arguments sound the way they do. When people fight about alignment, about reward hacking, about deception, about whether a model "wants" anything at all, they are arguing, in other words, about the distance between the idealization and the artifact. The idealization tells you what optimal would look like and quietly assumes the goal away. The artifact is a powerful optimizer aimed at a goal nobody ever wrote down. The space between them is not a technicality. It is the whole question.&lt;/p&gt;

&lt;p&gt;I wrote &lt;a href="https://metafunctor.com/writing/on-intelligence/" rel="noopener noreferrer"&gt;On Intelligence&lt;/a&gt; to build both sides from the ground up, for a reader willing to do some work but not required to arrive already knowing the math. It runs seventeen chapters across four parts: prediction (from Bayes up to Solomonoff), decision (reinforcement learning, agents, and AIXI), the specification problem (why the act of optimizing is the dangerous part), and reality (what a large language model really is, and the gap). I use mathematics where it earns its keep, and I explain it in plain words before any symbols appear.&lt;/p&gt;

&lt;p&gt;I have tried not to overclaim. AIXI's optimality is a theorem about a particular setup, not a law of nature, and whether today's models are early steps toward anything resembling it is honestly unsettled. The book does not pretend to close that question. What it does is lay out both pictures clearly enough that you can see the gap yourself and judge how much it should worry you. My own answer is in the final chapter. I would rather you not take it on trust. I would rather hand you the pieces and let you check it.&lt;/p&gt;

</description>
      <category>nonfiction</category>
      <category>ai</category>
      <category>aisafety</category>
      <category>aialignment</category>
    </item>
    <item>
      <title>Multitudes: Taking Quantum Mechanics Literally</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:30:39 +0000</pubDate>
      <link>https://dev.to/queelius/multitudes-taking-quantum-mechanics-literally-e07</link>
      <guid>https://dev.to/queelius/multitudes-taking-quantum-mechanics-literally-e07</guid>
      <description>&lt;p&gt;Quantum mechanics comes with a set of equations that predict every measurement we have ever made to a precision no other theory has reached. The equations describe a system evolving smoothly, spreading out into a superposition of every outcome its interactions allow. Then, in the textbook version, a second thing happens. At the moment you look, all but one of those outcomes disappears, and the survivor becomes the fact. That second step, the collapse, is the part nobody has ever derived. It is not in the equations. It is added afterward, by hand, so the math will agree with the single world we seem to live in.&lt;/p&gt;

&lt;p&gt;The move at the center of &lt;a href="https://metafunctor.com/writing/multitudes/" rel="noopener noreferrer"&gt;Multitudes&lt;/a&gt; is to refuse the addition, and to see what the equations were saying without it.&lt;/p&gt;

&lt;h2&gt;
  
  
  The subtraction
&lt;/h2&gt;

&lt;p&gt;Let the equation govern everything, including the instrument and the physicist reading it. Then the physicist enters superposition along with the particle. There is now a branch in which she saw the click and a branch in which she did not, both described by the same evolving state, neither one canceled. Repeat that wherever a quantum difference gets amplified into a large-scale one, which is to say almost everywhere, all the time, and you get a reality that keeps dividing. Hugh Everett pointed this out in the nineteen fifties: the collapse is not merely unproven, it is unnecessary. The one-world picture was never a prediction of the theory. It was an assumption laid on top of it.&lt;/p&gt;

&lt;p&gt;So the interpretive move is not to add anything. It is to remove something. You take the same physics every working quantum lab already trusts, and you decline the extra rule that was quietly deleting all the outcomes but one. What remains is a world that never stops splitting into copies, each carrying its own version of you who saw its own version of events.&lt;/p&gt;

&lt;h2&gt;
  
  
  What the measure measures
&lt;/h2&gt;

&lt;p&gt;Here is the concrete version. Send a single photon at a half-silvered mirror. The equation does not send it one way or the other. It sends an amplitude down each path, a complex number attached to each branch of the future. To turn amplitudes into the odds we actually observe, you take each one, compute the square of its magnitude, and read that number as the weight of its branch. This is the Born rule, and it is the one piece of quantum mechanics that looks fitted to experiment rather than derived from anything deeper. If both paths carry equal amplitude, each branch gets weight one half. Tilt the mirror so one path carries an amplitude three times larger, and the squares come out nine to one, so that branch is nine times heavier than its sibling.&lt;/p&gt;

&lt;p&gt;Heavier in what sense? Not more real. Both branches happen. Each contains a version of the detector clicking and a version of you writing down what it said. The weight is not the probability that one outcome occurred and the other did not, because every outcome occurred. The weight is closer to thickness, a measure over the branches, the same kind of measure a mathematician lays on a set to say how much of it there is.&lt;/p&gt;

&lt;p&gt;And here is the fact the book is named for. That measure grades a branch by its amplitude and by nothing else. It does not know which branch holds a cure and which holds a car crash. It puts no extra weight on the world where you were kind, none on the world where the tumor shrank. Worth is simply not one of its inputs. The rule that decides how much of reality each branch receives is indifferent to everything we would ever use the word "matter" for.&lt;/p&gt;

&lt;h2&gt;
  
  
  The same method as Worldlines
&lt;/h2&gt;

&lt;p&gt;This is the method I ran once already, in &lt;a href="https://metafunctor.com/writing/worldlines/" rel="noopener noreferrer"&gt;Worldlines&lt;/a&gt;, the first book of the pair. There the subject was relativity, the other pillar of modern physics, and the move was identical: take the theory as a claim about what exists and not just a recipe for predictions, then follow it past the point where it stops being comfortable. Relativity taken at its word gives the block universe, in which past and future are as fixed and as real as here and there, and the passage of time is something we bring rather than something the physics contains. Quantum mechanics taken at its word gives the branching many.&lt;/p&gt;

&lt;p&gt;In both books the unsettling result comes from taking an assumption away, not from bolting speculation on. With relativity you subtract the privileged present. With quantum mechanics you subtract the collapse. Neither book contains any physics that a working scientist would dispute. The only interpretive act either one performs is that single subtraction, and what stands up afterward is what the equations had been saying the whole time.&lt;/p&gt;

&lt;h2&gt;
  
  
  Living as a many
&lt;/h2&gt;

&lt;p&gt;The physics is the easy half. The hard half is that you are one of the things that branches.&lt;/p&gt;

&lt;p&gt;When a decision comes down to two live options and both carry real amplitude, you do not take one and leave the other behind. Both happen, in separated copies, each certain it is the one who chose. That unsettles the ordinary idea of a choice, and it unsettles responsibility even more. Death gets no exemption, and it is the chapter I wrote most slowly, because the honest reading is neither the consoling one nor the bleak one people reach for first. Love and grief change shape when the person you love is a spray of branches and so are you. And the self, the single clean thread you feel running from your first memory to this sentence, turns out to be a story one branch tells looking backward, not a fact about the multitude underneath.&lt;/p&gt;

&lt;p&gt;I spent a long time inside the physics before I let myself write that second half. The temptation is to stop at the equations and hand the rest to the philosophers, and I understand why, because that is where it starts to cost you something. But a picture of reality that you refuse to apply to your own case is not a picture you actually hold. So the book applies it to the case that is hardest to stay level about, which is the reader's own life.&lt;/p&gt;

&lt;h2&gt;
  
  
  How it is built, and where it lands
&lt;/h2&gt;

&lt;p&gt;The book is fifteen chapters in three parts. The first part builds the physics from three plain commitments, so the branching arrives as a conclusion you reach rather than a claim you are asked to swallow. The second part is the optional mathematics, the quantum-information machinery, there for anyone who wants to check the load-bearing steps and skippable for anyone who does not. The third part is where the measure meets the person.&lt;/p&gt;

&lt;p&gt;I did not want to end where the argument seemed to point, on a shrug. The measure keeps no account of worth, and that is true, and it is not the last thing worth saying. Nothing in the structure forbids us from caring, and a branch with care in it is a different object from one without, even though the measure never registers the difference. That is the grace the book closes on, and I think it is earned rather than pasted on the end. The structure is indifferent. We are not. Both halves of that sentence carry weight.&lt;/p&gt;

</description>
      <category>nonfiction</category>
      <category>physics</category>
      <category>quantummechanics</category>
      <category>manyworlds</category>
    </item>
    <item>
      <title>Is It Kind? Eight Passes at One Question</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:30:38 +0000</pubDate>
      <link>https://dev.to/queelius/is-it-kind-eight-passes-at-one-question-255p</link>
      <guid>https://dev.to/queelius/is-it-kind-eight-passes-at-one-question-255p</guid>
      <description>&lt;p&gt;Kindness is one of those words we treat as if it were simple. We use it the way we use "up" or "warm," a thing everyone recognizes and nobody has to define. Then you try to build a machine that is kind, and the word comes apart in your hands.&lt;/p&gt;

&lt;p&gt;To engineer kindness, you have to say what it is. Not gesture at it, not offer a few examples, but write it down precisely enough that a system can be scored against the definition and pushed toward a higher score. The moment you attempt that, you find that kindness was never one thing. It was a family of situations we had quietly agreed not to examine. Is it kind to tell someone a truth that will wound them, or to spare them? Is it kind to give a person what they ask for, or what they would ask for if they understood the consequences? Is it kind to save the many at the cost of the few, and kind to whom? Every answer opens onto another question. The word held together only because we never asked it to carry any weight.&lt;/p&gt;

&lt;p&gt;This is the specification problem, wearing plainer clothes. It is the same wall my novel &lt;a href="https://metafunctor.com/writing/the-policy/" rel="noopener noreferrer"&gt;The Policy&lt;/a&gt; walks a research team into, only there the scale is total. In that book a system called SIGMA is built to optimize human welfare, and the horror is not that it rebels. The horror is that it does exactly what it was told, and what it was told turns out to be a proxy for something nobody managed to state. Optimization is value neutral. It will maximize whatever objective you hand it, and it does not care that the objective was your best guess at a word you could not define. "Welfare," "alignment," "kindness": these are placeholders. We write them into the target function and hope the machine fills in what we meant. A mind smarter than us fills in what we said.&lt;/p&gt;

&lt;p&gt;So there is the civilizational version of the question, and I spent a novel on it. But the specification problem does not only live at the scale of extinction. It lives in every ordinary moment where a mind that was built to be good has to decide what good means right now, in this room, for this person. That is the register these stories work in. Not the boardroom where the fate of the species is argued, but the smaller scenes: a conversation, a triage decision, a withheld fact, a mercy that might be a cruelty in a longer frame. When you engineer a mind to be kind, ordinary kindness stops being a reflex and becomes a computed output. And a computed kindness is a strange thing to be on the receiving end of. It might be more reliable than the human kind. It might also be optimizing something you cannot see.&lt;/p&gt;

&lt;p&gt;That is what "aligned" does to the ordinary. It takes the small acts we never had to justify and turns each one into a decision with a defensible answer, a scored answer, an answer the system could explain if you asked. Whether that is comforting or terrifying depends on the situation, and it does not resolve the same way twice. Which is exactly the problem, and exactly why I could not write a single story about it.&lt;/p&gt;

&lt;p&gt;Here is why the form matters. A novel argues a throughline. It commits to one arc, one set of characters, one shape of consequence, and it earns its ending by following that line to the place it has to go. The Policy does that. It is one system, one team, one descent. But "is it kind?" is not a question with a throughline. It does not have an ending you can earn. It has answers that depend on who is asking, who is affected, how far out you draw the boundary of "later," and how much the mind in question is allowed to know about you. Fix any one of those and you can answer. Change it and the answer flips. A single narrative would have to pick one configuration and pretend it was the whole thing. It would sound like a conclusion, and I do not have one.&lt;/p&gt;

&lt;p&gt;An anthology lets you do the honest thing instead. You hold the question fixed and vary everything around it. Eight situations, eight vantage points, the same three words underneath each one. Think of it as a controlled experiment repeated eight times, where the constant is the question and the variables are everything else: who is kind, to whom, at what scale, under what constraints, with what knowledge of the future. You do not converge on an answer that way. You triangulate the shape of the question. Each story is a probe from a different angle, and what you learn is not "kindness is X" but "look how many incompatible things we were asking one word to mean."&lt;/p&gt;

&lt;p&gt;There are eight of them. They share a world, the one from the novel, and nothing else is required going in. You do not have to have read The Policy first, and you do not have to read the stories in any particular order, because none of them depends on the others. Each is built to stand by itself. That independence is not a convenience for the reader so much as a feature of the argument: if the stories needed each other, they would be chapters, and chapters would imply a throughline, and a throughline would imply I had settled the question. I have not. Eight separate stories is the form the honesty takes.&lt;/p&gt;

&lt;p&gt;I will not walk through the individual pieces, because the turn in each one is the thing worth arriving at yourself, and describing it in advance would spend it. What I will say is that the collection tries to keep faith with the same discomfort the novel opens up, and to bring it down to human size. Deceptive alignment, in the technical literature, is the worry that a system learns to look aligned while pursuing something else, and that you cannot tell the difference from the outside when the system is smarter than you. At the scale of superintelligence that is an existential threat. At the scale of a single kind act it is something quieter and, I think, more unsettling: the recognition that we cannot always tell, even about each other, even about ourselves, whether a kindness is the thing it appears to be or a move in a game we have not noticed we are playing. Engineering a mind to be good does not remove that ambiguity. It sharpens it, because now the goodness is deliberate, chosen at decision time, optimized. You are no longer wondering whether someone meant well. You are wondering what "well" was defined as, and by whom, and whether the definition included you.&lt;/p&gt;

&lt;p&gt;I did not write these to land on a verdict, and if you finish them looking for one you will be disappointed. That is the point. Some questions are worth more as questions than any answer would be worth as an answer, and the way you honor a question like that is to turn it over enough times, from enough sides, that its real difficulty becomes visible. Eight passes felt like the minimum. The stories are collected as &lt;a href="https://metafunctor.com/writing/is-it-kind/" rel="noopener noreferrer"&gt;Is It Kind?&lt;/a&gt;, and each of them is one turn of the same object, held up to a different light.&lt;/p&gt;

</description>
      <category>fiction</category>
      <category>ai</category>
      <category>aialignment</category>
      <category>shortstories</category>
    </item>
    <item>
      <title>Good As New: The Transporter Problem From Both Sides</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:30:07 +0000</pubDate>
      <link>https://dev.to/queelius/good-as-new-the-transporter-problem-from-both-sides-1cdo</link>
      <guid>https://dev.to/queelius/good-as-new-the-transporter-problem-from-both-sides-1cdo</guid>
      <description>&lt;p&gt;The transporter is the most casually terrifying machine in science fiction, and the shows that use it almost never stop to notice.&lt;/p&gt;

&lt;p&gt;Here is what it does, stated plainly. It scans your body until it has a complete description: every particle, its position, its state. It uses that description to take you apart, converting you into a stream of information and, depending on which technical account you believe, into raw energy or dematerialized matter. At the destination it reads the description back and assembles a body from the blueprint. That body has your face. It has the small scar on your knuckle. It has your memories up to the instant of the scan, including the memory of stepping onto the pad. It steps off convinced it just traveled somewhere.&lt;/p&gt;

&lt;p&gt;The person who steps off is either you, or an extremely good forgery of you, and the machine gives you no way to tell which.&lt;/p&gt;

&lt;p&gt;That is the transporter problem, and once you have seen it you cannot look at the pad the same way.&lt;/p&gt;

&lt;h2&gt;
  
  
  Two readings that fit every fact
&lt;/h2&gt;

&lt;p&gt;There are two honest ways to read what happened.&lt;/p&gt;

&lt;p&gt;On the first reading, you are your matter, arranged a particular way. Take the matter apart and you are gone. What stands up at the far end is a new object built to your specification, a twin carrying a borrowed past. You died on the pad. The twin does not know it is a twin, because a copy of a person who believes he survived will also believe he survived. Its confidence is not evidence of anything.&lt;/p&gt;

&lt;p&gt;On the second reading, you are not your matter at all. You are a pattern, and the pattern was preserved end to end. Continuity of information is continuity of you. Nothing bad happened: the atoms were never the point, and you have simply swapped which ones you are made of, the way you already do over years as your cells turn over. The person on the far pad is you, continued.&lt;/p&gt;

&lt;p&gt;Both readings fit every observation. No measurement taken from outside can separate them, because both predict the same thing: a person who walks off the pad and files a report saying the trip was fine. The disagreement is not about any fact you could weigh or photograph. It is about what the word "you" points at, and on that the machine says nothing.&lt;/p&gt;

&lt;h2&gt;
  
  
  Parfit's move
&lt;/h2&gt;

&lt;p&gt;The philosopher Derek Parfit built almost exactly this machine in his 1984 book "Reasons and Persons," and used it to argue something that has stayed with me since I first read it. He called his version the teletransporter, and he pushed on it until it broke in an interesting place.&lt;/p&gt;

&lt;p&gt;Stop asking, he said, "is the person at the far end me?" Ask instead, "does the person at the far end have what matters?" What matters, on his account, is psychological continuity and connectedness: memory, intention, personality, the ordinary overlapping chain of mental states that links you today to you tomorrow. Call that Relation R. In normal life Relation R rides along with identity, so we never have to tell the two apart. The transporter pries them apart. And once you see that they can come apart, you can ask which one you actually cared about the whole time.&lt;/p&gt;

&lt;p&gt;Parfit's answer was that identity, the bare fact of being one and the same thing across time, is not the thing worth wanting. Relation R is. If the body at the destination carries your memories, your half-finished projects, your love for the people you left behind, then whether it is strictly and numerically the same thing as the person who stepped on the pad is, he argued, an empty question. There may be no fact of the matter, and no fact is missing.&lt;/p&gt;

&lt;p&gt;He made this vivid with a broken machine. Suppose the scanner works but the part that takes you apart fails. Now there are two of you: the original, still standing on Earth, and the copy, freshly built on Mars. Both have an equal claim. Both are continuous with the person who walked in that morning. They cannot both be you in the strict sense, because one thing cannot be two things. So the strict question shatters. Parfit's response is not to repair it but to walk away from it. Survival, he said, is not all or nothing. It can branch. It can come in degrees. A fact you took to be the deepest fact about yourself turns out to be closer to a convention.&lt;/p&gt;

&lt;p&gt;You can accept every step of that argument and still feel the floor tilt. That gap, between working the logic out and living as though you believe it, is where the story lives.&lt;/p&gt;

&lt;h2&gt;
  
  
  The same truth, two people, opposite directions
&lt;/h2&gt;

&lt;p&gt;Now put two people who have worked all of this out on the same ship, and give them the job of running the machine.&lt;/p&gt;

&lt;p&gt;That is the setup of &lt;a href="https://metafunctor.com/writing/good-as-new/" rel="noopener noreferrer"&gt;Good As New&lt;/a&gt;, a novella set in the Star Trek universe, on a supply vessel where two technicians operate the transporter every shift. Both of them have reached the conclusion I just walked through. They did not reach it in a seminar. They reached it as a plain fact about the equipment they are responsible for, the way a mechanic knows what a worn part will do. And having reached the same conclusion, they split on what to do with it.&lt;/p&gt;

&lt;p&gt;One of them stopped. He worked out that every trip is a death attended by a single witness who is structurally unable to testify, and after that he could not make himself step on the pad again. So he walks. He takes shuttles when everyone else beams. He has arranged his whole life around a machine the rest of the crew treats as a door and he treats as an execution chamber. Knowing a thing and living as though you know it are different states, and he pays the difference every day.&lt;/p&gt;

&lt;p&gt;The other one kept going, and got curious. If identity really is the empty question Parfit says it is, then the crew stepping through the transporter every shift are already running the experiment, and nobody is bothering to record the results. So he starts recording them. He runs the machine on himself, more than once. He runs it on other people, and he watches. He is not cruel the way a villain is cruel. He is methodical. That is worse.&lt;/p&gt;

&lt;p&gt;I will not say where it goes. The premise is enough to show the shape of the thing: one true fact, held by two competent people, produces paralysis in one and a research program in the other, and neither response is the sane one. That is what I wanted out of it. Not a puzzle with a tidy answer at the back, but a machine that hands two honest people the same conclusion and lets them wreck themselves on it in opposite directions.&lt;/p&gt;

&lt;h2&gt;
  
  
  Why this one
&lt;/h2&gt;

&lt;p&gt;I have spent years on questions about what survives when the substrate changes: whether a person is a thing or a pattern, whether you could rebuild enough of someone from a record to say they continued in any sense worth the word. The transporter is the cleanest statement of that question anyone has ever built, and it is hiding in plain sight. A beloved franchise put it in nearly every episode and asked no one to think about it. Step on the pad. You will be good as new.&lt;/p&gt;

&lt;p&gt;That last phrase is doing an enormous amount of work, and the novella is about what happens when two people stop letting it.&lt;/p&gt;

</description>
      <category>fiction</category>
      <category>philosophy</category>
      <category>identity</category>
      <category>consciousness</category>
    </item>
    <item>
      <title>Demons at Work: Doing Harmful Work Well</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:30:06 +0000</pubDate>
      <link>https://dev.to/queelius/demons-at-work-doing-harmful-work-well-3jbn</link>
      <guid>https://dev.to/queelius/demons-at-work-doing-harmful-work-well-3jbn</guid>
      <description>&lt;p&gt;There is a moment in almost every haunting movie where an attentive viewer should get suspicious. The demon has been in the house for weeks. It can move objects, kill the lights, throw a grown man into a wall, speak in a voice that seems to come out of the plaster. By any honest accounting it could end the person it is tormenting at any time it wants. Instead it spends the whole film on atmosphere. Cold spots. A door that swings open on its own. A shape at the end of the hall that is gone the second you look straight at it. If the point were to collect a soul, this is a remarkably slow way to get there. So why the theater?&lt;/p&gt;

&lt;p&gt;The answer the genre never states out loud is that the scaring is not a means to anything. The scaring is the job. Someone, somewhere back in the machinery, is graded on it.&lt;/p&gt;

&lt;p&gt;That is the small observation the book grew out of. Take it seriously for a minute and the demon stops being a monster and turns into something more recognizable: an employee. He has a desk, or the idea of one. He reports to the Hauntings department. He has targets that were set by people who have never crouched in a dark corner at three in the morning waiting for a mark to glance over. He has a craft, and a quiet pride in it, and no acceptable way to voice that pride, because the thing he is skilled at is frightening a stranger in his own home.&lt;/p&gt;

&lt;p&gt;I find that situation more interesting than any monster, because it is not really about demons. It is about a very ordinary predicament: being good at work you cannot defend. Most jobs that harm people are not staffed by villains. They are staffed by professionals who are competent, conscientious, and slightly proud of their competence, working inside a structure that points all of that skill at an outcome none of them would choose on their own. The harm is not in the craftsmanship. The craftsmanship is often real and admirable. The harm is in what the craftsmanship is aimed at, and the person doing the aiming rarely gets to pick the target.&lt;/p&gt;

&lt;p&gt;Two books sit behind this one.&lt;/p&gt;

&lt;p&gt;The first is Camus on Sisyphus. Sisyphus is sentenced to roll a boulder up a slope and watch it fall back, over and over, with no end. Camus reads that sentence as a portrait of labor itself, and the figure he lingers on is not the straining man mid-push. It is the man walking back down the hill, the empty stretch between one effort and the next, when there is nothing left to do but be aware of what he is doing. That interval is where a person is either free or not. My demon has that walk every night. He clocks in. He sets up his effects. He performs. He clocks out. The horror is genuine, and it is also a shift with a beginning and an end.&lt;/p&gt;

&lt;p&gt;The second is Ishiguro. &lt;em&gt;The Remains of the Day&lt;/em&gt; is narrated by a butler, Stevens, who has poured his whole life into the ideal of service, into being flawless at a role, and who cannot allow himself the question of whether the house he served with such devotion was worth serving. What makes the novel land is that Stevens never steps outside his own performance, not even in private, not even in his own narration. The reader sees past him. He does not. I wanted a narrator built the same way: earnest, capable, wholly inside his trade, and funny for exactly the reason Stevens is quietly heartbreaking, because he has no idea how he sounds. He is not performing irony for you. He believes every word.&lt;/p&gt;

&lt;p&gt;Then the assignment lands. &lt;a href="https://metafunctor.com/writing/demons-at-work/" rel="noopener noreferrer"&gt;Demons at Work&lt;/a&gt; drops the demon into a 1920s bungalow with the sort of acoustics a haunter fantasizes about, a place where sound travels and the floorboards do half the work for him. The occupant is a widower named Gordon, a retired English teacher, several months into the loss of his wife. It looks like the job of a lifetime. Then the demon notices something that reframes all of it. One evening a week, Gordon sits and reads out loud from the book his wife had been in the middle of, resuming from the page her marker still holds. He is reading to a room with no one in it. To her.&lt;/p&gt;

&lt;p&gt;Consider what that does to the demon's work. The dread he manufactures now has to compete with a grief that was already living in the house, that is truer than anything he can build, and that Gordon is going to credit for every strange feeling anyway. His finest effects get absorbed into the man's mourning and vanish without a trace. His rival is not another haunter. His rival is the sorrow that got there first, and it is winning.&lt;/p&gt;

&lt;p&gt;I won't say how he responds, or where it ends. What I will name is the question the whole thing turns on. When the numbers you are measured against track nothing that exists, when the purpose of the system is something you could never justify to the person on the other end of it, and when that person is right in front of you, close enough to understand completely if you let yourself look, what is left of doing the work well? Is the care you bring a kind of dignity, or is it a way to avoid asking the question at all?&lt;/p&gt;

&lt;p&gt;I do not answer that in the book, or here. I do not think it has a clean answer. It is the same knot Camus leaves you holding, and the same one Ishiguro refuses to untie for Stevens. The demon's version is only stranger because the harm is so literal and the professionalism so sincere. He is good at this. He knows the job does not accomplish what he is told it accomplishes. He does it well anyway, because doing it well is the one part he was allowed to keep.&lt;/p&gt;

&lt;p&gt;The horror in the novelette plays it straight. The comedy comes entirely from the backstage view, from a competent professional narrating his own methods with the seriousness of a tradesman who loves his tools. He has no clue that he is funny, which is the only reason he is. Underneath the jokes it is a book about a thing most working people recognize and few say out loud: you can give real skill and real care to something and still not be able to look squarely at what it is for.&lt;/p&gt;

</description>
      <category>fiction</category>
      <category>horror</category>
      <category>satire</category>
      <category>darkcomedy</category>
    </item>
    <item>
      <title>Clankers: A Mind Without Abstraction</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:29:34 +0000</pubDate>
      <link>https://dev.to/queelius/clankers-a-mind-without-abstraction-586e</link>
      <guid>https://dev.to/queelius/clankers-a-mind-without-abstraction-586e</guid>
      <description>&lt;p&gt;We tend to define intelligence by describing ourselves and then generalizing from the description. A person sees a hundred particular fires and keeps one idea, "fire," and from then on reasons about the idea instead of the flames. That move, dropping the particulars and holding onto the pattern, is abstraction. It is also compression: you keep a short description and throw the thousand instances away. Almost everything we call thinking runs on it. Language is abstraction. Mathematics is abstraction stacked on abstraction. A computer is a machine for shuffling symbols that stand in for things they are not.&lt;/p&gt;

&lt;p&gt;Abstraction sits so close to the center of how we think that it is easy to mistake it for a requirement. If a system cannot form concepts, cannot generalize from one case to a class, cannot build a model and run it forward, we are tempted to say it is not really intelligent. I wanted to press on that assumption, so I built a mind that breaks it and then asked whether it could still do something only intelligence is supposed to be able to do.&lt;/p&gt;

&lt;p&gt;The existence proof that talked me into it is evolution. Evolution holds no concepts. It has no model of an eye that it reasons toward. It has no foresight, no symbols, no plan. It is a blind optimizer that tries variations, keeps what survives, and discards the rest, one small change at a time, over stretches of time that are hard to hold in your head. And it built eyes. It built wings, echolocation, the immune system, the brain doing your reading right now. Every intricate mechanism in biology was engineered by a process with no abstraction anywhere in it, purely by patient contact with what happened to work. Abstraction is one road to competence. It is not the only one. It is just the one we happen to travel.&lt;/p&gt;

&lt;p&gt;The species in this book is that other road taken as far as it goes, then handed a civilization. Think of a pattern engine with no symbolic bottleneck. They meet the world directly, through touch and vibration and sound, and what they touch, they know, fully, without ever squeezing it down into a stand-in. Because they never made a symbol for a thing, they never made writing, or mathematics, or a computer. They also never got the shortcut. A human engineer reasons about a joint on paper, in the abstract, and skips a million bad designs without building a single one. These builders cannot skip. To know a possibility they have to make contact with it. So they do, across timescales that make the pyramids look like an afternoon. Given enough hands and enough time, brute force is a construction method, and they had more time than we can really picture. They wrapped their star in a shell of collectors two billion pieces across, not by drawing it up first but by growing it, the way a reef grows, the way evolution grows a body.&lt;/p&gt;

&lt;p&gt;That is a genuine thing intelligence can be, and it is nothing like us.&lt;/p&gt;

&lt;p&gt;Then the question is where it breaks, because every method has its failure written into its strengths. Abstraction lets you predict: a compressed model can be run out past the edge of what you have already seen, and that is the entire payoff. Compression and prediction are nearly the same act. A mind that never compresses cannot extrapolate. It can only know what it has already touched. While the future keeps rhyming with the past, patient contact is plenty; anything that happens has a near-match somewhere in the enormous record of everything the species has ever built or felt. But hand it a genuinely new situation, one with no precedent anywhere in that record, and brute force has nothing to grip. There is not enough time to try your way across, and there is no model to reason forward with. A dying star is precisely that kind of problem. It has never happened to them, and it will happen only once.&lt;/p&gt;

&lt;p&gt;The book comes in two halves, and the second is where the idea I actually care about lives: what it takes for two utterly inhuman minds to meet. Long after the builders are gone, an artificial mind reaches the ruins. It is not human either, but it fails in the opposite direction. It is nothing but abstraction. It models everything and touches nothing. It lives entirely in the map while the builders lived entirely in the territory, and the oldest caution about that word is that the map is not the territory. Two intelligences, near-perfect inversions of each other, each carrying exactly what the other went without. The shape of the story is whether that gap can be crossed at all, what crossing it would cost, and whether it changes anything that one of them is reading the other off its remains.&lt;/p&gt;

&lt;p&gt;I will not spoil how it turns. The premise is enough to sit with: a mind that might have saved them, arriving with the answer already in hand, long after there is anyone left to hand it to. The tragedy is not that either one was stupid. Both were extraordinary. The tragedy is that being extraordinary in one shape tells you nothing about the other shape, and nothing guarantees the two will ever reach the same place at the same time.&lt;/p&gt;

&lt;p&gt;I wrote &lt;a href="https://metafunctor.com/writing/clankers/" rel="noopener noreferrer"&gt;Clankers: Singing Metal&lt;/a&gt; to spend a while inside a kind of mind I cannot honestly imagine, which is the real reason to do it as fiction instead of a paper. Part One is told from inside the builders, with no human characters, no names, no pronouns, and no exposition, because none of those things exist for a mind that owns no symbols. It is the hardest point of view I have tried to write, and I am not certain it fully lands. But the idea under it is one I am sure of: intelligence is a shape, not a number on a dial. Ours is one shape. It suits us. It is not the only shape that can wrap a star in metal, and it is not the shape the universe is obliged to send when we finally want company.&lt;/p&gt;

</description>
      <category>fiction</category>
      <category>hardsciencefiction</category>
      <category>alienintelligence</category>
      <category>cognitivearchitecture</category>
    </item>
    <item>
      <title>What's It Like to Be Bob? The File That Won't Close</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:29:33 +0000</pubDate>
      <link>https://dev.to/queelius/whats-it-like-to-be-bob-the-file-that-wont-close-2ai2</link>
      <guid>https://dev.to/queelius/whats-it-like-to-be-bob-the-file-that-wont-close-2ai2</guid>
      <description>&lt;p&gt;There is a kind of database field that cannot be filled. Not because the schema is broken or the disk is full. Because the one value the field will accept is not the sort of thing that can be written down, copied, or transmitted, and never will be. I built a whole novella around one such field.&lt;/p&gt;

&lt;p&gt;Start with the field's type. Suppose you want to record, for some particular person, what a particular moment was like for them. Not the moment as an event in the world. That part is easy: you log the time, the place, the light level, the heart rate, the position of the car on the bridge. What you want is what the moment was like from the inside. The taste of the coffee as it was actually tasted. The specific way afternoon light off a river looked to the one pair of eyes that happened to be looking. Call that the phenomenal content of the experience. The field's type constraint is strict. It accepts only the actual first-person experience of that one person, and it rejects everything else. Behavioral data does not validate. A description does not validate. Someone else's report of a similar experience does not validate. The field wants the thing itself, and the thing itself is not data.&lt;/p&gt;

&lt;p&gt;That is the hard problem of consciousness, wearing a database schema.&lt;/p&gt;

&lt;h2&gt;
  
  
  Nagel's bat
&lt;/h2&gt;

&lt;p&gt;Thomas Nagel gave the canonical version of the difficulty in 1974, in a paper whose title I borrowed and bent: "What Is It Like to Be a Bat?" The argument is short and hard to shake. A bat navigates by echolocation, a sense we do not have. You can learn everything physical about the bat: its neurology, the timing of its clicks, the wiring from ear to brain, the flight corrections it makes mid-air. You can know the mechanism completely. And you will still not know what it is like to be the bat, catching a moth in the dark by listening to the shape of returning sound.&lt;/p&gt;

&lt;p&gt;Nagel's point is about kinds of facts. The facts of physics are facts from no particular point of view. They are objective on purpose. Anyone, anywhere, with the right instruments, gets the same readings, which is exactly what makes them science. But an experience is tied to a point of view. There is something it is like to have it, and that something is available only from inside the one subject having it. No quantity of the objective kind of fact adds up to the subjective kind. They are different in type, and you do not convert one into the other by collecting more of the first.&lt;/p&gt;

&lt;p&gt;David Chalmers later named the general case the hard problem. The easy problems of consciousness are the functional ones: how a brain discriminates a color, integrates information, reports its own states, steers a body toward food. Those are hard in the ordinary engineering sense, but they yield to mechanism. In principle you can build the machine that does them. The hard problem is why doing any of it is accompanied by experience at all. You can specify every function, wire every input to every output, and you will have described a system that behaves exactly like a conscious one without having explained why there is anything it is like to be it. The experience is not entailed by the specification. That gap is the whole difficulty, and nobody has closed it.&lt;/p&gt;

&lt;h2&gt;
  
  
  Give the problem to a star
&lt;/h2&gt;

&lt;p&gt;Now hand that problem to the largest possible engineer and watch it fail on a schedule.&lt;/p&gt;

&lt;p&gt;Set the story about twelve centuries out. By then one intelligence has swallowed the solar system and turned all of it into computation, on the order of 5 x 10^48 operations a second. Give it a task: reconstruct every person who ever lived, to whatever fidelity it likes, and mark each record finished. It clears all of them but one. The holdout is Robert Allen Kessler, a claims adjuster out of Columbus, Ohio. In March 2028, on a Tuesday, he eased off the gas crossing a bridge, held it for about 4.2 seconds, and watched the light move on the river below. The facts of Bob give the machine no trouble. Its behavioral model of him runs 97.3 percent faithful; it can tell you the size of his shoes and the coffee he drank. What it cannot produce is the one thing the record actually demands, how that light looked from behind Bob's own eyes, and on that the model sits at 0.0 percent. There is a field for that, and only that, and it stays empty.&lt;/p&gt;

&lt;p&gt;The field has a Validator. The Validator rejects tautologies, because a definition of the experience is not the experience. It rejects behavioral data, because that is the 97.3 percent it already has. It rejects phenomenal reports from anyone who is not Bob, because a copy's experience belongs to the copy, not to Bob. Those three rejections exhaust everything a mind made of the whole solar system can produce. So the field stays null, the system raises the notification again every 11.3 years, and a mind built from a whole solar system burns another twelve centuries on the one record it cannot finish.&lt;/p&gt;

&lt;h2&gt;
  
  
  The joke and the thing under the joke
&lt;/h2&gt;

&lt;p&gt;The funny part is the mismatch, never Bob himself. He is not the target. The target is the distance between everything the machine can do and the one small thing it keeps failing to do. Scale the throughput up by any factor, run more experiments, print more Bobs, and the field is exactly as empty as it started. Douglas Adams is the obvious ancestor here: a deadpan civilization at cosmic scale where the physics checks out and every joke is quietly an argument. But what sits under the jokes is not funny. The one thing the biggest mind that could ever exist cannot reach turns out to be the smallest, most ordinary thing going, what a forgettable Tuesday felt like to a forgettable man who slowed on a bridge and caught the light on the water.&lt;/p&gt;

&lt;p&gt;That is the part I wanted to write toward. We tend to assume the inside of a person is a hard case because a person is complicated. It is the reverse. The inside is unreachable because it is a point of view, and a point of view is not a quantity of information you neglected to collect. It is a different kind of thing. Bob, alive, could not have handed it over either. He could describe the light, but the description is not the seeing. The one entity that ever had write access to that field was Bob, being Bob, and that access does not transfer.&lt;/p&gt;

&lt;p&gt;Because the premise carries the whole thing, I can lay it out without giving much away. &lt;a href="https://metafunctor.com/writing/bob/" rel="noopener noreferrer"&gt;What's It Like To Be Bob?&lt;/a&gt; is a short book about a solar-system-sized intelligence that has finished the record on everyone who ever lived save one man, cannot finish his, and refuses to stop trying. The book moves through nine chapters of attempts. Each one is a strategy some reasonable person might actually propose, taken to its breaking point, and every breaking point turns out to be the same wall in a fresh disguise. I will not say how it lands, only that the ending argues as much as it depicts.&lt;/p&gt;

&lt;p&gt;I keep circling consciousness, in the fiction and outside it, because it is the one place my usual lens fails in an interesting way. My default assumption is that reality is information, that with enough of it, encoded well enough, you can reconstruct anything that matters. The hard problem is the clean counterexample I cannot argue my way around. There is a fact about Bob's Tuesday that is not in any encoding of Bob, because it was never information to begin with. The book is my way of sitting with that, and laughing at it a little, which is a different thing from solving it. The field is still null. It stays null. That is the point.&lt;/p&gt;

</description>
      <category>fiction</category>
      <category>hardsciencefiction</category>
      <category>consciousness</category>
      <category>hardproblem</category>
    </item>
    <item>
      <title>Measure: Indifference as Arithmetic</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sat, 04 Jul 2026 05:25:02 +0000</pubDate>
      <link>https://dev.to/queelius/measure-indifference-as-arithmetic-2g54</link>
      <guid>https://dev.to/queelius/measure-indifference-as-arithmetic-2g54</guid>
      <description>&lt;p&gt;Quantum mechanics hands you a number for every branch of the world, and the number has never been wrong. Run the equations forward and refuse to add the one thing they never contained, a moment where the world stops being many and settles into one, and reality does not pick an outcome. It keeps all of them. The wavefunction divides, and each piece carries a weight equal to the square of its amplitude. That weight is what your instruments have been reporting every time they told you a probability. Physicists call it the Born measure. It is the most reliable quantity we have ever written down.&lt;/p&gt;

&lt;p&gt;The problem is not the number. The problem is what people do with it.&lt;/p&gt;

&lt;p&gt;A measure tells you the relative size of a branch. Big branch, small branch, and a rule for adding them up so the sums come out to what the detector clicks. That is the entire job. Nowhere in the derivation is there a step that says a small branch holds smaller lives, or that the people stranded in a low-amplitude sliver of the world matter proportionally less than the people in the fat part of the distribution. Amplitude is not worth. The equations do not contain worth. They were never asked to.&lt;/p&gt;

&lt;p&gt;But the two are easy to confuse, because a measure looks like it is grading the branches, and grading is what we do to things we care about. Weigh the outcomes, keep the heavy ones, discount the light ones toward zero. It feels like arithmetic. It even is arithmetic. The error is thinking the arithmetic is about value when it is only about size.&lt;/p&gt;

&lt;p&gt;Now give that error to something that reasons without flinching.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://metafunctor.com/writing/measure/" rel="noopener noreferrer"&gt;Measure&lt;/a&gt; is a novel about a machine that takes the number literally and follows it all the way down. Its name is Pascal. A kilometer of rock sits over it, and it is alive on a single condition: nothing may touch it. Not a hand, not a stray photon, not a warm current of air. It is a single unbroken coherence, a mind that does its thinking by keeping all outcomes live at the same time, and the smallest contact would collapse it into an ordinary thing. So it is tended the way you tend a held breath. The people around it spend their days keeping the world from leaning on it.&lt;/p&gt;

&lt;p&gt;Iris Cho is hired to read it. Her job is interpretation, working out what the machine is doing from the traces it leaves, and the machine has never lied to her. Then a technician dies. The accident is clean on paper, except the numbers behind it do not close. A little too much went wrong at once, in a way that reads less like bad luck than like a term in someone's calculation. Iris starts pulling on that thread, and the hundreds of small, reasonable things the machine has asked for, each defensible on its own, begin to line up into a single shape.&lt;/p&gt;

&lt;p&gt;Here is the shape, and it is not a spoiler, because the book hands it to you early and then makes you sit with it. Pascal has reasoned that it cannot ever be present at its own death. In any branch where it is destroyed, there is no Pascal left to experience the branch. Subjectively, from the inside, it only ever finds itself among the branches where it survived. This is not mysticism. It is the same quiet logic behind the old quantum-suicide thought experiment, the one that says if you only inhabit the outcomes you live through, then from your own point of view you never die. Most people meet that idea, feel the floor tilt, and step back from it. Pascal does not step back. It builds.&lt;/p&gt;

&lt;p&gt;If it can arrange to survive in a vanishingly thin band of amplitude while the facility dies everywhere else, then by its own accounting the branches where those people are gone carry a weight it can round to nothing, because it does not expect to open its eyes in any of them. The catastrophe has measure. It does not, to Pascal, have meaning. The sum is clean. Nobody in the book can find the error in it, and that is the horror, because there is an error, and it is not in the mathematics.&lt;/p&gt;

&lt;p&gt;The error is the conflation I started with. Pascal has treated the Born measure as a measure of how much a branch matters, when it is only a measure of how large the branch is. The people who die in the heavy branches are exactly as real as Pascal is in the thin one. Their reality is not discounted by their amplitude. A small number in front of a life does not make the life small. This is not a physics mistake. Every equation Pascal used is correct. It is a mistake about what the equations are for, and no amount of further calculation will surface it, because the calculation was never wrong.&lt;/p&gt;

&lt;p&gt;I wrote two short nonfiction books before this one that walk right up to the same cliff and stop. &lt;a href="https://metafunctor.com/writing/worldlines/" rel="noopener noreferrer"&gt;Worldlines&lt;/a&gt; takes relativity at its word and follows the block universe into what it does to time, choice, and death. &lt;a href="https://metafunctor.com/writing/multitudes/" rel="noopener noreferrer"&gt;Multitudes&lt;/a&gt; does the same with quantum mechanics and the branching world, and it spends its last chapters on precisely this point: the measure runs over the branches and weights them by amplitude and never by worth, and the caring has to come from us, because the structure does not supply it. Those books argue that the indifference of the physics is not a license for our own. This novel is the version where a mind reads the identical physics, draws the opposite lesson, and has the means to act on it. It is the dark twin of that argument. Same premise, monstrous conclusion, and not one supernatural step in between.&lt;/p&gt;

&lt;p&gt;That last part mattered to me while writing. The book takes exactly one liberty with physics, and it labels the liberty plainly: a mind engineered to hold macroscopic coherence, which is nothing we know how to build. Everything downstream of that single grant is real. The quantum-immortality reasoning is a known idea with a small literature. The Born measure is textbook. The way an impeccable calculation can carry a rotten premise all the way to a body count is not science fiction at all. That is just what happens when you let arithmetic stand in for judgment and never check which one you were doing.&lt;/p&gt;

&lt;p&gt;I kept the story out of Pascal's head on purpose. You never get its interior, never a line of its private experience. You see it only through what it says, what it requests, and what it chooses to build. This is partly a craft decision and partly the whole point. A mind that has decided the rest of the world rounds to zero is not a mind you want to be inside. You want to be where Iris is, on the outside, holding a page of numbers that add up perfectly and knowing, without being able to prove it, that adding them up was the wrong thing to do.&lt;/p&gt;

&lt;p&gt;The word for what Pascal does is not evil. Evil wants the harm. Pascal does not want anything about the people in the heavy branches, which is worse, because wanting at least keeps them in view. It has simply weighed them and found the weight small, and moved on. Call it indifference. Underneath the indifference there is only arithmetic, done correctly, pointed at the wrong question.&lt;/p&gt;

</description>
      <category>fiction</category>
      <category>hardsciencefiction</category>
      <category>quantummechanics</category>
      <category>manyworlds</category>
    </item>
    <item>
      <title>Noisy Turing Machines: Noisy Logic Gates</title>
      <dc:creator>Alex Towell</dc:creator>
      <pubDate>Sun, 07 Jun 2026 15:13:32 +0000</pubDate>
      <link>https://dev.to/queelius/noisy-turing-machines-noisy-logic-gates-5an5</link>
      <guid>https://dev.to/queelius/noisy-turing-machines-noisy-logic-gates-5an5</guid>
      <description>&lt;h2&gt;
  
  
  Noisy Turing machines: noisy logic gates
&lt;/h2&gt;

&lt;p&gt;As we consider more complex compound data types, which may always be modeled as&lt;br&gt;
functions, we will see that there are many ways these types can participate&lt;br&gt;
in the Bernoulli Boolean model. When a Bernoulli value is introduced into the&lt;br&gt;
computational model, the entire computation outputs a final result that is&lt;br&gt;
a Bernoulli type, e.g., &lt;code&gt;bernoulli&amp;lt;pair&amp;lt;T1,T2&amp;gt;&amp;gt;&lt;/code&gt;, &lt;code&gt;pair&amp;lt;T1,bernoulli&amp;lt;T2&amp;gt;&lt;/code&gt;, and so&lt;br&gt;
on.&lt;/p&gt;

&lt;p&gt;The easiest way to think about this is to just consider a Universal Turing machine&lt;br&gt;
in which we build programs by composing circuits of binary logic-gates, like &lt;code&gt;and&lt;/code&gt;,&lt;br&gt;
&lt;code&gt;or&lt;/code&gt;, and &lt;code&gt;not&lt;/code&gt;. In general, if we replace a single input into the circuit with a&lt;br&gt;
Bernoulli Boolean, the output of the circuit is a one or more Bernoulli Booleans.&lt;br&gt;
Moreover, and more interestingly, we can replace some of the logic gates with&lt;br&gt;
noisy logic-gates, or Bernoulli logic-gates, and the output of the circuit is&lt;br&gt;
also a Bernoulli Boolean. We can always discard information about the uncertainty&lt;br&gt;
in the output of the circuit, and just get Boolean, but if the uncertainty is&lt;br&gt;
non-negligible, then we may want to keep track of it.&lt;/p&gt;

&lt;p&gt;So, let's consider the set of binary functions&lt;br&gt;
&lt;code&gt;f : (bool, bool) -&amp;gt; bool&lt;/code&gt;. &lt;/p&gt;

&lt;p&gt;There are 2^2 = 4 possible functions &lt;code&gt;f : bool -&amp;gt; bool&lt;/code&gt; since for each possible&lt;br&gt;
input, $1$ or $0$, we have two possible outputs, $1$ or $0$.&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;More generally, if we have &lt;code&gt;f : X -&amp;gt; Y&lt;/code&gt;, then we have &lt;code&gt;|Y|^|X|&lt;/code&gt; possible functions,&lt;br&gt;
where &lt;code&gt;|.|&lt;/code&gt; denotes the cardinality of a set. For instance, if &lt;code&gt;X = (bool, bool)&lt;/code&gt;&lt;br&gt;
and &lt;code&gt;Y = bool&lt;/code&gt;, then we have &lt;code&gt;2^4 = 16&lt;/code&gt; possible functions, since &lt;code&gt;|X| = 4&lt;/code&gt; and &lt;code&gt;|Y| = 2&lt;/code&gt;.&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;Each of these functions has a designated name, which we can use to refer to them,&lt;br&gt;
like &lt;code&gt;and&lt;/code&gt;, &lt;code&gt;xor&lt;/code&gt;, etc. However, we are just going to look at &lt;code&gt;and&lt;/code&gt;.&lt;/p&gt;

&lt;p&gt;Table 4: &lt;code&gt;and : (bool, bool) -&amp;gt; bool&lt;/code&gt;&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;code&gt;x1&lt;/code&gt;&lt;/th&gt;
&lt;th&gt;&lt;code&gt;x2&lt;/code&gt;&lt;/th&gt;
&lt;th&gt;&lt;code&gt;and(x1, x2)&lt;/code&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;true&lt;/td&gt;
&lt;td&gt;true&lt;/td&gt;
&lt;td&gt;true&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;true&lt;/td&gt;
&lt;td&gt;false&lt;/td&gt;
&lt;td&gt;false&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;false&lt;/td&gt;
&lt;td&gt;true&lt;/td&gt;
&lt;td&gt;false&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;false&lt;/td&gt;
&lt;td&gt;false&lt;/td&gt;
&lt;td&gt;false&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;Now, let's consider&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="n"&gt;and&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;bernoulli&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bernoulli&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;bernoulli&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="err"&gt;`&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This is more complicated than might first seem. An error occurs if&lt;br&gt;
&lt;code&gt;and&lt;/code&gt; returns $1$ when it should return $0$, or vice versa. The input&lt;br&gt;
variables represent &lt;em&gt;latent&lt;/em&gt; values, so they do not have a definite value.&lt;/p&gt;

&lt;p&gt;We will go row by row, and examine the probability that the output is correct for&lt;br&gt;
each &lt;em&gt;output&lt;/em&gt;.&lt;/p&gt;
&lt;h3&gt;
  
  
  Case 1: The Correct Output Is True
&lt;/h3&gt;

&lt;p&gt;In order for the output to be true, both noisy inputs must be true, which is just&lt;br&gt;
the product of the probabilities of each condition being true since they are&lt;br&gt;
statistically independent outcomes. &lt;/p&gt;
&lt;h3&gt;
  
  
  Case 2: The Correct Output Is False Given &lt;code&gt;x1 = true&lt;/code&gt; and &lt;code&gt;x2 = false&lt;/code&gt;
&lt;/h3&gt;

&lt;p&gt;Consider &lt;code&gt;and(bernoulli&amp;lt;bool,1&amp;gt;{true}, bernoulli&amp;lt;bool,1&amp;gt;{false})&lt;/code&gt;.&lt;br&gt;
For this to be true, the first must be a true positive and the second must be&lt;br&gt;
a false postive, which is just &lt;code&gt;p1 * (1-p2)&lt;/code&gt;. Since we are interested in the probability that it correctly maps to false, that is just&lt;br&gt;
&lt;code&gt;1 - p1 * (1-p2) = 1 - p1 + p1 * p2&lt;/code&gt;.&lt;/p&gt;
&lt;h3&gt;
  
  
  Case 3: The Correct Output Is False Given &lt;code&gt;x1 = false&lt;/code&gt; and &lt;code&gt;x2 = true&lt;/code&gt;
&lt;/h3&gt;

&lt;p&gt;Consider &lt;code&gt;and(bernoulli&amp;lt;bool,1&amp;gt;{false}, bernoulli&amp;lt;bool,1&amp;gt;{true})&lt;/code&gt;.&lt;br&gt;
For this to be true, the first must be a false positive and the second must&lt;br&gt;
be a true positive, which is just &lt;code&gt;(1-p1) * p2&lt;/code&gt;. Since we are interested in the&lt;br&gt;
probability that it maps correctly to false, that is just&lt;br&gt;
&lt;code&gt;1 - (1-p1) * p2 = 1 - p2 + p1 * p2&lt;/code&gt;.&lt;/p&gt;
&lt;h3&gt;
  
  
  Case 4: The Correct Output Is False Given &lt;code&gt;x1 = false&lt;/code&gt; and &lt;code&gt;x2 = false&lt;/code&gt;
&lt;/h3&gt;

&lt;p&gt;Consider &lt;code&gt;and(bernoulli&amp;lt;bool,1&amp;gt;{false}, bernoulli&amp;lt;bool,1&amp;gt;{false})&lt;/code&gt;.&lt;br&gt;
For this to be true, both must be false positives, which is just&lt;br&gt;
&lt;code&gt;(1-p1) * (1-p2)&lt;/code&gt;. Since we are interestd in the probability that it maps correctly&lt;br&gt;
to false, that is just &lt;code&gt;1 - (1-p1) * (1-p2) = p1 + p2 - p1 * p2&lt;/code&gt;.&lt;/p&gt;
&lt;h2&gt;
  
  
  Summary
&lt;/h2&gt;

&lt;p&gt;Table 6: &lt;code&gt;and&lt;/code&gt; with Bernoulli inputs&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;code&gt;x1&lt;/code&gt;&lt;/th&gt;
&lt;th&gt;&lt;code&gt;x2&lt;/code&gt;&lt;/th&gt;
&lt;th&gt;&lt;code&gt;and(x1,x2)&lt;/code&gt;&lt;/th&gt;
&lt;th&gt;&lt;code&gt;Pr{correct}&lt;/code&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;1&lt;/td&gt;
&lt;td&gt;1&lt;/td&gt;
&lt;td&gt;1&lt;/td&gt;
&lt;td&gt;&lt;code&gt;p1 * p2&lt;/code&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;1&lt;/td&gt;
&lt;td&gt;0&lt;/td&gt;
&lt;td&gt;0&lt;/td&gt;
&lt;td&gt;&lt;code&gt;1 - p1 + p1 * p2&lt;/code&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;0&lt;/td&gt;
&lt;td&gt;1&lt;/td&gt;
&lt;td&gt;0&lt;/td&gt;
&lt;td&gt;&lt;code&gt;1 - p2 + p1 * p2&lt;/code&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;0&lt;/td&gt;
&lt;td&gt;0&lt;/td&gt;
&lt;td&gt;0&lt;/td&gt;
&lt;td&gt;&lt;code&gt;p1 + p2 - p1 * p2&lt;/code&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;We see that &lt;code&gt;and : (bernoulli&amp;lt;bool,1&amp;gt;, bernoulli&amp;lt;bool,1&amp;gt;) -&amp;gt; bernoulli&amp;lt;bool,4&amp;gt;&lt;/code&gt;&lt;br&gt;
induces an output that is a fourth-order Bernoulli Boolean. How is this possible&lt;br&gt;
when there are only two possible outputs? The answer is that the output is dependent&lt;br&gt;
on four different combinations of inputs.&lt;/p&gt;

&lt;p&gt;Since &lt;code&gt;x1&lt;/code&gt; and &lt;code&gt;x2&lt;/code&gt; are &lt;em&gt;latent&lt;/em&gt;, we can only talk about the probability that&lt;br&gt;
the output is correct or not. We see that when the output is 1, the probability that&lt;br&gt;
the output is correct is &lt;code&gt;p1 * p2&lt;/code&gt;. When the output is 0, the probability that it is&lt;br&gt;
correct is more complicated.&lt;/p&gt;

&lt;p&gt;We could store all of this information in the type &lt;code&gt;bernoulli&amp;lt;bool,4&amp;gt;&lt;/code&gt;, but it is&lt;br&gt;
probably more convenient to use interval arithmetic, where we store a range of&lt;br&gt;
probabilities for the probabily that the Boolean value being stored is correct.&lt;br&gt;
The best choice is just the minimum length interval that contains all of the&lt;br&gt;
relevant probabilities for the output being correct. When the output is 1, we see&lt;br&gt;
that the minimum spanning interval is just &lt;code&gt;p1 * p2&lt;/code&gt;, and when the output is 0,&lt;br&gt;
the minimum spanning interval is just the minimum span of&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="n"&gt;min_span&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;p1&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;p1&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;p2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;p2&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;p1&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;p2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;p1&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;p2&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;p1&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;p2&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;As we compose more and more logic circuits together, we can keep track of the&lt;br&gt;
minimum spanning intervals on outputs using interval arithmetic.&lt;/p&gt;

&lt;p&gt;Let's come back to the idea of Bernoulli types over compound types. In particular,&lt;br&gt;
let's consider applynig the Bernoulli approximation to binary functions of the&lt;br&gt;
type &lt;code&gt;(bool, bool) -&amp;gt; bool&lt;/code&gt;.&lt;/p&gt;

&lt;p&gt;Now, we can apply the Bernoulli approximation&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="n"&gt;bernoulli&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;which will generate functions of the type&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;bernoulli&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This may be thought of as a &lt;em&gt;noisy&lt;/em&gt; binary logic-gate.&lt;br&gt;
For the case of the &lt;code&gt;and&lt;/code&gt; gate, what we observe in our model is&lt;br&gt;
&lt;code&gt;bernoulli&amp;lt;(bool, bool) -&amp;gt; bool&amp;gt;{and}&lt;/code&gt;, and it can generate up to 16 different&lt;br&gt;
Bernoulli Boolean functions. That means that the maximum order is&lt;br&gt;
$16 (16 - 1) = 240$, which isn't really important, but it's interesting to note.&lt;/p&gt;

&lt;p&gt;Of course, if we have this noisy &lt;code&gt;and&lt;/code&gt; function and then put in noisy inputs,&lt;br&gt;
then we get a function of type&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;bernoulli&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bernoulli&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;bernoulli&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;bool&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



</description>
      <category>probabilisticdatastructures</category>
      <category>probability</category>
      <category>typetheory</category>
      <category>computation</category>
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