No Royal Road

Ptolemy once asked Euclid whether there was any shorter way to a knowledge of geometry than through the Elements, and Euclid answered that there was no royal road to geometry.

Proclus, Commentary on the First Book of Euclid’s Elements (5th century)¹

Ptolemy’s question is a good one and everybody asks it. He was not being lazy. He was a king with a country to run who wanted the results of geometry without the thirteen books, and in most of life that request is reasonable and gets granted. Euclid’s answer is famous because it is the unusual case: a road where the walking is the knowing, and nobody can hand you the far end of it.

The hard part was never the question. The hard part is that from the near end of any road, the two kinds look identical.

Which matters more now than it used to. Most of what we have been handed lately will take a swing at anything you put in front of it. A new kind of tool will not.

The answer that arrives first

There is a class of model that works the way recognition does. Hand it a paragraph and a list of statements and it tells you which statement the paragraph entails: one forward pass, a couple of hundred milliseconds, no chain of thought and no scratchpad. It does not deliberate.

People are shipping a great deal with this. At the time of writing there are 620 public builds on Jev’s site:² 234 tools and apps, 89 agents and browsers, 85 research and data, 77 games and real time, 55 triage and routing, 12 under Trading and markets. Scroll it for a while and the energy is unmistakable. A tool that enforces the review-comment rules a linter cannot express. A converter that has a large model describe every style in a house style guide once, offline, so a small model can pick one per paragraph at runtime. Something that highlights the emotion in each sentence of Dostoevsky as you scroll.

What you cannot tell, from a listing, is which of these came from somebody working out exactly where the recognition problem in their domain begins and ends, and which came from somebody reaching for the interesting new thing. Both produce a build and a demo, both read identically in one line, and I am not going to pretend I can sort them. A finished thing does not record the road it came by. The move is nearly as invisible from the inside, which is the part worth dwelling on. There is a well-worn test for it, three arithmetic questions where the wrong answer arrives before you have decided to answer.³ A bat and a ball cost $1.10, the bat costs a dollar more than the ball, and ten cents is simply there, already formed. Forty-four percent of a cohort of medical students got all three right; one in ten got none.⁴ A room of circuit judges averaged 1.23 out of three.⁵

The usual reading of that test is a scolding: engage the slow system, override the fast one, be more rigorous. I think that reading is wrong, or at least that it describes the least interesting thing going on. Nobody in that room decided to skip the arithmetic. What happened is that the question turned up in a recognisable costume. A word problem with two numbers in it is a request to do an operation on those two numbers, so an operation is what arrives: $1.10 minus $1.00. The costume never supplied the answer. It supplied the kind of answer being asked for, which was enough, because the kind is where the error already lives.

This is ordinary and almost entirely invisible. Nobody consults their health before answering “how are you” with “fine”, and nobody decides to treat a multiple-choice question as a choice among the options rather than an argument with the question. The shape of what you are asked proposes the shape of what you say back, and what reaches you is never the proposal, only the reply, already assembled.

That is also what it is to look at a problem and see a classification task. The shape proposes the tool, the tool works in the demo, and whether the problem was ever really that shape does not come up again.

What cannot be handed over

So I picked a domain where I could count. Two weeks and 581 commits: a small recognition model playing Pokemon FireRed, with everything it is asked written down.

name	what it asks
YES_NO	The game is asking a YES or NO question. Which answer advances the goal?
DANGER	Is our Pokemon close to fainting?
SWITCH	Which of our Pokemon should we send out?
HEAL	The party is hurt. What should we do about it?
BATTLE	What should we do on this turn of the battle?
DEPOSIT	Which of these should we send to the PC?
FORGET	Which of these moves is the least useful to keep?
WITHDRAW	Which of these does the party need most?

Eight. Measured over 80,349 game ticks across nineteen runs, the model is consulted on 1.65% of them. On the other 98.35%, nothing asks it anything, because the code already knows.

Aristotle has a distinction that fits this better than anything in the modern literature. Techne is the knowledge of making, statable as rules and taught by transmission: a builder can tell you how to build. Phronesis is judgement exercised on particulars, and he is explicit that it resists reduction to rule, because no general statement reaches all the way down to a particular. It comes from experience and cannot be handed over.⁶

Which is Euclid’s answer in another vocabulary. Techne has a royal road; it is the kind of knowing that can be told to you. Phronesis does not, and that is not a defect in how we teach it.

Those eight are where the phronesis lives. Everything else is techne, and techne is what code is for. Which route is shortest is a breadth-first search; which side of a cave a ladder lands on is a table lookup; whether the party can afford six Potions is subtraction. A model asked any of these returns something fluent, plausible and frequently wrong, and nothing about the answer tells you which you got. It is the bat and the ball. It will say ten cents all day.

Movement is the case that taught me most, because it feels like phronesis. Playing the game, you experience deciding where to walk. But the deciding is the destination and the walking is Dijkstra, which is why there is no MOVE question in that list of eight.

A tick has five stages, and one of them is a neural network.

Stage	What it does	Who decides
Perception	Save blocks and map layouts out of RAM into typed state	Code
Premise	Render that state as English prose	Code
Policy	Walk the rungs, first one that fires wins	Code
Ballot	Only if a rung asks for one: score statements against the premise	Model
Executor	Turn the decision into a list of button presses	Code

Most ticks: perception, premise and policy run, a rung fires, and the executor presses the buttons. On 98.35% of ticks, nothing asks the model anything.

The other 1.65%: a rung asks for a ballot. The model scores statements against the premise, never actions, and the winner goes to the executor.

step

1 2

One detail of the ballot stage turned out to matter more than anything else about it. The model is never offered actions, only statements: not “you should use SOLARBEAM”, which is a claim about the future that nothing in the premise can entail, but “SOLARBEAM does the most damage to this opponent”, which the premise either supports or does not. Only one of those is a question a recognition model can be right about.

A cut, not a seam

The eight did not shrink. I had assumed they would, that I leaned on the model early and clawed decisions back as I came to understand the game, and the repository says otherwise.

questions the model is asked

048

3 8

lines of Python

010k20k

11,714 19,827

22 Sep27 Sep2 Oct

table

date	questions	lines of Python
22 Sep	3	11,714
23 Sep	6	13,181
27 Sep	8	14,679
28 Sep	8	16,218
2 Oct	8	19,827

The questions reached eight on the 27th of September and never moved again. Everything learned after that date arrived as code instead: the Sevii island chain, a hidden waterfall prerequisite, six floors of a puzzle cave, Victory Road, the long grind at the Pokedex. Five thousand further lines of it, and not one new question.

Which is the part worth sitting with. Understanding does not turn into better questions for the model. It turns into code, and the model’s share is whatever has not been turned into code yet. So the line between the two columns is not a seam in Pokemon FireRed at all. It marks how far along the road I had got by the 27th of September.

Foucault opens The Order of Things by laughing at a taxonomy of animals from a Borges story, where the categories include those belonging to the Emperor, those that are embalmed, those drawn with a very fine camelhair brush, and those that from a long way off look like flies. His point is not that the list is silly. It is that every taxonomy looks like that from far enough outside and like nature from inside, and that the ordering comes first and conditions what can then be known.⁷ My two columns are a taxonomy. Arithmetic and qualitative are not properties the cartridge has. They are a cut I made, and the cut is doing work that gets credited to the finding. You can watch it move: movement was qualitative until the week I understood it well enough to write a pathfinder, and then it was arithmetic, and the change was in me. Each column is defined by the other besides, one being what I worked out and the other what is left, neither with any content without its partner.⁸

The rule that looked like it worked

A run sat in Cerulean Cave for forty hours and gained nothing. It was surfing, and it pressed south forty thousand times into a step the engine refuses. Tiles carry an elevation and a surfing player can come ashore onto some of them and not others; my rule said water to anything, and the game says water to a shore. The cartridge holds 6,136 seams where water meets a shore and 102 where it meets a ledge, and the router had been wrong about all 102 since the day it was written.⁹

The sorting was correct. Whether you can step from here to there is arithmetic, it belongs in the first column, and that is where I had put it. What I got wrong was the arithmetic, and that is a different failure from the one the taxonomy usually gets accused of. Filing something in the wrong column is a mistake somebody can argue with you about. Filing it in the right column and then being wrong about it is silent, because the entire premise of that column is that nothing checks it. The model that might have noticed was never handed the question, by design.

And the seam itself is not a clean edge. “Can I step here” looks like bedrock until it turns out to rest on a rule you have misread, at which point it was never arithmetic you had, only arithmetic you believed you had. The two columns feel like different materials from inside the project and they are not. They are one material, divided at whatever point I stopped walking.

Which is where the standing temptation lives. When the deterministic side turns fiddly, the obvious move is to hand it back: let the model decide where to walk. That trade is on offer at every one of these boundaries, and here it would have failed for the plainest reason, which is that the model did not know about elevation either, and would have answered anyway.

Meno asks Socrates how you can possibly look for something when you do not know what it is, since you would not recognise it even on finding it.¹⁰ The dialogue treats this as a puzzle to be dissolved. As a description of debugging it is simply accurate. The 102 seams were in the cartridge for twenty-two years. Nothing prevented me reading them except that the rule I had already written looked like it worked, and a rule that looks like it works does not generate the question that would find it.

Ptolemy’s question

Software has always had an easy way. The framework adopted without reading what it does. The library whose failure modes you learn about in production. The abstraction in the middle of your system performing an operation you could not describe if asked. Every one of those is Ptolemy’s question, and most of the time the answer is kinder than Euclid’s: there is a shorter way, take it, nobody reads the kernel before writing a web app. A career spent refusing to stand on anything unexamined is a career spent reimplementing sockets.

What is new is that you can now get a model to have a go at almost anything. The shorter way runs into places that never had one, including places where nobody has yet worked out what the longer way would even consist of. And because the output is fluent, the difference between having understood your problem and having routed around it can stay invisible indefinitely. How do you know which road you are on?

The choice underneath is the old one, and it is the only one here that was ever really a choice: how much of the problem are you willing to actually understand?

Those eight questions were not available to me at the start. They are a residue. Each is what remained after some candidate question turned out to have an answer instead, nineteen thousand lines of finding out that the thing I was about to ask about was not a judgement at all. Every finding of that kind deletes a question. They all look obvious once written, and that is the difficulty, because a thing that is obvious afterwards was not thereby available beforehand.

So the right question is not an input to the work. It is what the work leaves behind, and no amount of care at the outset reaches it. Which is why none of the tooling reaches it either: all of it is addressed to the part that was never the bottleneck, and addressed there because that part is legible and purchasable and the other part is neither.

And it is why a model that can only recognise turns out to be a better instrument for thinking than a model that can do anything. A capable model will absorb your ignorance about your own problem. It answers whatever you ask in whatever shape you ask it, and the places where you did not know what you were asking are precisely the places where the fluency runs thickest, because there is nothing there to contradict it. A model that can only choose between statements you wrote yourself cannot do that for you. It stalls, visibly, at every point where you have not yet worked out what the question is. The stalling is the instrument. You are not being helped, you are being shown the edge of what you have understood, which is the one thing no amount of capability will hand you.

That is the trade, and it is worth being plain that it is a trade. It is slower. It is more work. It will not suit most problems, and for most problems it should not. But for a problem you actually need to understand, as opposed to one you need results from, the constraint is the whole point: you cannot route around your own ignorance with an instrument that has no fluency to route with.

Ptolemy could have been handed every theorem in the Elements and still not have been a geometer, and he would have had no way to tell.

Footnotes

1. Proclus, A Commentary on the First Book of Euclid’s Elements, trans. G. R. Morrow (Princeton, 1970), 68. The anecdote reaches us eight centuries after Euclid and is almost certainly apocryphal; a near-identical story has Menaechmus saying the same thing to Alexander. It has survived because the sentiment is right, not because the meeting happened. ↩

2. Counts from shipwithjev.com, October 2026, and they move quickly. ↩

3. Frederick, S. (2005). Cognitive reflection and decision making. Journal of Economic Perspectives, 19(4), 25-42. Frederick’s own emphasis is on the intuitive answer being impulsive, arriving before deliberation is attempted, which is the part I think survives; the debiasing literature built on top of it is a separate claim. ↩

4. Tay, S. W., Ryan, P., & Ryan, C. A. (2016). Systems 1 and 2 thinking processes and cognitive reflection testing in medical students. Canadian Medical Education Journal, 7(2), e97-e103. ↩

5. Guthrie, C., Rachlinski, J. J., & Wistrich, A. J. (2007). Blinking on the bench: How judges decide cases. Cornell Law Review, 93(1), 7-32. Tay et al. caution against reading the gap too directly: the judges answered the questions embedded in a longer questionnaire over 45 minutes, the students in a dedicated 10 to 15 minute sitting. ↩

6. Aristotle, Nicomachean Ethics, VI.4-5 and VI.7-8 (1140a1-1142a30). Techne is the disposition concerned with making, accompanied by a true account; phronesis is concerned with action and with particulars, which is why Aristotle says the young can become geometers but not practically wise, since phronesis requires experience that time alone supplies. ↩

7. Foucault, M. (1966). Les Mots et les choses, preface. The taxonomy is from Borges, J. L. (1942), “El idioma analítico de John Wilkins”, and is Borges’s invention rather than a real encyclopedia, which Foucault knew and which does not weaken the point. ↩

8. The move is Derrida’s, in De la grammatologie (1967): an opposition of this kind is never a neutral pair, one term is privileged and treated as prior, and the privileged term turns out to be defined by the exclusion it performs rather than by any content of its own. ↩

9. Measured by walking every map layout in the ROM and counting adjacencies where a surfable water tile touches a walkable non-water tile, bucketed by the elevation on each side. 6,136 are elevation 1 to 3. The 102 at 1 to 4 are confined to four cave maps, one of which is Cerulean Cave 1F, which holds nineteen. ↩

10. Plato, Meno, 80d-e. Socrates answers with recollection, which I am not endorsing; the paradox is more durable than the solution. ↩