The logical piano
System 1 models, a fourth gate, and the automation that did not come
- it consumed no coal, because its rate of consumption was too high
- we do not want it to do its own business, but ours
- more correct in their calculations
- the secret of all reasoning machines is after all very simple
- a proposition is in itself neither probable nor improbable
- as reliable as a fourth logic gate
- every turn re-reads everything that came before it
- it can do whatever we know how to order it to perform
- such labour can always be purchased at an easy rate
A logical piano: the machine W. S. Jevons had built in 1869. Its face shows the 16 combinations of 4 terms and their negatives, ABCD, ABCd and so on to abcd. Its 21 keys enter a premise as an equation: 8 letters for the subject, the copula, 8 letters for the predicate, an "or" on each side, a full stop that enters the premise and a finis that clears the machine. "Every A is a B" is A = AB. A premise strikes out the combinations that do not agree with it. The example: every A is a B, and every B is a C, 10 keys in all. A = AB strikes out 4 combinations (those that are A and not B), B = BC strikes out 4 more (those that are B and not C), and 8 of the 16 stand: ABCD ABCd aBCD aBCd abCD abCd abcD abcd. What stands says of A that it is ABC, of B that it is BC, of what is not B that it is ab, of what is not C that it is abc. Beside the keys, a table of 9 rows and 8 columns: for anything at all, and for each of the 8 terms, how many of the combinations left under it are under each term. Of the 2 left that are A, 2 are C. Of the 6 left that are C, 2 are A, and of the 4 left that are B, 2 are A. Of the 2 left that are not C, 2 are not A, and of the 4 left that are not B, 4 are not A: the premises turned round, which nobody keyed. Of the 8 left, 6 are C. Of the 2 left that are A, 1 is D, for the premises say nothing of D. 3 more examples. "Every A is a B or a C, and no B is a C" (A = AB | AC, B = Bc) strikes out 2 and 4 and leaves 10; of the 4 left that are A, 2 are B. "A = a", a contradiction, strikes out all 16: nothing is left, and every share is 0 of 0. With no premise 16 stand, and of the 8 that are A, 4 are C: any term gives any other 1 in 2. The live figure needs JavaScript: the machine played key by key, the 4 examples, the 21 keys to enter up to 5 premises of one's own, and the table.
It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle—they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
—A. N. Whitehead, An Introduction to Mathematics (1911), ch. 5. P. 61, from the chapter on the symbolism of mathematics, written the year after the first volume of Principia Mathematica. The sentence before the passage gives the mechanism: "by the aid of symbolism, we can make transitions in reasoning almost mechanically by the eye which would otherwise call into play the higher faculties of the brain." The emphasis is mine.
it consumed no coal, because its rate of consumption was too high
Manchester, 1869. William Stanley Jevons, professor of logic and of political economy at Owens College, took delivery of a machine he had designed and a clockmaker in Salford had built. It stood about 3 feet high, had 21 keys, and looked, he had written to his brother while it was being built, like "a large accordion or a very small piano". Jevons to Herbert Jevons, 23 June 1868, in Papers and Correspondence of William Stanley Jevons, vol. III, p. 185, as David Dunning quotes it in "Logical Piano Lessons" (Computer History Museum, 2022); the height and the clockmaker are in the article "Logic Machines" of the Encyclopedia of Philosophy (1967). The machine is in the History of Science Museum at Oxford, inv. 18230. He was the son of a Liverpool iron merchant whose firm had failed in the railway crash of 1848, and he had spent 5 years of his youth as assayer at the new mint in Sydney, weighing gold, before he came home to study logic under De Morgan. On 20 January 1870 he showed the machine to the Royal Society. On its face stood the 16 combinations that can be made of 4 terms and their negatives, ABCD, ABCd and on to abcd, which he called the logical alphabet. One pressed the keys as one would write a sentence, a subject, a copula, a predicate, a full stop, and rods inside removed from the face every combination the sentence had made impossible. What remained was the conclusion, or rather every conclusion at once, to be read off by whoever stood before it. "The actual process of logical deduction," he told the Society, "is thus reduced to a purely mechanical form." Babbage had shown that "material machinery is capable, in theory at least, of rivalling the labours of the most practised mathematicians"; this was a smaller thing, and it worked. It was, on the usual reckoning, the first machine to solve a complicated problem of logic faster than a person could without one. W. Stanley Jevons, "On the Mechanical Performance of Logical Inference", Philosophical Transactions of the Royal Society 160 (1870), 497–518, at pp. 500 and 498, read 20 January 1870. A premise is an equation: "every A is a B" is A = AB, the As being the same things as the As that are Bs. The figure at the head of the page is the machine by this description, with the layout of the keys from the frontispiece of his Principles of Science (1874): finis, "or", d D c C b B a A, copula, A a B b C c D d, "or", full stop. The reckoning is the Encyclopedia's. He drowned in 1882, at 46, bathing off the coast near Hastings.
Jevons is remembered for another book. In 1865, at 29, he had published The Coal Question, which asked how long the cheap coal on which Britain's industry stood could last, and John Stuart Mill praised it in the House of Commons the next spring. Its seventh chapter met the comfortable reply that engines were growing more economical every year, so that the same work would need less and less coal. He answered with a history of the steam engine, and with a sentence that has outlived the question:
It is wholly a confusion of ideas to suppose that the economical use of fuel is equivalent to a diminished consumption. The very contrary is the truth. […] It is the very economy of its use which leads to its extensive consumption.
—W. Stanley Jevons, The Coal Question (1865), ch. VII, "Of the Economy of Fuel". The ellipsis is mine. The engine of Savery, he goes on, the first that raised water by fire, was so wasteful that "the cost of working kept it from coming into use; it consumed no coal, because its rate of consumption was too high." Every improvement since, Newcomen's, Watt's, had cut the coal an engine burned for a given work, and at each the consumption of coal had risen.
On 15 September 2026, a company in San Francisco named a model after him. TypeSafe AI had been founded in 2024 and had spent 2 years out of sight; its chief executive, Diogo Almeida, is one of the authors of the paper of 2022 that showed how a network trained to continue text could be made into an assistant that follows instructions, by a method called reinforcement learning from human feedback (RLHF), which every chat model since has used. Long Ouyang, Jeff Wu, Xu Jiang, Diogo Almeida and 16 others, "Training language models to follow instructions with human feedback", arXiv:2203.02155 (4 March 2022), the InstructGPT paper. Almeida, "Introducing System One Models & Jev", TypeSafe AI, 15 September 2026, with a seed round of $40 million led by DCVC; the founders are Almeida, Erik Gafni and Sasha Sheng. The launch post says the model is named for Jevons, in the expectation that machine intelligence will go the way of coal. The model, Jev, cannot write. It takes a state, which may be a ticket, a contract, a log, the transcript of an agent's last 40 steps, and with it a set of typed questions, and it returns for each question one of 3 kinds of answer: a Choice among up to 255 named options, a Score on a ladder of 2 to 10 described levels, or a Noul, the chance that a statement is true. Every answer comes with its probabilities, all the questions are answered in 1 pass, and nothing is generated, so that no sentence, no malformed record and no invented field can come back. It answers in 70 to 500 milliseconds, at 4.2 cents for a million tokens read and nothing for the answer. The launch post gives the whole design in a phrase, "unstructured state in, typed probabilistic decisions out", and calls the kind a System One Model, after the fast and effortless half of Daniel Kahneman's account of the mind. The numbers are TypeSafe's, from the launch post and the documentation of jev-1.13.0. Noul is from Bernoulli. The price drew the headlines, and the absence of text is the invention; Almeida's own gloss, the same day, was "The gains aren't free: Jev can't generate text." Within 3 weeks, Cloudflare had released 2 models of the same kind with their weights, Clef and Clef-flash, post-trained from Alibaba's open Qwen models of 27 and 9 billion parameters and answering to the same interface; a small laboratory, Convai Innovations, had released a third, Laya, of 421 million parameters; and reconstructions of the training had begun to appear on arXiv. Cloudflare's post announcing Clef and Clef-flash, 1 October 2026: the Apache license, a median of 209 and 39 milliseconds, 24 and 9 cents a million tokens. Laya is built on the ModernBERT encoder. Cloudflare says "decision model", TypeSafe "System One Model"; the first is the better name, for reasons that will appear. The keyboard keeps returning in the names. Cloudflare's is the sign at the head of a staff that says in what register the notes after it are to be read; laya is the Indian musician's word for tempo; and the economist of coal, for whom the first is named, built a piano.
Set the 2 machines side by side, for they do the same thing. Each is handed an alphabet of answers declared in advance, 16 combinations on a face or 255 options in a request, and each is forbidden to answer outside it. The piano decides by rule: a premise is keyed, and what does not agree with it is struck out, with certainty and with no possibility of error but a slipped rod. Where the premises are silent it is silent too. Key that every A is a B and every B is a C, and ask of the As how many are D: 1 of the 2 combinations left, the machine says, which is its way of saying nothing. Jev decides where no premise has been keyed. Nobody has told it which tickets are urgent or what makes a clause unusual; it was trained, and it answers with a number, 0.83, on which a program is expected to act. What that number is, and what stands behind it, is most of what there is to understand about the kind, and it will take the Vienna of 1921 and a weather bureau to say.
The piano was judged in its own century, by a better logician than its maker. In 1887, after Allan Marquand at Princeton had rebuilt it in a simpler form, Charles Peirce wrote for the first number of the American Journal of Psychology an essay on what such machines could and could not do:
Every reasoning machine, that is to say, every machine, has two inherent impotencies. In the first place, it is destitute of all originality, of all initiative. It cannot find its own problems; it cannot feed itself. It cannot direct itself between different possible procedures. […] This, however, is no defect in a machine; we do not want it to do its own business, but ours. The difficulty with the balloon, for instance, is that it has too much initiative, that it is not mechanical enough. We no more want an original machine, than a house-builder would want an original journeyman, or an American board of college trustees would hire an original professor.
—C. S. Peirce, "Logical Machines" (1887). American Journal of Psychology 1 (1887), 165–170; the ellipsis and the emphasis are mine. Of the piano he observes that all it shows at the end is the list of the combinations the premises have left, from which the conclusion has still to be picked out, as the figure leaves it to the reader. In a letter to Marquand of 30 December 1886 he had drawn logic in batteries and switches, in series for "and" and in parallel for "or": the earliest known sketch of what became the logic gate.
TypeSafe's slogan is this sentence in 5 words: "We're building prod, not God." Its manifesto says that the company is not chasing the moving goalpost of artificial general intelligence, since the models of today have long passed the threshold of intelligence at which enormous value could be made, and that what is missing is a place for that intelligence to live in software. As a judgment on the year it is hard to fault. The frontier laboratories have organized themselves around 1 model that is to do everything, and the measure of progress has been what that model can do at its best, a proof, a program, an exam; whether anything can be left alone with it has been a second question. Almeida calls the belief the mono-model Kool-Aid, and he is entitled to the phrase, having mixed some of it. The slogan and the manifesto are on TypeSafe's site; the Kool-Aid is from his conversation with Ben Horowitz and Martin Casado on the a16z podcast, 28 September 2026, where he also doubts that the field is on a path to recursive self-improvement. But Peirce's sentence has a first half, and the slogan leaves it out. A machine that does our business cannot find our problems. Someone has to find them, cut them to the machine's alphabet, and answer for what it decides, and the account of who that is turns out to be older than the piano.
we do not want it to do its own business, but ours
Almeida has made his case in public since the spring: at conferences, in 2 long interviews in the weeks after the launch, in essays on his own site, and on 12 November from the stage of the AI Engineer Code Summit, under slides the first of which asks what is going on in AI, in the 3 letters engineers use for the question. The talk at the AI Engineer World's Fair in the summer, first announced as "What's next after RLHF?"; the conversations with Latent Space (21 September 2026) and with Ben Horowitz and Martin Casado on the a16z podcast (28 September); the essays "(KV) Cache Rules Everything Around Me" (9 September) and "The Bitterest Lesson" on completeskeptic.com; and the keynote of 12 November, which Latent Space reported as "The Jev Revolution". The slide reads "WTF is going on in AI?". It is 1 argument told to different rooms, and it starts from the paper he signed. A language model that has been through RLHF is a machine for pleasing a reader. Its judge in training was a person comparing 2 answers; what it gives back is prose; and the person who receives the prose is the last stage of the system, placed there to catch whatever is wrong with it. He calls this assistance, and observes that it has been the industry's only product. Even the agents that write software for hours stand on that side of the line, since somebody reads the result before it ships: "Claude Code is still part of the assistance era." From the World's Fair talk, which sets the 2 eras in 2 columns. Automation is the other thing. A program acts on what the model returns and nobody reads it, and that asks of the output 2 properties prose does not have: it must be a value a program can branch on, and it must come with a number that says how far it is to be trusted. His name for the arrangement is "programs in the loop". From the Latent Space interview, where the 3 answers of Jev are also matched to the constructs of a programming language: a Choice is a switch over an enumeration, a Noul is the condition of an if, a Score is what one sorts or thresholds by. The evidence he offers is the state of the trade. For all that the models can do, he told Horowitz and Casado, nobody will yet leave one alone at a drive-through window; in the keynote the same model is Einstein 95 times in 100 and Mr. Bean the other 5.
Most of this is right, and it is said too seldom by people who have worked inside the laboratories. The first thing he has right is the measure. Progress at the frontier is counted by the best a model can do: the hardest proof, the longest task, the examination passed. The autumn's emblem was a Millennium problem attacked by some 10,000 agents for 88 hours. And then disputed, on the ground that the formal proof did not say what the prose beside it said it said. I went through that episode, and what a proof is when a machine has produced it, in The painted rock. Whether a thing can be left alone is counted at the other end, by what it does the worst time in 20, and the 2 numbers have little to do with each other: one asks whether there is a run in which the model succeeds, the other whether there is a run in which it fails. A field that reports the first and sells the second will overpromise as a matter of arithmetic, without anyone lying. The second thing is the judge. RLHF closes the loop of learning with a rater's preference between texts, and no fact enters that loop except through the rater's eye. The third is the type. A paragraph has none; a program cannot branch on it without a second model to read it, whose reading is again a paragraph.
And he is right about the phrase the industry reached for when the unreliability became plain. "Human in the loop" has been offered as a kind of automation, and it is the opposite of one. A process in which a person approves each step runs at the speed, the cost and the attention of that person; it is assistance with the roles relabeled, and the more capable the model, the more of the person's day goes to reading what it wrote. There are 3 places a person can stand to a machine that decides: in the loop, passing each decision; on the loop, taking the exceptions and auditing a sample; and before the loop, deciding what the questions, the options and the thresholds are to be. Automation is the move from the first place to the other 2. It is never the removal of the person, and here the engagement with Almeida has to become critical, because the pitch sometimes sounds as if it were.
The documentation of Jev gives the pattern for using it: act on a Noul above 0.7, act on its denial below 0.3, and send what falls between to a person. This is an old design, and it has an author. In 1957 C. K. Chow, an engineer at Burroughs working on machines to read printed characters, showed that a recognizer which may decline to answer does best by a single rule: answer when the probability of the likeliest reading exceeds a threshold, and otherwise reject, the rejects going to an operator; in 1970 he gave the exact trade between the errors such a machine makes and the share it rejects. C. K. Chow, "An optimum character recognition system using decision functions", IRE Transactions on Electronic Computers EC-6 (1957), 247–254, and "On optimum recognition error and reject tradeoff", IEEE Transactions on Information Theory 16 (1970), 41–46. Bank checks and letters were sorted on this plan for the half century that followed, with clerks keying what the readers rejected. Two things follow from Chow, and the first is in Almeida's favor. The rule is optimal only if the probabilities are true ones; with numbers that merely rank the cases, the threshold means nothing fixed. A calibrated probability is therefore the precondition of the oldest architecture of automated judgment, and to have seen that the frontier's post-training destroys it, and to have built a company on restoring it, is a real insight. The second is against the pitch. The size of an automation is the share of cases on which the machine is sure enough, at the error one will tolerate, and calibration does not enlarge that share; it only reports it truthfully. A model can be perfectly calibrated and never sure. What is being sold as reliable intelligence is, in Chow's terms, an honest reject rate, which is worth a great deal and is a different thing.
The reject pile has its own literature. Lisanne Bainbridge's "Ironies of Automation" of 1983, written about chemical plants and flight decks, observed that the designer who automates what can be automated leaves the operator the remainder, which is whatever the designer could not work out how to automate; that the operator, no longer practiced on the ordinary cases, is then asked to take over on the extraordinary ones; and that watching a machine that is nearly always right is a task people do badly. Automatica 19 (1983), 775–779. The middle band of a decision model is that remainder in a pure form. It holds, by construction, the cases a good model could not tell apart, and it delivers them to a clerk who no longer sees the easy ones that kept a clerk's judgment in repair. The desk where the band arrives is not in the talks. It is where the cost of a thresholded automation is paid, and a company that takes "automation is not human in the loop" as its creed owes its customers an account of the human on the loop.
There is a deeper way to put what he has seen, and it shows where his own product is weakest. A learning system is closed by whoever tells it that it was wrong, and there have been 3 such judges. The first is the rater, who prefers; RLHF is his. The second is the checker, a compiler, a suite of tests, the kernel of a proof assistant, which accepts or refuses; the reinforcement learning from verifiable rewards behind the coding and proving systems is his, and it is why the frontier's triumphs are in code and mathematics, where a checker exists. The third is the event: the ticket was reopened or it was not, the loan defaulted, it rained. A calibrated decision is a statement about events, and nothing but events can score it. Almeida's third objective is the third judge, and in naming it he has named the thing the field lacks. But Jev, by TypeSafe's own account, is trained on synthetic data throughout: tasks, states and outcomes composed for the purpose, with no customer's records among them. An outcome that was composed did not happen. It is a label, given by whatever wrote the case, and the rater has come back in through the door marked "event". The probabilities such training produces are calibrated to a world its makers wrote, and how they fare at the border of that world is a question for measurement, which outsiders have begun to supply.
The other way out of the chat box keeps the person and widens the loop. Thinking Machines Lab, founded by Mira Murati in 2025, showed in May 2026 what it calls interaction models: a model that takes in and gives out in turns of 200 milliseconds, with a fast model at the front and a reasoning model working behind it, trained from scratch at 276 billion parameters of which 12 billion are active at once. Its manifesto of July, "The Future Worth Building Is Human", states the aim as the extension of human will and judgment, leans on Hayek and Polanyi for the claim that the knowledge that matters is tacit and dispersed, and locates the fault of the assistant in its channel: "a small text box and a long wait". Thinking Machines Lab, the preview of interaction models, 11 May 2026 (the model is TML-Interaction-Small), and "The Future Worth Building Is Human", 10 July 2026. The 2 companies agree on the diagnosis and divide on whether the person is the cost or the point. TypeSafe's remedy is a better accounting of the machine's doubt; Thinking Machines' is a better anthropology of the person's knowledge. Each is weakest where the other is strong. If what a person knows cannot be told, as Polanyi held, a wider channel carries more telling and no more of the knowledge, and the judgment stays where it was, which makes the product assistance by design and for good; that is an honorable bet on the kind of work in which a decision is made once, by someone who must answer for it, and it leaves untouched the decision made 10 million times a day, for which a person in the loop is not judgment but latency. Peirce's sentence holds both halves. We want the machine to do our business, and it is ours.
more correct in their calculations
Paris, the Year II. Gaspard de Prony, an engineer of bridges and roads at the head of the new land survey, had been charged by the Republic with tables of logarithms and of trigonometric functions for the decimal division of the quadrant, on a scale meant to make them the largest monument of calculation ever raised: the logarithms of the sines and tangents of the 100,000 parts of the right angle, the logarithms of the numbers to 200,000, carried to 14 places and beyond. It was more arithmetic than he and every assistant he could hope for would finish in their lives. The way out came to him, by the account Charles Babbage copied down nearly 40 years later, in a bookshop, where he opened The Wealth of Nations at its first chapter, on the making of pins:
À peine avait-il parcouru les premières pages, que, par une espèce d'inspiration, il conçut l'expédient de mettre ses logarithmes en manufacture comme les épingles.
He had scarcely run through the first pages when, by a kind of inspiration, he conceived the expedient of putting his logarithms into manufacture like pins.
—quoted by Charles Babbage, On the Economy of Machinery and Manufactures (1832), §243. From the chapter "On the Division of Mental Labour"; the translation is mine. The French is from a note of 1820 on the proposal that the British government share the cost of printing the tables. They filled 17 folio volumes in manuscript and were never printed whole.
He divided the work into 3 sections. In the first sat 5 or 6 of the best mathematicians in France, Legendre among them, who did no arithmetic at all: they found the formulas by which the functions could be computed by differences. The second, 7 or 8 calculators, turned the formulas into numbers, set up the sheets, and checked what came back. The third did the work, and Babbage, who saw in it the charter of his own engine, describes its members precisely:
The members of this section, whose number varied from sixty to eighty, received certain numbers from the second section, and, using nothing more than simple addition and subtraction, they returned to that section the tables in a finished state. It is remarkable that nine-tenths of this class had no knowledge of arithmetic beyond the two first rules which they were thus called upon to exercise, and that these persons were usually found more correct in their calculations, than those who possessed a more extensive knowledge of the subject.
—Babbage, Economy of Machinery, §244. Many of them, on Ivor Grattan-Guinness's reading of the records, had been hairdressers, whom the end of aristocratic wigs had left without a trade: "Work for the Hairdressers", Annals of the History of Computing 12 (1990), 177–185. The emphasis is mine.
Almeida's keynote has a pyramid on one of its slides, named for the essay it comes from, "The Bitterest Lesson", whose formula is "doing the right task > data > compute > algorithms". The essay rests on the paper he co-signed, where the instructed model of 1.3 billion parameters was preferred by raters to the plain GPT-3 of 175 billion, and on a figure in its appendix, by his account, in which instructed models the size of GPT-2 do as well. De Prony built his pyramid in 1794 out of people, and it has the proportions written on it. By the head, nine-tenths of the intelligence in his manufacture was of the third kind; it was cheap, and it was more correct than the kinds above it, because it knew less. The men who knew only 2 rules could not be tempted by a third. That is the whole of what the keynote calls reliable intelligence, stated 2 centuries early: reliability bought by narrowness, the unoriginal journeyman of Peirce. And Babbage drew from it the principle that still carries his name, which is the price list of Jev set against a frontier model's:
We have seen, then, that the effect of the division of labour, both in mechanical and in mental operations, is, that it enables us to purchase and apply to each process precisely that quantity of skill and knowledge which is required for it: we avoid employing any part of the time of a man who can get eight or ten shillings a day by his skill in tempering needles, in turning a wheel, which can be done for sixpence a day; and we equally avoid the loss arising from the employment of an accomplished mathematician in performing the lowest processes of arithmetic.
—Babbage, Economy of Machinery, §250. The emphasis is mine. Of the third section he had said, in §245, that its labour, "which may almost be termed mechanical", could "always be purchased at an easy rate", and that a calculating engine, once complete, would be "a substitute for the whole of the third section of computers".
A company that asks a frontier model whether a ticket is about billing employs the accomplished mathematician in the lowest processes of arithmetic, at the mathematician's wage and with the mathematician's habit of having a better idea. So far the old book is on Almeida's side. But it also shows what is strange about the present, which his opening slide asks about and does not answer. De Prony's manufacture was mechanized from the bottom. Babbage's engine was a machine for the third section and nothing else, adding differences; the second section's work, turning a formula into a procedure a machine could follow, became a profession and is called programming; and the first section stayed human for 150 years. The laboratories of the 2020s have gone at the pyramid from the top. They have built the mathematician, or something that can sit an examination as one, and the hairdressers' bench is still staffed by people. The reason is the checker. The first section's work can be verified after the fact, by a proof, a test, a referee, and where a result can be checked a worker who is brilliant 1 time in 20 is worth his salary, since the other 19 cost only a retry. The third section's work is done at volume and goes out unread. There the worker must be right 19 times in 20 and must say which is the twentieth. The frontier has been building for the examination hall, and the trade is done at the bench.
The name TypeSafe gave the kind does not survive a reading of the book it comes from. Kahneman's System 1 "operates automatically and quickly, with little or no effort", which is the property being borrowed; it is also, on every page after the first chapter, the seat of overconfidence. Daniel Kahneman, Thinking, Fast and Slow (2011), ch. 1. The 2 systems are from Keith Stanovich and Richard West; Kahneman calls them characters in a story and warns against taking them for parts of the brain. It answers an easier question than the one asked, takes the coherence of the little it sees for evidence, and does not keep count of the alternatives it passed over; doubt, in that book, is work, and is assigned to System 2. A System 1 that reports how far it should be trusted is in Kahneman's terms a contradiction, and "decision model", Cloudflare's plainer word, claims less and is true. What the psychology does offer the engineer is the paper Kahneman wrote with Gary Klein, the leading defender of expert intuition, to find out where the 2 of them agreed. They agreed on 2 conditions. A fast judgment deserves trust where the world it judges is regular enough to be learned, and where the judge has had long practice with feedback that came quickly and could not be mistaken; so the anesthetist and the fireground commander can be believed, and the picker of stocks and the forecaster of politics cannot, however sure they feel. Daniel Kahneman and Gary Klein, "Conditions for Intuitive Expertise: A Failure to Disagree", American Psychologist 64 (2009), 515–526. I know of no better statement of where a decision model may be let off the leash. The questions to put to a deployment are theirs: is there a regularity here, and has this model been scored against what happened?
Where a fast judgment comes from is the other thing the name hides. In people it is slow judgment, repeated until it no longer needs to be carried out: the master sees the move because he once calculated a thousand like it. In machines the mechanism has been built on purpose. The programs that learned Go and chess without teachers kept 2 parts, a search that deliberated and a network that guessed, and trained the network to guess what the search would conclude, so that each game's deliberation was laid down as the next game's intuition; a paper of 2017 that named the scheme expert iteration took Kahneman's title for its own. Thomas Anthony, Zheng Tian and David Barber, "Thinking Fast and Slow with Deep Learning and Tree Search" (NeurIPS 2017); the same scheme is in AlphaGo Zero. Yoshua Bengio's lecture at NeurIPS in 2019, "From System 1 Deep Learning to System 2 Deep Learning", used the pair the other way about, as a diagnosis: fast, unconscious pattern-matching was what the networks already did, and what was missing was the slow part. Yann LeCun's "A Path Towards Autonomous Machine Intelligence" (2022) has a reactive mode and a planning mode, the second compiled into the first by practice. Thinking Machines' quick model at the front and reasoning model behind are the same pair. A System 1 is a distillate, and the question to ask of any is what it was distilled from. For Jev the answer has to be the frontier it disowns. Synthetic cases with their outcomes are not found; I take it that larger and slower models wrote them, and the base it was post-trained from was pretrained by someone at the scale Almeida says he would not pay for with a billion dollars in hand. Prod is God's distillate. That is no objection to the product, but it is one to the slogan: the right task was cheap to find because the scale had already been paid for, by others.
Which brings the pyramid up against the lesson it is named to outdo. Richard Sutton's "The Bitter Lesson" of 2019 drew from 70 years of the field the moral that "general methods that leverage computation are ultimately the most effective", and that whatever researchers build in of their own knowledge of a domain helps at first and is then overtaken. Rich Sutton, "The Bitter Lesson", 13 March 2019. To put the task above the data and the data above the compute sounds like a correction of this, and it is not one. Sutton's lesson concerns how a task is solved, and has nothing to say on which task to set; that the instructed small model beat the uninstructed large one shows that the laboratories had been training for the wrong thing, which is a finding about specification, and the specification came from people who knew what an instruction was. The comparison was also judged by raters whose preference was the very signal the small model had been tuned on, and the small model stood on the same pretraining as the large. What the result licenses is modest and useful: once general methods have made a capable base, the choice of what to ask of it is worth more than another order of magnitude. It does not license the suggestion that the task replaces the scale. NLP before 2018 was all tasks, a model for sentiment and a model for entities and a model for intent, and the general models ate every one of them. If the decision models keep their ground it will be because their specialty is an interface and not a domain, any state and any typed question, which is a narrowness the bitter lesson has not yet been tried against.
Sutton himself has since moved the standard further off, and not fairly. In 2025 he told an interviewer that the language models have no goal and learn nothing from consequences: "There's no ground truth in large language models." On Dwarkesh Patel's podcast, 26 September 2025. By that measure Almeida is on the right road and has stopped early, since an outcome composed in advance is not a consequence. But the remark is wrong about pretraining, and seeing why it is wrong is the shortest way into the machine. A language model in training is asked, some trillions of times, for the chance of each word that could come next, and is then shown the word that came. That is a ground truth, and the rule by which the model is scored against it is of exactly the kind TypeSafe has rediscovered. The decision model was inside the language model all along.
the secret of all reasoning machines is after all very simple
The secret of all reasoning machines is after all very simple. It is that whatever relation among the objects reasoned about is destined to be the hinge of a ratiocination, that same general relation must be capable of being introduced between certain parts of the machine.
—C. S. Peirce, "Logical Machines" (1887).
In the piano the relation is exclusion, and the parts are rods. In a transformer the relation is relevance, and the parts are 2 lists of numbers multiplied together. The machine is simple at great scale, and it is worth going through once slowly, because the System 1 models are made by opening it at a particular place.
A text is cut into tokens, pieces of words, of which GPT-3 had 50,257. Each token is looked up in a table and becomes a list of numbers, 12,288 of them in the largest GPT-3, and the lists pass through layers, 96 there. A layer does 2 things at every position. In the first, attention, the position puts a question to every position before it. Its list is turned by one matrix into a query; every earlier list has been turned by a second matrix into a key and by a third into a value; the query is multiplied with each key, number by number, and the products summed, so that each earlier position gets a single score; an exponential turns the scores into shares that add to 1; and the position takes in the values in those shares. This is Peirce's hinge. Whatever it is for one word to bear on another, the subject on its verb, the "not" on what it denies, the third line of a contract on the ninth, is introduced between 2 parts of the machine as the product of a query and a key, and what the matrices should be for the products to come out useful is all that training finds. In the second, a small network of 2 layers works on the position alone. Each adds what it finds to the list, which is thus a running account that every layer reads and amends. After the last layer the list at each position is multiplied with a table that has a row for every token, giving 1 number for each of the 50,257, a logit, and the exponential again turns the logits into shares. That is the whole output of the network: at every position, a probability for every token that could come next. The shape is that of the largest model in Tom Brown and others, "Language Models are Few-Shot Learners" (2020), table 2.1. In practice a layer runs several queries at once, 96 heads there, each with lists of 128 numbers; and positions are made known to the lists by a further device. I drew the same machine as a loom in The shape of thought.
Nothing in this writes. Writing is a loop outside the network: a token is drawn by lot from the probabilities at the last position, appended to the text, and the network is run again; a paragraph of 300 tokens is 300 runs. The model the laboratories sell as a writer is, inside, a decision model with a single primitive, a Choice among 50,257 options with its probabilities, asked again at every token. And it was trained as one. Pretraining shows the network a text and scores it, at every position, by the logarithm of the probability it gave to the token that in fact came next. That score has a property worth a name. If the next tokens really arrive with certain frequencies, the model's expected score is highest when its probabilities are exactly those frequencies and lower for any other report, so that the only way to do well is to say what one finds; statisticians call such a rule proper, and this one, the logarithm, is the oldest. I. J. Good, "Rational Decisions", Journal of the Royal Statistical Society B 14 (1952), 107–114. The loss a language model is trained on, cross-entropy, is this score with the sign changed, and perplexity is its exponential. A pretrained language model is therefore calibrated on text, to the extent that it has learned anything; of the things to which it gives 0.7, about 70 in 100 come. OpenAI measured this on GPT-4 and printed the 2 pictures side by side. On a set of multiple-choice questions the pretrained model's stated probabilities were off by 0.007 on average. After the post-training that made it an assistant, by 0.074. OpenAI, "GPT-4 Technical Report", arXiv:2303.08774 (2023), figure 8: expected calibration error on a subset of MMLU, before and after. Saurav Kadavath and others had found the same of earlier models in "Language Models (Mostly) Know What They Know", arXiv:2207.05221 (2022). Almeida's remark to a16z that GPT-3 was well calibrated in its first days is this observation from the inside. The calibrated decision is not something to be added to a language model. It is what a language model is before it is taught to please, and RLCD, whatever else it is, gives back what RLHF took.
There are 3 ways to get a typed answer out of such a machine, and they differ in how far in one reaches. The first is to let it write. The question is put, the model produces "urgent" or a line of JSON, and a constraint on the lottery (at each step, only tokens that keep the output well-formed may be drawn) guarantees the shape. The probability of the answer is then nowhere: it is spread over every path of tokens that would have spelled it, and what the model says of its own confidence, if asked, is more text. The second is to read the logits. Put the question so that each answer is a single token, A, B or C; run the network once; take the probabilities of those tokens at the last position, and divide by their sum. No lottery, no loop. This works better than it has a right to, and it has 3 defects: the mass of an answer is split among its spellings (" Yes", "yes", "YES"), options that need several tokens cannot be compared fairly with options that need one, and the letters themselves carry a bias, some models preferring "A" whatever it stands for. Ari Holtzman and others, "Surface Form Competition" (EMNLP 2021); Chujie Zheng and others, "Large Language Models Are Not Robust Multiple Choice Selectors" (ICLR 2024). An audit posted on 9 November 2026 puts numbers on the 3 ways for the open decision models. On a set built to catch models that answer by surface cues, the decision models of 4 billion parameters and more were off by 0.030 to 0.087, a generating model read at its logits by 0.144, and the same model answering in JSON by 0.378: Julien Delaunay, "Can the Confidence and Decisions of System 1 Models Be Trusted?", arXiv:2611.12521. The third is to replace the table. In the language model the last multiplication is with a fixed table of 50,257 rows. In a decision model the rows are made at the time of the request, from the caller's own options: the text of each option goes through the network and comes out a list, the question's position comes out a list, the 2 are multiplied, and the exponential is taken over the options and nothing else. A row for anything but an option does not exist. That is the precise sense in which such a model cannot hallucinate, and it is no more mysterious than the fact that the piano cannot display a 17th combination.
This last is how the outside accounts describe the family. Clef, whose weights and recipe are public, keeps its Qwen backbone frozen, adds low-rank adapters to the backbone's matrices, and sets on top what Cloudflare calls a joint schema head, a small transformer over the backbone's final lists that gives 1 logit to each option and an exponential to each question; nothing is generated, and inference stops where a writing model's would begin. A low-rank adapter (Edward Hu and others, "LoRA", 2021) leaves a matrix as it is and learns a correction to it that is the product of 2 thin ones. At Clef's rank of 256, the correction to a matrix of 5,000 by 5,000 has 2.56 million numbers where the matrix has 25 million. Cloudflare's post credits an earlier experiment of Matt Mastracci's, which read answers off a model's log-probabilities. Di Zhang's reconstruction of Jev arrives at 2 parts of the same kind: a head that scores options by an inner product, and a way of packing many questions into 1 run by a mask. Di Zhang, "What Is RLCD?" (September 2026). TypeSafe has published neither architecture nor training; its launch post speaks of a new architecture with a parallel sampler. Laya goes a step further back, to an encoder in the line of BERT, in which every token reads every other in both directions and there was never a loop to remove. A typed head on a transformer, read in 1 run, is the classifier of 2019. What is new in the family is that the classes arrive with the request. The mask is the part worth a picture.
Several questions about one state, 5 ways. A request is a state of 20,000 tokens and 8 questions of 40 tokens each, a question with its options; an answer is read at the last token of its question. A token reading a token, itself included, is a pair: the work of attention. 1. Each from the state alone. 1 request, 1 pass: a question reads the state and itself and no other question, so that the mask of attention is a tree with the state for its trunk. 20,320 tokens computed, 206,416,560 pairs. No answer can hang on another question, in whatever order they are asked. 2. One after another. 1 request, 1 pass, under the ordinary mask of a model that writes: a question reads the state, itself and every question before it. 20,320 tokens and 44,800 pairs more than the first way, which is nothing; but an answer can hang on what was asked before it. 3. Each in its own request. 8 requests, the state read in every one: 160,320 tokens, 1,606,486,560 pairs, 7.78 times the first way (28.48 times with 32 questions). If the state is kept from one request to the next, this is the first way again. 4. Written out as text. The model reads as in the second way and then writes the answers, 12 tokens each, every token written a pass of the whole network that waits for the one before: 20,416 tokens, and 97 passes in place of 1 (385 with 32 questions). 5. Written by diffusion. The model reads as in the second way, and the answers then stand as a block of noise that the network refines all at once, every token of the block reading the state, the questions and the whole block, in passes that each settle 20 tokens: 20,800 tokens computed, 216,261,040 pairs, 1.05 times the first way, and 6 passes in place of 97 (21 with 32 questions). The masks are drawn small, for 16 tokens of state and 4 questions of 4 tokens: 432 pairs in the first way, 528 in the second, 210 in each request of the third, 820 in the fourth and 848 in the fifth, with answers of 2 tokens. The live figure needs JavaScript: the 5 masks, and the counts for states of 2,000, 20,000 and 200,000 tokens and for 1, 8 and 32 questions.
The mask of attention is the table of who may read whom. A model that writes has a triangle, every token reading all that came before it and none that come after, and under the triangle a second question reads the first, with its options and whatever the network made of them. The audit found the consequence in the open models: put several questions into 1 request and some answers change, on 22.4% of 1 test set for the smallest model, of 0.8 billion parameters, and on 0.1 to 0.2% for one of 4 billion. In a tree each question reads the state and itself. Its siblings are invisible to it, the order of asking cannot matter, and the state is read once for all of them. The arithmetic in the figure has a small surprise, which is that the tree saves nothing over the triangle, 44,800 pairs in 206 million. What it buys is independence. The saving is against the other 2 ways: against asking each question in a request of its own, which reads the state 8 times, and against having the answers written, where each of 96 tokens is a run of the whole network that must wait for the one before it. There is a fifth way, newer than the family, which lets the answers be written but all at once. A diffusion language model begins the 96 tokens as a block of noise and refines the whole block together, each token reading the context and every other token of the block, in passes that each settle some 20 of them; the 96 passes become 5, for 1.05 times the tree's pairs, since every pass computes the block again. Google's DiffusionGemma (released 10 June 2026; arXiv:2608.00146), a model of 26 billion parameters, refines blocks of 256 tokens at about 20 tokens to a pass and writes 1,107 tokens a second where the Gemma 4 of its size writes 303; it trails that model on the benchmarks, and Google notes that writing in parallel can cost more to serve. Inception's Mercury models are the commercial instance. It is the loop taken off by other means, and the one thing it cannot offer is the tree: inside the block every answer reads every other.
That last difference is where the prices come from. A model being served has 2 gaits. In the first, which the trade calls prefill, the whole prompt goes through the network at once, every position in parallel, and the work is arithmetic the hardware was built for; in the second, decode, a single token goes through, then another, each run reading every weight in the model to produce 1 token. Reading is cheap by the token and writing is dear, which is why output is priced at 4 or 5 times input, and why a long answer is slow however fast the chip. A decision model never changes gait. By the usual reckoning of 2 operations for each parameter and each token, a model of 27 billion parameters does 54 billion operations a token, 5.4 × 1014 for a state of 10,000 tokens, which is of the order of a second on 1 modern accelerator and can be shared out among several; and when it is done, every answer to every question is there. The 2 operations a parameter are from Jared Kaplan and others, "Scaling Laws for Neural Language Models" (2020), and leave out the part of attention that grows with the context. Cloudflare gives a median of 209 milliseconds for Clef and 39 for the smaller model; Jev's 70 to 500 are TypeSafe's. The 70 milliseconds, the output that costs nothing, and the impossibility of a malformed record are 1 fact seen from 3 sides: the loop was taken off. What remains to be explained is the number, since a head that can only choose among the options can still be badly wrong about how sure it is.
a proposition is in itself neither probable nor improbable
Begin with what was done to the language model to make the assistant, since the decision models are that procedure with 1 part changed. The paper of 2022 has 3 stages after pretraining. In the first, about 40 contractors wrote good answers to some 13,000 prompts, and the model was trained to continue a prompt as they had, with the same logarithmic score as before. In the second, the contractors were shown, for each of 33,000 prompts, between 4 and 9 answers the model had produced, and ranked them; a second network, a copy of the language model with its table of tokens cut off and a single number put in its place, was trained so that for any 2 answers of a ranking the difference of its numbers predicted which the contractor had preferred. This is the reward model. In the third, the language model answered 31,000 further prompts, the reward model gave each answer its number, and the language model's weights were moved, by the method called proximal policy optimization, so as to make answers with high numbers more probable: draw an answer by lot, and raise the logarithm of the probability of every token in it in proportion as its number beat the usual; with a penalty for straying, token by token, from what the first stage had taught. Ouyang and others (2022), §3 and appendix: a reward model of 6 billion parameters, trained on every pair of each ranking by the logarithm of the logistic of the difference of the 2 rewards, which is the model Bradley and Terry proposed for paired comparisons in 1952; the policy trained by PPO with a penalty on its divergence from the supervised model.
Look at the second network. It reads a text and returns a typed value, trained on recorded judgments, and it generates nothing: the reward model of 2022 is a decision model, kept in the back of the shop. Di Zhang's account of what TypeSafe did is that it brought it to the counter: "the reward model stops grading the product and becomes the product." "What Is RLCD?", where the head is read as a reward model's comparison of 2 answers widened to a choice among many, and scored by Brier's rule. And look at what the third stage does to the probabilities the first network had from pretraining. Nothing in it scores them against anything that happened. The number being climbed is a prediction of what a contractor would prefer, and contractors, like the rest of us, prefer an answer that sounds sure; a study of the reward models themselves found them leaning toward confident answers whatever their quality. Jixuan Leng and others, "Taming Overconfidence in LLMs: Reward Calibration in RLHF", arXiv:2410.09724 (2024). So the lottery is tilted, at every token, toward the continuation that pleases, and the model's probabilities cease to be reports of frequency and become instruments of a manner. The 0.007 that became 0.074 is this stage, measured.
The coding and proving systems replaced the contractor with a checker. A problem is posed, the model draws a group of answers by lot, a program marks each right or wrong, and each answer's tokens are made more or less probable according as its mark beat the group's average. Group relative policy optimization, from Zhihong Shao and others, "DeepSeekMath", arXiv:2402.03300 (2024), the method by which DeepSeek trained its reasoning model of 2025. The general name is reinforcement learning from verifiable rewards. This is the reward of an examination, and it is honest about the answer and silent about the doubt. Consider what it teaches a learner who must say how sure it is. Let the truth be that answer \(k\) comes with chance \(p_k\), and let the learner say \(q_k\). If it is paid 1 when an answer drawn from \(q\) is the one that comes, its expected pay is \(\sum_k p_k q_k\), which is greatest when all of \(q\) is put on the likeliest answer. A learner that knows an answer to be right 6 times in 10 does best under a checker by saying 10 in 10. The slope it climbs shows the mechanism. With the answers produced by an exponential over scores \(z_k\), with \(y\) the answer that came, and with \(e_k\) equal to 1 for that answer and 0 for the rest, the 3 rewards that matter here pull on the score \(z_k\) by
\[\underbrace{q_y\,(e_k-q_k)}_{\text{right or wrong}}\qquad\qquad\underbrace{e_k-q_k}_{\text{logarithm}}\qquad\qquad\underbrace{-2\,q_k\Big(r_k-\sum_j r_j\,q_j\Big),\quad r=q-e}_{\text{Brier}}\]The second is the pull of pretraining: toward the answer that came, away from the rest, by exactly the amount of the misstatement, so that it is at rest only when \(q\) is \(p\). The first is the second multiplied by \(q_y\), the probability the learner already gave to what came. It is taught in proportion as it already believed, hardly at all where it was surprised, and the rich answers get richer.
The third has a date and a place. In January 1950 Glenn Brier of the United States Weather Bureau published 3 pages on a nuisance of his trade. Forecasts were verified by schemes of marks, and a forecaster, he wrote, could let the scheme do his forecasting for him, hedging toward whatever scored best; under a mark for "rain" or "no rain" proved right, a forecaster who thought the chance of rain was 4 in 10 had no reason to say so. Brier proposed that the forecaster state the chance and be charged the squared distance between what he stated, over all the possible outcomes, and what occurred, and he observed that under this charge no forecaster could gain by stating anything but what he believed. Glenn W. Brier, "Verification of Forecasts Expressed in Terms of Probability", Monthly Weather Review 78 (1950), 1–3. The Bureau began issuing the chance of rain to the public across the country in 1965, and its forecasters became the standing example of calibrated experts: Allan Murphy and Robert Winkler, "Reliability of Subjective Probability Forecasts of Precipitation and Temperature", Applied Statistics 26 (1977), 41–47. They had what Kahneman and Klein ask for, a verdict every morning. A rule with that property is a proper scoring rule, and the logarithm and Brier's square are the 2 in common use. What Almeida calls the third objective, after the preference of a rater and the mark of a checker, is this: score the stated probability by a proper rule against what came. It is the forecaster's discipline brought to the machine that learned on the forecaster's opposite.
What a reward teaches. 4 learners, the same model, the same 3,000 cases, 4 rewards, trained in the page for 600 steps. A case is a point of a plane. It has 4 possible answers, and where it lies fixes the chance of each: near the middle a toss-up among the 4, far out along an axis nearly sure. The model is 12 numbers, enough to say the true chances exactly. The best that can be done is to have the first answer right on 0.70 of the cases. The learner rewarded as a checker rewards, with 1 when an answer drawn from what it says is the one that came and 0 when not: its first answer is right on 0.69 of the cases, and it says it is sure to 0.89 (0.82 after 100 steps, and still rising at 600). Over 10 bands of stated sureness, what it says and what it finds differ by 0.196. Told to act alone when it says at least 0.95, it acts on 56% of the cases and is wrong on 17.8% of those, where the rule promised at most 5%. At 0.99 it acts on 39% and is wrong on 12.6%. The learners rewarded by Brier's score and by the logarithm: right on 0.69, and they say 0.69. The gap is 0.002. At 0.95 they act alone on 7% of the cases and are wrong on 2.8% of those; at 0.90, on 16% and 5.3%. The learner trained with label smoothing, the logarithm against a target that keeps 0.1 back and spreads it over the 4 answers alike: right on 0.69, and it says 0.61. The gap is 0.080, and it is on the modest side. At 0.95 it acts alone on 1% of the cases; at 0.80, on 16%, where the proper learners act on 32%. A learner free to fit that target exactly would never say more than 0.925. All 4 put the cases in nearly the same order. Someone who knew the true chances and took the cases surest first, in any of the 4 orders, could decide 14 to 15% of them with 5% wrong. On cases twice as noisy as those of the training, all 4 are right on 0.53. The 2 proper learners still say 0.69: their gap is 0.157, and the rule at 0.95 still acts on 7% and is now wrong on 18%. The first learner's gap is 0.355, and it is wrong on 38% of what it takes. The live figure needs JavaScript: the plane as each of the 4 learners sees it, the 3 plots, the 600 steps to move through, the sureness the rule asks for (0.80, 0.90, 0.95 or 0.99), and the 2 populations.
The figure runs the experiment in the smallest world that has the phenomenon. Leave its fourth learner aside for the moment. The other 3 end with the same first answers, right on 0.69 of the cases where 0.70 is the most that can be had, and an examination would give them the same mark. They differ in what they say. The checker's learner says 0.89 and is still climbing when the training stops; the other 2 say 0.69, which is what they find. Give each the rule of the documentation, act alone above a threshold, and the first acts on 56% of the cases and is wrong on 17.8% of them under a rule that promised 5%, while the proper learners act on 7% and are wrong on 2.8%. A reconstruction on a real model found the same thing at scale. Its authors trained a small open model on arithmetic problems twice, once with the checker's reward and once with a proper score: the accuracies were 91.8 and 92.2%, and the share of problems each could be left to decide with no more than 5 in 100 wrong was 19% for the first and 81% for the second. Gao and Wang, "OpenJev-RLCD", arXiv:2609.38850 (September 2026): Qwen3-1.7B on GSM8K-Verify, against group relative policy optimization. Same marks, a fourfold difference in what can be automated. That is Almeida's thesis, and on this evidence it holds.
Three things the figure shows are less convenient for the pitch. The first is in the last plot. The line there is the same for every learner, because they rank the cases alike; the reward moved the point at which each sits on the line and left the line where it was. A perfect reader of any of the rankings could decide 14 to 15% of the cases at 5% wrong. So the improper learner's fault can be mended afterwards, by anyone with a few hundred recorded outcomes and 1 number to fit, a practice of 2017 that needs no new objective; Chuan Guo and others, "On Calibration of Modern Neural Networks" (ICML 2017): divide the scores by a single temperature chosen on held-out cases. Allan Murphy's partition of Brier's score, "A New Vector Partition of the Probability Score", Journal of Applied Meteorology 12 (1973), 595–600, is the theory: the score is a term for whether one means what one says, less a term for how far one's statements sort the cases, plus a term for the cases' own uncertainty. Training on a proper rule improves the first 2 together; rescaling repairs the first alone. what calibrated training buys over that is a number that can be used as it comes, on tasks for which nobody has outcomes yet. The toy flatters that remedy, and the reconstruction corrects it: its baselines had each been rescaled by a temperature before they were compared, and the fourfold difference survived the rescaling. A model that reasons before it answers is not 12 numbers with 1 ranking. A reward that pays for doubt changes what the reasoning is for, and then the line moves and not only the point on it. The second is how little is automated. The honest learners act alone on 7 cases in 100, because the world they were given is one in which most cases are hard to call, and calibration reports this without changing it. The size of an automation is set by how often the cases can be told apart, which is a fact about the task and the model's knowledge of it, and "calibrated" printed on a model says nothing on the point. The third is the switch marked "twice as noisy". Move the learners to a population whose outcomes are harder to call than those they trained on, and all are right on 0.53. The proper learners go on saying 0.69. The rule at 0.95 takes the same 7% and is wrong on 18% of it. Nothing in the learners has changed, and they no longer mean what they say. Calibration is a relation between a model and a population of cases, and belongs to neither alone. Every claim of the form "this model is calibrated" has a silent second clause naming the cases, and for a model trained on cases its makers wrote, the clause names those.
Why, then, the word "reinforcement"? Reinforcement learning is what one does when the thing to be improved cannot be differentiated: an answer drawn by lot, a move, a call to a tool. A proper score of a stated distribution is not such a thing. If the head gives its probabilities in 1 run, the score is a smooth function of them, its slope passes back through the network by the ordinary chain of derivatives, and the training is supervised learning with Brier's loss or the logarithm's, as the classifiers of 2019 were trained. The lottery returns only if something is drawn before the answer is given, and the one thing worth drawing is a stretch of reasoning. Then the slope through the answer is exact and the slope through the reasoning has to be estimated from samples, and the reconstruction measured what happens: the sampled part of the slope was 7 to 12 times the size of the exact part and swamped it, and a model trained naively on a proper score learned within about 100 steps to stop reasoning altogether, the surest way to a steady score being, I suppose, to draw nothing. The paper's best page is an identity. Score the average of what several drawn stretches of reasoning conclude, and the score is the average of their separate scores plus a term for how far they disagree, so that a proper rule applied to the mixture pays the reasoning to explore; the checker's reward, they show, is the same objective with that term left out, which may be why models trained on it reason toward 1 confident story. Their remedy was to calibrate first, by the exact slope with the reasoning held still, and to reinforce the reasoning afterwards with the calibrated score for its reward. Gao and Wang, as above; with reasoning their model reached 47.7% on MMLU-Pro against 42.3 and 42.4 for the 2 baselines. For a squared error the identity is the one Anders Krogh and Jesper Vedelsby gave for committees of networks in 1995. Earlier work on the same join: Mehul Damani and others, "Beyond Binary Rewards", arXiv:2507.16806 (2025), which adds Brier's score of a stated confidence to the checker's mark, and "Rewarding Doubt", arXiv:2503.02623 (2025). Jev, which reasons in no text and draws nothing, has no use for the lottery at all. Asked by Latent Space what RLCD is, Almeida called it a north star and not an algorithm, which I take to be the honest answer: the name records a lineage, RLHF, then verifiable rewards, then this, and what it names is a loss, and a great deal of care about what the loss is computed on.
Clef's recipe, being public, can be read against the theory, and it does not come out clean. The backbone is frozen and the adapters and the head are trained on a sum of 2 losses, Brier's and a cross-entropy with label smoothing; and a secondary objective, which Cloudflare also calls RLCD, gives part credit for an answer next to the right one on an ordered scale and rewards a record that is right in every field. Cloudflare's post of 1 October 2026. Its table has Clef ahead of Jev on 2 sets of customers' intents (94.2 on BANKING77, 97.4 on CLINC150) and far behind on graduate science, 48.0 against 78.3 on GPQA Diamond: a decision model knows what its base knew. Label smoothing is the habit of training against a target that puts a little on every wrong answer, \(\varepsilon/K\) on each of \(K\), and the rest on the right one. It is a good habit for a classifier that would otherwise grow too sure, and it is not a proper rule. The report that minimizes it is not the truth \(p\) but \((1-\varepsilon)\,p+\varepsilon/K\), the truth pulled toward the toss-up, so that a model trained on it understates what it knows by design, and understates most what it knows best. Rafael Müller, Simon Kornblith and Geoffrey Hinton, "When Does Label Smoothing Help?" (NeurIPS 2019), found that it often leaves a network better calibrated, which is an accident of networks being too sure and no property of the rule. For answers on an ordered scale there is a proper rule that gives exactly the credit for near misses that Clef's objective is after, Brier's score taken on the running totals: Edward Epstein, "A Scoring System for Probability Forecasts of Ranked Categories", Journal of Applied Meteorology 8 (1969), 985–987. Whether Clef's part credit is that rule or a reward on drawn answers, the post does not say. Adding Brier's loss to it does not take the pull away. The figure's fourth learner is trained this way, with a tenth held back. Its first answers are as good as anyone's, right on 0.69, and it says 0.61; told to act alone at 0.95 it acts on 1 case in 100 where the proper learners act on 7, and at 0.80 on 16 where they act on 32. A learner free to fit its target exactly could never say more than 0.925 of anything. The recipe works, to judge by the measurements, and it works as a regularized classifier does. Laya, the encoder, describes its own training as reinforcement against strictly proper scoring rules, which is at least the right noun. Convai Innovations, September 2026: ModernBERT-large, trained whole, 421 million parameters, a context of 512 tokens, about 33 milliseconds on a small accelerator.
Of Jev's training little is known, and what is known is all about data. TypeSafe describes itself as a data lab; the cases are synthetic, made task by task; and consistency is tested by planting strings in a state that should make no difference and seeing whether the answers move. The best way I know to say what such training produces comes from a neighboring field. A network trained on data sets drawn by the million from a written-down process, and scored by a proper rule on the points held back from each, comes to approximate the answer a statistician would compute who believed that process: its outputs are posterior probabilities under the prior its makers wrote. This is how the tabular model TabPFN is made, and it is an exact description of a decision model trained on synthetic cases. Samuel Müller and others, "Transformers Can Do Bayesian Inference" (ICLR 2022); Noah Hollmann and others, "TabPFN" (ICLR 2023) and "Accurate predictions on small data with a tabular foundation model", Nature 637 (2025). If the cases are made as such cases usually are, the latent fact (the ticket is urgent or it is not) is drawn first, the ticket is written to suit, and the model learns the chance of the fact given the ticket, for tickets written that way. Its 0.83 is a posterior under TypeSafe's prior over tickets. That is a respectable thing to be, and it locates the whole art where Almeida's pyramid says it is, in the making of the cases. It also locates the risk. The prior is unpublished, and the customer's tickets were not drawn from it.
The outside measurements read accordingly. An evaluator who ran Jev on 1,200 examination questions found its probabilities off by 0.031; another, on synthetic support tickets of his own, by 0.107, with the Nouls too modest and the Choices and Scores too sure, and with 1 task built to be unknowable on which the model was right 44.7% of the time while saying 0.74; the makers of Laya, on their set, by 0.246. Archer Hume (1,200 items of MMLU), Rajesh Beri and Convai Innovations, each on their own sets in the weeks after the launch; the measure is the expected calibration error over bands, the gap of the figure. TypeSafe's page on the model's unevenness is candid: Score is weak where the levels are numbers, and a statement and its denial put as 2 Nouls have been seen to add to 1.19. The audit cited above adds that the field labeled confidence in the answers it examined is computed from how spread the probabilities are, and says nothing of how often they are right. From 3 in 100 to 25 in 100, by who asks and what. These are not contradictory findings about a model. They are 1 finding about calibration, the one the switch in the figure makes: the model means what it says on cases like those it was trained on, and how like those yours are is not something it can tell you.
There was an account of this in print by 1921, in the book whose English the 18-year-old Frank Ramsey was then at work on. Wittgenstein's theory of probability takes 8 remarks of the Tractatus, and it is the theory of the piano. A proposition is true in certain of the combinations of its elements, which are its truth-grounds; and the probability that one proposition gives another is a count:
5.15 Ist Wr die Anzahl der Wahrheitsgründe des Satzes „r“, Wrs die Anzahl derjenigen Wahrheitsgründe des Satzes „s“, die zugleich Wahrheitsgründe von „r“ sind, dann nennen wir das Verhältnis: Wrs : Wr das Maß der Wahrscheinlichkeit, welche der Satz „r“ dem Satz „s“ gibt.
5.153 Ein Satz ist an sich weder wahrscheinlich noch unwahrscheinlich. Ein Ereignis trifft ein, oder es trifft nicht ein, ein Mittelding gibt es nicht.
5.155 Die Einheit des Wahrscheinlichkeitssatzes ist: Die Umstände – die ich sonst nicht weiter kenne – geben dem Eintreffen eines bestimmten Ereignisses den und den Grad der Wahrscheinlichkeit.
5.156 So ist die Wahrscheinlichkeit eine Verallgemeinerung. Sie involviert eine allgemeine Beschreibung einer Satzform. Nur in Ermanglung der Gewißheit gebrauchen wir die Wahrscheinlichkeit. – Wenn wir zwar eine Tatsache nicht vollkommen kennen, wohl aber etwas über ihre Form wissen. (Ein Satz kann zwar ein unvollständiges Bild einer gewissen Sachlage sein, aber er ist immer ein vollständiges Bild.) Der Wahrscheinlichkeitssatz ist gleichsam ein Auszug aus anderen Sätzen.
5.15 If Tr is the number of the truth-grounds of the proposition "r", Trs the number of those truth-grounds of the proposition "s" which are at the same time truth-grounds of "r", then we call the ratio Trs : Tr the measure of the probability which the proposition "r" gives to the proposition "s".
5.153 A proposition is in itself neither probable nor improbable. An event occurs or does not occur, there is no middle course.
5.155 The unit of the probability proposition is: The circumstances—with which I am not further acquainted—give to the occurrence of a definite event such and such a degree of probability.
5.156 Probability is a generalization. It involves a general description of a propositional form. Only in default of certainty do we need probability. If we are not completely acquainted with a fact, but know something about its form. (A proposition can, indeed, be an incomplete picture of a certain state of affairs, but it is always a complete picture.) The probability proposition is, as it were, an extract from other propositions.
—Wittgenstein, Tractatus Logico-Philosophicus (1921); the translation of 1922. The translation that bears C. K. Ogden's name was in the main Ramsey's. The emphasis is mine. The same year saw Keynes's Treatise on Probability, which also made probability a logical relation between propositions, and it was against Keynes that Ramsey wrote 5 years later.
Jevons's machine computes 5.15. The table beside its keys is the measure of the probability that each term gives each: with the chain keyed in, A gives C 2 of 2, C gives A 2 of 6, and what is not C gives what is not A 2 of 2, the premise turned round, which nobody keyed. With nothing keyed, every term gives every other 1 in 2, as 5.152 says of any 2 elementary propositions, and it will say so for ever, because a machine of this kind has no way to learn from a case. Where its premises are silent it is exactly ignorant, and it marks the fact by a fraction that does not move.
A decision model's number is of another kind and has the same grammar. It was learned, and it moves; but 5.153 holds of it without amendment. The ticket is urgent or it is not. The 0.83 is no property of the ticket, and no property of the model either. It is what certain circumstances give to the event, in the sense of 5.155, the circumstances being the state as far as the model reads it together with everything in its training that it cannot recite, and it is in the strict sense an extract: a summary of how cases of this form went, among the cases that were written for it. Change the cases and the same ticket gets another number, and neither number was wrong about the ticket. The remark that probability is needed only in default of certainty is also an engineering instruction. Where a rule can be keyed, key it. A refund over the limit needs no Noul, and a deal of what is being handed to decision models this autumn is of that kind.
Ramsey saw what the logical theory left out. In 1926, at 23, he proposed that a degree of belief is no relation between propositions and is to be measured in the believer, by "the extent to which we are prepared to act on it", most exactly by the bets he will take; and that the only law logic lays on such degrees is that they hang together, so that no set of bets a man accepts can be arranged to make him lose whatever happens. F. P. Ramsey, "Truth and Probability" (1926), printed in The Foundations of Mathematics (1931). A threshold in a program is a preparedness to act, written down. The Noul is a Ramsey number, trained by Brier's rule, and read by its buyers as if it were a ratio out of the Tractatus, fixed by the state and the statement alone; most of the confusion about what these models promise lives in the gaps between those 3. And Ramsey's one law is the test the documented model fails in the small. A statement at 0.6, say, and its denial at 0.59 add to 1.19; sell the model both tickets at its own prices and it has paid 1.19 for a certain 1. A program that acts on each above 0.5 will do the thing and its opposite.
as reliable as a fourth logic gate
The keynote's boldest sentence is that a decision of this kind can be made "as reliable as a fourth logic gate". The 3 answers are set beside AND, OR and NOT as primitives of the same rank, a small brain to be dropped into a program as a gate is dropped into a circuit, and programs are to be composed of them as circuits are composed of the others. The image of a little brain used as one uses a gate or a library is from the a16z conversation. It is a good line, and it fails in 4 separate ways, each of which says something about what these models are.
The first is that there are not 3 gates. One suffices. Henry Sheffer showed in 1913 that every function of truth can be built from a single connective, the joint denial of its arguments or equally the denial of their conjunction; Peirce had found it 30 years before and left it in a drawer; and Wittgenstein built the logic of the Tractatus on it, every proposition a result of 1 operation applied again and again (5.5). Henry M. Sheffer, "A Set of Five Independent Postulates for Boolean Algebras, with Application to Logical Constants", Transactions of the American Mathematical Society 14 (1913), 481–488. The processor of 16,271 gates that I wired from AND, OR and NOT in The painted rock could be wired from 1 kind, as real chips largely are, from NAND. That engineers draw 3 is a convenience of the drawing. And a set that already yields every function of bits has no vacancy: whatever a fourth gate did with bits, the 3, or the 1, could be wired to do. If Jev adds something, it adds nothing of the kind a gate adds. It runs on gates.
The second is that the 3 primitives are 1. A Choice is a selection among named options. A Noul is a Choice between 2, reporting 1 side. A Score is a Choice whose options stand in an order. S. S. Stevens's old table of the scales of measurement has the exact words: Choice is measurement on a nominal scale, Score on an ordinal one, and the scales on which quantities live, where one may ask how much and how many, are absent, as TypeSafe's page concedes when it says that Score is weak with numbers. S. S. Stevens, "On the Theory of Scales of Measurement", Science 103 (1946), 677–680: nominal, ordinal, interval, ratio. The correspondence with AND, OR and NOT comes to this, that 3 is 3. The correspondence Almeida gave Latent Space is the true one, and it is to control flow: a Noul is what stands in an "if", a Choice in a "switch", a Score in a comparison. Those are the places in a program where the world is consulted, and it is a real observation that programs have never had anything but brittle rules to put there.
The third is that gates compose and decisions do not. What a gate puts out is what a gate takes in, a bit, and it is by this that 176 of them make an adder and 16,271 a computer. A decision model takes in a state of unstructured text and puts out a distribution over labels. The types do not meet. To set one decision on another a program must stand between them, and it has 2 ways: collapse the distribution to a bit at a threshold, which throws the probability away at the first step, or write it into the next state as text, which the next model reads as it reads everything. Nor do the numbers compose by themselves. From a statement at 0.8 and another at 0.8, the chance of both lies anywhere from 0.6 to 0.8, and nothing in the 2 answers says where; a run that answers many questions side by side, each blind to the others, returns the margins of a table whose cells it never computed. Even NOT, the cheapest gate there is, 1 less the input, is not something the model reliably does to its own output: the statement and its denial that add to 1.19 are a NOT that is off by 0.19.
The fourth is the word "reliable", and here a figure is better than an argument.
An adder of 176 gates (96 AND, 48 OR, 32 NOT) adds 2 numbers of 16 bits as a sum is added on paper, in 16 columns of 11 gates: 2 groups of 4 that say whether 2 bits differ, and 3 that make the carry. Now let each gate, each time it answers, answer wrong with a certain chance. One sum, each gate erring once in 100: 37,114 + 23,600 = 60,714, and the adder says 60,715. 1 gate of the 176 answered wrong, in the first column from the right. 262,144 sums at each of 34 rates, 8,912,896 sums in all, added 32 at a time. A gate erring once in 100,000: the sum comes out right 99.8% of the time. Once in 10,000: 98.6%. Once in 1,000: 86.8%. Once in 100: 24.4%. Once in 20: 0.2%. 3 adders whose gates err apart, with 2 of the 3 deciding each bit of the sum: 100%, 100%, 99.3%, 61.2% and 0.7% at the same 5 rates. 3 adders that err together are 1 adder. The share of sums in which no gate errs at all, the least the adder can be right: 99.8%, 98.3%, 83.9%, 17.1% and 0.0%. The chip the adder comes from has 16,271 gates, and while it writes 1 + 1 = 2 each of them answers 64,150 times: 1.04 billion answers. For 99 runs in 100 to pass without a single wrong answer, a gate may err once in 104 billion. The live figure needs JavaScript: the sum gate by gate, 2 dozen more sums at the same rate drawn small, the curve of the share right, and the 5 rates to choose among.
The adder is the one from the chip that wrote 1 + 1 = 2: 176 gates, 16 columns. Let each gate answer wrong once in 100,000 times and the sum is right 99.8% of the time; once in 1,000, 86.8%; once in 100, 24.4%. A decision model that says 0.95 and means it is wrong once in 20, by its own account and at its best, and an adder of such parts gets 2 sums in 1,000 right. The adder is the small case. The chip it was taken from asks 16,271 gates to answer 64,150 times each while it writes its one line, 1.04 thousand million answers, and for 99 runs in 100 to pass without a single wrong one a gate may err once in 104 thousand million. The comparison is unfair in the way that matters. A transistor gate does not fail once in 20 or once in a million; its makers count failures in units of a thousand million hours, and the entire art of digital design, the discipline that let 16,271 gates be trusted to run in sequence, rests on that. Software is deep in the same way. A program in which 14 decisions must each be right, each right 19 times in 20 and failing apart, comes out right less than half the time. 0.95 to the 14th power is 0.49. The unit of failure is the FIT, 1 failure in 109 hours of a device.
There is a classical answer, and it sharpens the point. In lectures at Caltech in January 1952 von Neumann asked how a reliable organism could be made of unreliable organs, treating error, in his words, not as an "extraneous and misdirected or misdirecting accident" but as part of the process to be designed. His answer was redundancy: carry every signal on many lines, compute it many times, let the majority restore it; and he showed that this succeeds, to any reliability one likes, on 2 conditions, that the parts err less often than a bound he put near 1 in 100, and that they err independently. John von Neumann, "Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components", in Automata Studies (1956), 43–98. The dashed line of the figure is the simplest case, 3 adders and a vote: it lifts 86.8% to 99.3% when gates err once in 1,000, lifts 24.4% only to 61.2% at once in 100, and is no help at once in 20. And it does anything at all only for adders that err apart. Three that err together are 1 adder. A decision model asked the same question of the same state 3 times errs together with itself; TypeSafe tests for exactly this consistency and is right to prize it. So the virtue it advertises forbids the classical cure. To have errors that fall apart one must ask models that differ, or put the question on evidence that differs, and then one is building what von Neumann built, an organism designed around the error of its organs, which is a long way from dropping in a gate.
What the thing is, if it is no gate, the documentation has already said without noticing. Two thresholds, 0.7 and 0.3, and a band between them where the output is not to be acted on: that is the plan of the circuit Otto Schmitt drew in the 1930s for turning a wandering voltage into a clean bit, 2 thresholds in place of 1 so that a signal near the line does not chatter, and it sits wherever a digital system touches the world. A decision model is a transducer. It stands at the edge where unstructured state becomes a typed value, as a converter stands where a voltage becomes a number, and the engineers of that edge have never spoken of reliability as the logic designers do. They speak of calibration, which is their word and means the comparison of an instrument with a standard, under stated conditions, on a certificate with a date; of drift, and of the interval after which the comparison must be made again; of the budget of error that a design can carry. They know, too, that the edge is where the guarantees of logic stop: a latch that samples a signal from outside can hang between 0 and 1, and no circuit removes the possibility, only makes it rare. Wittgenstein's remark that measuring would not be what we call measuring without a certain constancy in what the measurements give (Philosophical Investigations §242) is the philosophy of the calibration certificate. I read it at length in The painted rock. This is the tradition the decision models belong to, and it is a better one for them than the one the keynote claims. An instrument with a known error, a stated range and a date of calibration is something engineers have built bridges on. It is not a gate, and nothing built on it will be exempt from knowing its error.
And there is one thing the type does that deserves the keynote's enthusiasm, though it is not reliability. A critic put the limit exactly: "Jev constrains the shape of the output. It does not constrain the judgment." Anthony Maio, in his analysis of the launch. A well-typed wrong answer is the most dangerous kind, since nothing downstream can see that it is wrong. But consider what a wrong answer was before. An assistant's error was a sentence among sentences: a field that did not exist, a confident paragraph, a refusal, an apology. It had no place where it could be entered. A wrong Choice among 5 routes is an error of a kind: it falls in a cell of a table, it can be counted against the cell beside it, its rate can be watched for drift and priced. Nobody has ever kept a confusion matrix of an essay. The type gives an error its civil status, a name and an address and a column in a register, and errors that can be registered can be budgeted, insured and engineered around, which is the only sense in which any instrument has ever been reliable. The phrase is Wittgenstein's, for whom the philosophical problem about a contradiction was its civil status, its place in the life of those who run into it (Investigations §125).
every turn re-reads everything that came before it
The other half of Almeida's autumn is an essay on money, and it is the best thing he has written. Its subject is a quantity inside the transformer that the trade calls the KV cache, and its claim is that this quantity, and no property of the models' minds, now decides what agents can be built. "(KV) Cache Rules Everything Around Me", completeskeptic.com, 9 September 2026, from which the heading is taken. The essay replays a public set of traces of coding agents against a price list, and finds what the model writes to be 9 to 18% of the bill.
Recall what attention does. At every layer a position asks its question of all the positions before it, and for that each earlier position must offer a key and a value, 2 lists of numbers computed from its own running account. Under the triangle mask those lists depend on nothing that comes later. So when a text is extended, every key and every value already computed stands, and a provider that has kept them need only compute the new positions, each of which still reads all the old keys. The kept lists are the cache. What they save is the old positions' own work, their turns through the small networks and their own questions; what they cannot save is that every new token must look at every old one. And they are not small. For a model of 64 layers that keeps, for each token in each layer, 8 keys and 8 values of 128 numbers, a token is 131,072 numbers, a quarter of a megabyte at 2 bytes each, and a context of 100,000 tokens is 26 gigabytes held in the fastest memory a data center owns, for as long as the provider is willing to wait for the next turn. The shape is an assumption for the arithmetic, of the order of the larger open models, and no particular maker's. Providers keep such a cache for minutes, charge something to write it and little to read it; a commenter on the essay points out that the little is not nothing, since the memory is occupied whether or not the turn comes.
Now an agent. It is a loop: the model reads the task, writes a thought and a call to a tool, the tool answers, and the task, the thought, the call and the answer all go back in for the next turn, with what that turn adds, and so on. Nothing is ever taken out, because taking something out of the middle would change every key and value after it and the cache would be lost from that point. "Every turn re-reads everything that came before it."
What an agent reads. An agent is a loop: the model reads everything so far, writes a little, a tool answers, and all of it goes back in for the next turn. Here the context starts at 20,000 tokens, a tool sends back 3,000 tokens a turn and the model writes 1,000. Prices are in tokens of fresh input: a token written by the model costs 5; a token of input that the provider keeps for the next turn costs 1.25; a token read again from what was kept costs 1/10. 100 turns, nothing taken out. The model writes 100,000 tokens and reads 21.8 million, 218 for each token it writes; the context of the last turn is 416,000 tokens. The bill is 3,158,400: reading again 67.7%, what the model wrote 15.8%, fresh input 13.2%, the extra to have it kept 3.3%. Every token counted once at its price comes to 916,000; the bill is 3.4 times that. Turn 2 costs 12,000 and turn 100 costs 51,200, of which 80.5% is for reading again. 25 turns: reading again is 37.0% of the bill and writing 29.2%. 400 turns: 89.0% and 5.5%, and the bill is 36,578,400. If only 95% of what was kept is found again at each turn, the bill of 100 turns is 1.39 times as large; at 89%, 1.86 times. Memory. If the context is rewritten as 20,000 tokens of notes whenever it passes 100,000, the 100 turns cost 2,088,000 and 400 turns 8,728,000; but 25 turns cost 526,200, more than the 428,400 of taking nothing out. A memory that grew only as the logarithm of the turns, rewritten at every turn, would cost 5,623,830 for 100 turns, more than taking nothing out, and 26,430,575 for 400, less. A rewritten memory costs less to read than a kept one only when it is under 0.08 of its size. Edited in place. If, past 100,000 tokens, the oldest answers of the tool are each replaced by a note of 300 tokens that the model writes (98 edits in 100 turns), and everything after an edit is read again at the full price, the 100 turns cost 3,797,350, which is 1.20 times taking nothing out; if what stands after an edit is taken from what was kept all the same, 2,174,700, which is 42.7% less than that and 0.69 of taking nothing out. For 400 turns, 17,642,350 and 16,019,700. The last turn, at 416,000 tokens, given to a model at 1/5 the price that has kept nothing, costs 2.05 times what the first model asks; at 100,000 tokens, 1.33 times. Giving a turn away pays only to a model under 0.15 of the price at 100,000 tokens, and under 0.10 at 400,000. What is kept. For a model of 64 layers that keeps 8 keys and 8 values of 128 numbers for each token in each layer: 131,072 numbers a token, 262,144 bytes at 2 bytes each, 26.2 GB for 100,000 tokens and 109 GB for the last turn. If a token read again cost 1/40, reading again would be 34.4% of the bill and writing 32.2%. The live figure needs JavaScript: the tape of the session, a row a turn, and its bill, for 25, 100 and 400 turns, the 5 memories, 3 shares found again and 2 prices of reading again.
The figure is my own arithmetic, with round numbers and the ratios of the price list the essay uses, and it lands where his replay of real traces lands. In 100 turns the model writes 100,000 tokens and reads 21.8 million, 218 for each it writes. Reading what it has already read is 67.7% of the bill; what it wrote, the part anyone would call the work, is 15.8%; a bill made by counting each token once would be less than a third of the true one. At 400 turns the rereading is 89.0%. Let the cache miss 1 time in 9, which is the hit rate he cites for Claude Code, and the bill grows 1.86 times in my model and 1.84 in his. His session costs $1.07 million with every read found again and $1.97 million at 89%; the shares of his bill are close to mine. The agreement means only that the essay's results follow from the price list and the shape of a loop, which is its point.
Three consequences follow, and the third is the one that matters. The first is that the price of writing, which is what everyone compares, is nearly beside the point for an agent. The second is that an agent's cost is set by engineering nobody sees: the order of the prompt, whether a tool's description changed, whether 2 turns were 5 minutes apart. The third is that the cache repeals Babbage's principle. Most turns of an agent are small: open this file, is the test green, go on or stop. They are work for the third section, and they are done by the first, at 416,000 tokens of context, because the first holds the cache. Hand the last turn of the figure to a model at a fifth of the price, which has kept nothing and must read it all at its own full rate, and it costs 2.05 times as much; at a context of 100,000 tokens, 1.33 times; a cheaper model would have to cost a tenth before the handing-over paid. The accomplished mathematician does the lowest processes of arithmetic because nobody else has his papers. Mental labor cannot be divided when the memory cannot be handed over, and that, more than any ceiling on what the models know, is why the agents of 2026 are 1 large model talking to itself.
Is this a limit on intelligence, as it is sometimes put? I think it is a limit of another kind, and that the difference bears on what to build. The cache is the bookkeeping of 2 decisions, each of which was a triumph. The first is that the network reads everything: a transformer's memory is the whole of its context, with nothing summarized away, which is why it beat the recurrent networks that squeezed the past into a state of fixed size. The second is that the reading is cached by prefix, so that it is cheap to append and ruinous to revise. Together they make a memory that only grows. Now look at what the price list does to the alternatives, in the figure's other settings. Rewrite the context as notes when it passes 100,000 tokens and 100 turns cost a third less, but 25 turns cost more than leaving everything in, because a rewriting is read back at the full price and the full price is 12 times the cached one; a rewritten memory is cheaper to read than a kept one only if it is under 0.08 of its size. Take the best memory one could ask for, one that needs only the logarithm of the turns, and rewrite it at every turn as such a memory must be: it costs more than keeping everything for 100 turns, and wins only when the session is several hundred long. Under these prices the cheapest memory is the one that never thinks about what to keep. Forgetting, summarizing, delegating and revising are not ornaments of intelligence. They are a good part of what the word means in a person, and the price list teaches agents to do none of them. That is the restriction, and it is real; but it is laid on by an accounting, and accountings change. One provider, the essay notes, has already cut the price of a token read again to a quarter of what it was; at a fortieth of the price of fresh input, writing is again a third of the bill.
For anyone who wants to train models and not only to price them, this is where the open ground is, and it is ground a small laboratory can stand on. Almost no model has been trained with the bill in its objective. Pretraining asks for the next token given all the previous ones, and never once asks which of the previous ones were worth keeping; the memory of every agent in service is managed by rules written around a model that has no opinion on the matter. The first serious attempt appeared 2 weeks after Jev. A group at the University of Washington and Meta, around Luke Zettlemoyer and Pang Wei Koh, treats the context as a file and hands the model a shell on it: it may delete a tool's stale answer, replace 40,000 tokens by a note, move what it will want to where it will look. With no training for the purpose, a model allowed to do this is 11.4% more accurate on a benchmark of browsing for 21.5% less arithmetic, and 5% better on tasks that run 12 hours for 59% less; trained by reinforcement to do it, a model of 9 billion parameters gains 47.6% for 12% less. The page a builder should read twice is the plumbing. An edit in the middle of a context ought to cost the cache from that point on, and the figure's fourth memory counts what that means: let each old answer of the tool be replaced by a note of 300 tokens once the context passes 100,000, read everything after the edit again at the full price, and 100 turns cost 1.20 times what they cost with nothing taken out. The group's answer, which it calls suffix cache reuse, is to keep the keys and values of the text that survives an edit and slide them to their new places, although they were computed while the deleted text was still there to be read. That is an approximation, a memory of having read what has since been removed, and they report that it costs no accuracy and saves 35% of the arithmetic of serving; in the figure's fifth memory it turns the 1.20 into 0.69. So the rule that a kept state is exact or worthless, on which the whole price list rests, was negotiable all along, and the negotiating was done by 13 people with a patch to an open serving engine. They report too, with a candor I would like to see become general, that small models given the power to edit seldom use it, and that an editable context is a new door for an attacker. Shao and others, with Luke Zettlemoyer and Pang Wei Koh, "Context Language Models", arXiv:2609.37725 (29 September 2026): BrowseComp-Plus and EdgeBench; the trained model is a Qwen of 9 billion parameters, and the reuse is a patch to SGLang, measured on a Qwen of 27 billion. Notice what kind of thing an edit of memory is. Keep this, drop that, replace these 40,000 tokens by a note: it is a Choice, made at every turn, about a state. One of the keynote's slides is headed "Agents beyond the KV cache", and the two halves of the argument meet there. The natural keeper of a large model's memory is a small model that decides, cheaply and with a stated doubt, what the large one will see; it can be trained by a proper rule against an outcome that arrives by itself, namely whether the agent, later, needed what was dropped.
it can do whatever we know how to order it to perform
Lady Lovelace wrote that of Babbage's second engine, in the note that is quoted against machines more often than it is read:
The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths. Its province is to assist us in making available what we are already acquainted with.
—Ada Lovelace, Note G to her translation of Menabrea's "Sketch of the Analytical Engine" (1843).
Read as an account of training, her second sentence is exact. A network is ordered by its loss and does whatever we know how to write there, and for 8 years what has been written is 1 order with amendments: predict the next token, of text that people left on the internet, with a transformer whose weights are fixed when the training stops and whose only memory afterwards is the context it rereads. The people who left the large laboratories this year to found small ones, which the trade has begun to call neolabs, can each be placed by the clause of that sentence they refuse. One count this month has 45 such companies, and other tallies put some 40 billion dollars behind them; it sorts 27 by their bets, that learning itself must change, that language is the wrong medium, that the data which matters was never on the internet, that the arithmetic is the bottleneck, that research can be the product. The Decoder, "Frontier Radar #5" (November 2026). Its verdict is that the bets with a product or with data nobody else holds look strongest, and that learning differently is at once the most central and the least shown. Lovelace's sentence gives a harder test than the size of a round. For a person who trains models a direction exists on the day its order can be written down and run, and by that test the bets stand at very different dates.
Take the refusal of language first, since its order was written this year and is 2 lines long. A generative model predicts what it will see, every pixel or every token, and so spends itself on whatever in the scene cannot be predicted, the flicker of leaves, the exact wording. Yann LeCun's alternative has an encoder turn each observation into a short list of numbers, the embedding, and a predictor guess the next list from this one and the action taken; the error is measured between lists and nothing is ever drawn. "JEPA is not generative AI", he says, and his new company has raised more than a billion dollars on it. AMI Labs: 1.03 billion dollars, at a valuation of 3.5 billion before the money. The difficulty is as old as the idea and is the reason it took a decade. Train the encoder together with the predictor and the pair has a perfect and worthless solution, which is to give every observation the same embedding, for an encoder that says nothing is never surprised. The remedies were a succession of devices: a second encoder trailing the first, gradients stopped on one side, an encoder trained beforehand and frozen, terms that prize variance, 6 weights to balance in the recipe that came before. The paper that introduces LeWorldModel replaces them by 1 term with 1 weight. Take the embeddings of a batch, project them on directions drawn at random, and along each direction test whether the projections are spread as a normal curve would spread them, by comparing their characteristic function with the normal one at a few frequencies; add the failure of the test to the loss. A cloud all of whose shadows are normal is a round normal cloud, by a theorem of 1936, and a round cloud cannot be a point. Lucas Maes, Quentin Le Lidec, Damien Scieur, Yann LeCun and Randall Balestriero, "LeWorldModel", arXiv:2603.19312 (March 2026), after Balestriero and LeCun's LeJEPA. The test is that of Epps and Pulley (1983), the theorem Cramér and Wold's. The model has 15 million parameters and an embedding of 192 numbers, trains on 1 accelerator in a few hours, and plans up to 48 times faster than a world model built on a large pretrained encoder.
A world model in a space of its own. A point is found anywhere on a table with walls, pushed, and seen through a retina of 24 by 24 cells, each as bright as the point is near; every cell flickers at every look by an amount nothing predicts (spread 0.15). An encoder of 1,152 numbers turns a look of 576 numbers into an embedding of 2; a predictor of 8 numbers guesses the embedding of the next look from this one and the push. Encoder and predictor are trained together, twice, on the same 384,000 looks (1,500 steps of 128 moves, 221,184,000 readings of a cell). On the error of the guess alone. After 1,500 steps the error is 8.4e-20 and the embeddings of all the looks are spread over 2.0e-10 (0.20 before the training, 1.1e-2 after 100 steps): every look is given the same embedding. The error is 1.07 times the spread of what is guessed, worse than guessing the mean; 71% of what is left of the embedding is flicker; and the plans of this model end 0.80 from the goal. On the error plus a test of normality. The embeddings of a batch are projected on 16 directions drawn at random, and along each their characteristic function is compared with a normal one at 5 frequencies; the difference is added to the error. After 1,500 steps the error is 0.062, the embeddings are spread over 0.69, a straight-line reading of them tells 95% of where the point is (94% after 100 steps), and the flicker is 3% of them. The error is 0.06 of the spread of what is guessed. Plans. Shown a goal through the same retina, a model takes at each of 8 steps, of 64 pushes no longer than 0.35, the one whose predicted embedding is nearest the goal's. Over 1,000 plans, begun 1.03 from the goal on average: the second model ends 0.20 away, doing nothing 0.82, the first model 0.80, a planner told the place 0.03. The live figure needs JavaScript: both trainings step by step, the table as each encoder places it, what each number of the embedding weighs in a look, and a point the reader moves and pushes.
The figure trains the idea twice, in the page, in a world small enough to watch. A point is found anywhere on a table, pushed, and seen through a retina of 576 cells, every one of which flickers at every look; the encoder is a table of 1,152 numbers that turns a look into 2, and the predictor is 8 more. On the error alone the training is a complete success. After 1,500 steps the error of prediction is 8.4 × 10−20, and the embeddings of all the looks lie within 2.0 × 10−10 of one another. With the test added the error is 0.062, worse by 17 orders of magnitude, and the 2 numbers tell 95% of where the point is, the flicker reduced to 3% of them. Then each model is made to plan as LeWorldModel plans, by trying actions in its own space: shown a goal through the same flickering retina, it takes at each step, of 64 pushes, the one whose predicted embedding lies nearest the goal's. Over 1,000 plans of 8 steps the model trained with the test ends 0.20 from the goal, having begun 1.03 away. Doing nothing ends 0.82 away. The collapsed model ends 0.80 away, which is doing nothing by other means; and a planner told where the point is ends 0.03 away, which measures what the 2 numbers still do not know.
The toy shows why the term works, and shows as plainly where it is an assumption. The test asks the embeddings to be a round normal cloud. My table is a square on which the point may be anywhere, and no straight-line reading of a square is a round cloud, so the test is never passed, only weighed against the error; the cloud in the figure is 0.69 wide where 1 was asked. A world of 3 rooms, or 10 digits, or sentences, is further still from any such cloud, and an encoder with more freedom than mine will bend its map to fit the prior. The model drops the flicker because the flicker cannot be predicted, and what cannot be predicted is not the same as what does not matter: whatever in a scene bears on the goal without bearing on the next embedding goes out with it. And the plan needed a goal that could be shown, a look to be matched. For an arm and a cube that is natural, and the larger model of the family drove robot arms last year after 62 hours of their recordings. For the work the assistants are sold for, the goal is a sentence, and the road from an embedding of pixels to a goal stated in words is the part nobody has written. It is still worth seeing that this is the decision models' own move. Both refuse to generate. One answers in a head over the caller's options, the other predicts in a space it has learned, and both hold that the lottery over tokens is where the trouble enters. Almeida grants the idea its promise and calls LeCun's old argument against language models, that errors must compound token by token until a long answer is surely wrong, refuted by experience. Agents do now run for hours. I think the argument was wrong as he made it and is right as the adder has it. Errors compound wherever nothing checks them. The long runs were rescued by tests and compilers, which is to say by the second judge, and a chain of decisions has no compiler.
The refusal of frozen weights stands at an earlier date. An agent on its tape is a model that can learn only by rereading: what it finds out in a session it keeps by paying to read it again, and loses when the session ends. Several of the new companies exist to say that this is the real limit and that a model should go on learning from what it does, in its weights, as Sutton has asked for 40 years. One claims a method that needs a hundredth of the data and has shown no model; another raised a billion dollars in October to learn from few examples; a third is valued at 32 billion and has published neither a model nor a paper. Core Automation (Jerry Tworek and Rohan Anil), Flapping Airplanes and Safe Superintelligence, in that order. David Silver's Ineffable Intelligence makes the bet from the side of reinforcement, with 1.1 billion dollars of seed money. What has been published is narrower and more useful. The obstacle to learning in the weights is that it unlearns: teach a network a new fact by gradient descent and it forgets old ones, because every weight serves every fact. A group at Meta replaced some of a transformer's inner layers by a memory, a large table of slots of which a question reads only the few whose keys agree with it most, and then asked which of those to write when a new fact arrives. Their answer is a librarian's. Write the slots that this fact reads often and the rest of what the model knows reads seldom, a ranking borrowed from the retrieval of documents. After learning the same new facts, a model finetuned whole had lost 89% of its score on old questions, one finetuned through low-rank adapters 71%, and theirs 11%. Lin and others, "Continual Learning via Sparse Memory Finetuning", arXiv:2510.15103 (October 2025); the ranking is the term frequency and inverse document frequency of search engines. A sequel, arXiv:2604.05248, fits such a memory to a model of half a billion parameters on a desktop machine.
Learning without forgetting. A layer of 8,192 slots, each with a key that never changes and a value of 16 numbers, 131,072 numbers in all. A fact is a question, a point on a sphere in 32 dimensions, and an answer of 16 bits; questions come in 32 topics, the commonest with 101 of the 384 old facts and the next with 47, and 2 questions of a topic agree by half. The layer answers with a sum of values. Read densely, every slot answers as much as its key agrees with the question; read sparsely, only the 16 slots whose keys agree most. 384 old facts are stored exactly; 3,297 slots are read by at least 1 of them and 4,895 by none. Then 384 new facts arrive one at a time, and each is learned at once and exactly, by the smallest change of the values the writer may make. A fact is kept when all 16 bits of its answer still have their sign. Dense, every slot it reads written (4,177 for the first new fact): after 1 new fact 76.0% of the old facts are kept, after 2, 41.7%, after 8, 15.4%, after all 384, 2.3%; half are gone at new fact 2. Of the new facts themselves 0.8% are still held at the end. Sparse, all 16 slots written: 71.9% of the old facts kept at the end (36.6% in the commonest topic), 83.3% of the new ones held; 3,326 slots written in all. Sparse, only the 4 slots whose keys agree most: 26.8% kept, half gone at new fact 202, none kept in the commonest topic, 47.1% of the new ones held; 1,152 slots written. Sparse, only the 4 slots the old facts read least: 94.5% kept (84.2% in the commonest topic, 99.4% of all the old bits right), 79.9% of the new ones held; 1,208 slots written. The live figure needs JavaScript: the layer slot by slot as each writer writes it, the 4 curves, and the old facts kept topic by topic, at every one of the 384 new facts.
The figure is that experiment with everything removed but the mechanism. A layer of 8,192 slots holds 384 facts exactly, their questions in 32 topics of which a few are common; 384 new facts then arrive one at a time, and each is learned at once and completely, by the smallest change the writer is allowed. Read densely, as a layer of rectified units reads, the layer writes 4,177 of its slots for the first new fact, and it has 76.0% of the old facts after 1 new one, 41.7% after 2, 15.4% after 8 and 2.3% at the end. Read 16 slots at a time and written in all 16, it keeps 71.9%. The surprise is the third writer. Write only 4 of the 16, the 4 whose keys agree most with the question, and the layer keeps 26.8%: fewer weights moved and far more forgotten, because the keys that agree most with a question are the keys of its topic, which every old fact of that topic reads too. Write instead the 4 that the old facts read least, and it keeps 94.5%. Sparsity is not the idea. The ranking is, and its price is in the same picture: the commonest topic, with 101 of the old facts, keeps 84.2% of them where the rare topics keep nearly all, since a memory is crowded where knowledge is dense, and the new facts are themselves held a little less well than by the writer that spends 16 slots on each, 79.9% against 83.3%.
That is a result about storing, and the companies' claim is about learning. A fact has an address, and the librarian's rule works because the address of a new fact can be told apart from the addresses of old ones. A skill has none. Getting better at a job by doing it changes how every case is read, which is the dense writer's situation exactly, and for that the order is still unwritten, since nobody has said what, in a day of an agent's work, the reward is and who judges it. Continual learning is the form in which the event would be the judge at every step. Until someone writes that loss the companies are valued on the conviction of their founders, who may be right, and who have published nothing by which to tell.
Two refusals concern the loop and not the lesson. Diffusion keeps the words and drops the order of writing them, as the fifth mask showed, and it is no longer anyone's secret: Google's open model writes at more than 3 times the speed of its ordinary sibling, scores below it, and comes with the warning that time saved is not arithmetic saved. The other refusal is stranger, and for a person with 1 accelerator it is the most instructive result of the year. A network of 7 million parameters, 2 layers applied over and over to a scratchpad of its own, solves 44.6% of the first ARC set and 7.8% of the second, with no pretraining and no words. It holds the puzzle, a proposed answer and a latent state, and repeats 2 lines: improve the state from all 3, several times, then improve the answer from the state; a loss on the answer after every round teaches each round to mend the last. Its predecessor, nearly 4 times the size, had credited a hierarchy borrowed from the brain; the smaller model dropped the hierarchy and did better, and an independent analysis traces the scores of both to efficiency, to conditioning on the task and to arithmetic spent at test time more than to anything in the architecture that reasons. Alexia Jolicoeur-Martineau, "Less is More: Recursive Reasoning with Tiny Networks" (2025), after the Hierarchical Reasoning Model of 27 million parameters (40.3 and 5.0% on the same 2 sets). The analysis is arXiv:2512.11847; arXiv:2511.16886 reaches 24% with 0.8 million parameters. It is a solver for 1 family of puzzles and no general mind. But it breaks a dichotomy on which the whole family has traded. Kahneman's 2 systems entered the trade as 2 gaits, 1 pass or many written tokens, and here is deliberation that writes nothing: depth bought with time in the latent, a loop inside the pass, with the number of rounds itself a decision. A decision model allowed 6 silent rounds on its hard cases and 1 on its easy ones would not contradict Jev. It is the obvious next experiment, it fits on a desk, and so far as I can find nobody has yet scored one with a proper rule.
The remaining refusals I can only place. The companies that say the data was never on the internet have chosen the event for their judge in its purest form, an experiment that comes out or does not, and have bought robots and furnaces to hold it; those that make research the product have chosen the checker at its best, a proof assistant that cannot be flattered. Both orders are written, and both are games of capital. Thinking Machines refuses the solitude of the model, and I have said what I think the bet is. Its interaction models are trained from scratch at a size that puts the work out of reach of anyone without its capital, and its manifesto has yet to show that a wider channel moves judgment and not only words. But it is the one company saying that the unit of intelligence may be a person with a machine, and Peirce would have recognized the thought. By Lovelace's test, then, the world model's order is written and is being scaled by people with a billion dollars; diffusion's is written and owned; the memory that does not forget is written for facts; the silent loop is written, small and almost unexplored; and learning from one's own work, the bet with the largest valuations, has no order yet. The money and the dates run nearly opposite, which is how the ground should look to anyone hoping to arrive before the money does.
such labour can always be purchased at an easy rate
Babbage wrote that of the third section, and it is about to be true of a kind of judgment. If so, the work worth doing lies elsewhere, and where is what I most wanted to know when I began. The dates give half the answer and the judges the other half. Here is how the two sort the ground for someone who wants to train models and has no laboratory's budget.
Some directions have chosen the event for their judge and have their order written, and they are the ones I would enter. The first is the join that the System 1 models leave undone, doubt with reasoning. A model that thinks before it answers and then says truthfully how sure it is does not exist at any size that matters; the proper rules and the lottery pull against each other, as the reconstruction found, the published attempts are few, and the reasoning need not be written at all, if the silent loop can be made to carry it. It is also work for small machines. The reconstruction was run on a model of 1.7 billion parameters, the open decision models are trained as adapters on frozen backbones or as encoders of 400 million, the recursive solver has 7 million, and this is the first new family in years whose open state of the art can be reproduced on 1 accelerator, or a few. Clef and Laya are both published under the Apache license, with their weights. The second is forecasting proper: train on questions about the world that have since resolved, with Brier's rule for the reward and nobody's preference anywhere in the loop. "Outcome-based Reinforcement Learning to Predict the Future", arXiv:2505.17989 (2025), trained a model in this way on questions from prediction markets. Its difficulty is one of bookkeeping, and the people who have kept books will know it: every fact needs 2 dates, when it was so and when it was known, and a model may be scored only against what happened after everything it has read, pretraining included. Sutton's complaint is answered here and nowhere else in the field, since the ground truth is the future, and it arrives without being written by anyone. The third is the memory of agents, which now has 2 published mechanisms and no proper score: a Choice at every turn about what the large model will see, and a choice at every fact about which slots to write, each with an outcome the session itself supplies.
Close to these, and the best model of how to do synthetic data in the open, is the work on priors. TabPFN was pretrained on some 130 million tables that never existed, each drawn from a process its authors have described in print; it now handles tables of 50,000 rows and 2,000 columns in 1 run, with no training on the table in hand, and the company that makes it was bought by SAP in the summer. Prior Labs; the acquisition was announced on 4 May 2026 and closed on 17 July. Everything Almeida says about the primacy of the task is true of it. The difference is that its prior can be read, and argued with. A decision model's probabilities are posteriors under a prior over cases, and a prior that is a trade secret cannot be audited by the people who will act on its numbers. The practice I would like to see imposed on the family is the instrument-maker's: publish the generator, or publish the calibration against each customer's own outcomes, with a date.
What I would not enter is the model as a product. TypeSafe had the family to itself for 14 days. On 29 September OpenAI announced a Decisions API, which by its own engineer's account is no specially calibrated model but one of the company's general ones set to answer in a head; it reached every customer on 22 October, at more than twice Jev's price, and within a month at least 6 other vendors had shipped decision models of their own. TechCrunch's report of OpenAI's developer day; the engineer is Nikunj Handa, the model GPT-6 Luna, the prices 0.10 dollars and 0.042 for a million tokens read. TypeSafe has since been valued at 7.6 billion dollars. TypeSafe's reply is that what protects it is its synthetic data. I think that is half right. A head over the options is a week's work for anyone with a base model, the proper rule is in a journal of 1950, and the one thing that cannot be copied in a month is a record of cases with what happened next, which is data nobody can write. Whoever holds such a record for 1 trade, claims with their settlements, tickets with their reopenings, loans with their defaults, is better placed than the maker of any general decision model, and need train nothing larger than an adapter.
One idea I would leave to others for now. The small model that keeps the power to think and looks its facts up, Andrej Karpathy's cognitive core of perhaps a billion parameters, assumes that knowing and reasoning come apart, and what is known of expertise says the reverse: the master's quick judgment is his knowledge, laid down. The memory of slots is the first evidence I know for his side, facts with addresses, written without disturbing the rest; the dense writer, losing 5 old facts in 6 to 8 new ones, is the evidence for the other. Both may be right, and neither yet offers a loss one could write on a board.
What these sort into is a rule of thumb. Enter where the order is written and the money has not arrived, where the judge is an event, where the base can be someone else's, and where the scarce thing is cases with their outcomes truthfully kept. That is the third section's work, and it has always been where the tables were actually made.
The name on the model deserves a last look. Jevons's paradox says that an economy in the use of a thing enlarges its consumption, and its first instance in his chapter is the engine that preceded all economy: Savery's, which "consumed no coal, because its rate of consumption was too high". The frontier model is in that position toward decisions. It is so dear by the judgment, and so unfit to be left alone, that nobody spends it on the million small ones; the assistants have consumed almost none of the world's deciding. If the paradox holds, the decision models will not replace that spending but begin it. Every ticket will be asked 20 questions because the twentieth costs nothing, programs will consult the world in places where they now assume, and the total of machine judgment in service, with its stated rate of error, its middle bands and its desks, will be larger than anyone has budgeted for. I would not lean on the forecast. Its author was a confident forecaster and a poor one: he foresaw Britain's progress checked within a century for want of cheap coal, dismissed petroleum as a scarcer essence of the same thing, and, expecting a famine of paper, laid in a store so large that his children were still writing on it 50 years after his death. The paper is in Keynes's centenary essay on Jevons (1936); the petroleum in chapter VIII of The Coal Question. Britain's output of coal peaked in 1913. A calibrated model has been named for a man who was not.
His machine is the better guide. He showed it to the Royal Society as a proof about thinking, and he said exactly how much of thinking it left:
To the reader of the preceding paper it will be evident that mechanism is capable of replacing for the most part the action of thought required in the performance of logical deduction. Mental agency is required only in interpreting correctly the grammatical structure of the premises, and in gathering the purport of the reply.
—W. Stanley Jevons, "On the Mechanical Performance of Logical Inference" (1870), p. 517.
Two places, then, before the first key and after the last. The assistant kept its person at the second, reading every reply. The decision model moves him to the first: to the terms on the face, the options a question may have, the threshold at which a number becomes an act, the cases against which the number was made true. None of the 21 keys does that. It is what Whitehead's sentence leaves over when the operations we can perform without thinking have been extended as far as they will go, and it is still strictly limited in number, still needs fresh horses, and is still to be kept for the decisive moments.