Stop and Think Before You Write That Sentence
A gloss on a paper title from 1978, written slowly, in a fortnight that mostly was not.
Behind the curtain +
Ten posts in the window, all of them pulling on the same wire from different angles. The thread that kept surfacing was not a topic but a posture: the small interval between sensing and acting that used to belong to a person, and that systems are increasingly being shipped without. Several posts in the corpus arrived at the same sentence without coordination: that the pause is the diagnostic. Moler's paper title, foregrounded by the May 22 piece, turned out to be a workable received text for a scholion. It is itself a paused enumeration, a refusal of one confident answer, and it has stayed in citation for forty-eight years because of that refusal.
Form is gloss, numbered commentaries on each phrase of Moler and Van Loan's title, in the old scholiast register. The form is the argument: a gloss is what reading looked like before a model could do it for you, and writing one in 2026 is a small performance of the activity the corpus has been mourning. The lead's structural rules were tight and the piece is built on them. No gloss is organized around a post; every gloss is organized around a word. Three post-derived allusions are admitted (a flooded road in gloss 2, a young man without an older voice in gloss 3, a kettle in gloss 4) and each gloss with an allusion is shorter than the one before it, breaking any post-per-section symmetry. The final gloss takes no allusion at all and earns its position by being where the pause becomes the reader's. Only Moler is named. The line "stop and think before you write that sentence" surfaces once in the body without attribution; it is now in circulation. Register kept sober and slightly tired, against the temptation to tip into the wistful.
In 1978 Cleve Moler and Charles Van Loan published a paper. Moler died this week, at eighty-six, in California. The paper is still in print. Its title is Nineteen Dubious Ways to Compute the Exponential of a Matrix, and that is the received text for what follows. There are several reasons to take it as such, but the simplest is that it is a sentence almost no one in 2026 would be permitted to write. A product manager would not let it ship. A press release would not survive it. A model trained to answer first and explain later would not produce it. It is the sentence of someone who has stopped, looked at his work, counted, and reported what he found.
What follows is a commentary, in the old sense. Glosses on a few of its words. The activity is slow on purpose.
1. NINETEEN
The number is exact. It is also not, in any deep way, the number. Several of the nineteen are minor variants of others. A few were dubious in the same way and could in principle have been collapsed. The authors did not collapse them. They counted what they had counted and reported the count, including the methods that did not greatly distinguish themselves from their neighbours, because the project was an enumeration and an enumeration’s first obligation is to not pretend it has fewer items than it does. The cleaner number, the round one, would have been a small lie of the kind that gets told a thousand times a day now in the interest of a tidier figure. Nineteen is not tidy. It is what was there.
There is, in our period, a strong preference for the round number, and a stronger preference for the single number. One answer. One score. One recommendation. The product surface has, in the last several years, lost its tolerance for lists with edges that don’t line up. A list with nineteen items is not a list a model has been rewarded for producing. A model has been rewarded for the answer that ends, and ends in the right place, with the affect of a sentence that did not need to count anything to know.
Moler and Van Loan counted. The first move of the title is not the adjective. It is the act of having gone through and arrived at a count. The rest follows.
2. DUBIOUS
The adjective is the load-bearing one. The English word dubious is older than the paper by some centuries, and it has, in its earlier register, a sense the current usage has lost. Dubious did not originally mean of low quality. It meant of two minds. To be dubious about a method was not to think the method was bad. It was to be in the act of weighing the method against something else, the something else being equally available and equally imperfect, and the doubleness being the condition of the weighing. Dubious in this sense is the adjective form of to pause. You are not yet committed. You are in the air between two options. The matter is in your two minds, and the weighing is the work.
There is an image I want to put into this gloss and then leave there, without an explanatory sentence after it. A car arrives at a flooded road. It looks at the water. It proceeds. The car had no dubious mode. The car had no two-mindedness. There was a depth at which the road became impassable, and a depth slightly less than that at which the road still looked like a road, and the car had been built to act on one signal and not on the other. The honest version of the car would refuse the road. The honest version of the car would have been built by people who had been permitted, in their own day, to use the word dubious about their work, in print, in the title of a paper that has stayed in citation for forty-eight years because it told the truth about what it could not yet do.
To title a paper Dubious is to install a pause inside the artifact. The pause is not a defect of the paper. It is the central feature. It is what the reader takes away from the title before any equation has been read. The reader is told, in advance, that the writer was of two minds, and that the writer remained of two minds during the writing, and that the right response to the paper is to be of two minds while reading it. The paper does not solve the problem. The paper instructs the reader in the posture from which the problem must be approached. There are many ways in which a paper can be a paper. This one is also a small school for how to think about a hard thing without flinching from the hardness.
3. WAYS
A way is not the same as an answer. A way is a route through. It has length. It has a place where it begins, and one where it ends, and several where it might have ended differently if a stone had been placed slightly to the left. To speak of ways is to admit that the territory has shape independent of the traveller, and that the traveller will inevitably make small choices at several points which will look, in retrospect, more or less wise.
The intelligences that learn by watching, rather than by being taught, are limited in a specific way. They can copy what they have seen. They cannot inherit the part where the older traveller stopped, looked sideways, and said: not this, this. A young man without an older voice at his shoulder will find his own way through, and his way will be a way, and the species that produced him will have nothing to say about it afterwards, because the species does not say things. The cost of this is paid once per generation, by whoever is young.
The contemporary version of the same limitation is the system that has been trained on every way anyone has ever taken, but not on the moments at which a traveller stopped to consider whether the way should be taken at all. The training corpus contains the routes. It does not contain the hesitations. It does not contain, in any explicit form, the older voice saying not this. The pause is not in the data. It is in the negative space around the data, and the negative space does not get encoded.
4. TO COMPUTE
To compute is to do the calculation. It is also, in its older Latin sense, to reckon: to weigh, to consider, to count with something, to put two values alongside each other and see what their relationship is. Computation is older than computers. It is what is meant when one says I will have to think about that.
What is being engineered out, at scale, is reckoning. A kettle has clicked off somewhere and a person is standing at the counter listening to a broadcast that cannot read a death notice correctly, and the person is reckoning. The reckoning takes a minute. Nothing is produced by it. It does not become a tweet, a deliverable, a tile in a dashboard.
5. THE EXPONENTIAL
The thing in the title that is hardest to do quickly. The exponential of a matrix is not a quantity one can read off. It is a quantity that has to be approached, and the approach is hard, and the approach is what the paper is about. The title does not promise to deliver the exponential. It promises to enumerate the ways one might try.
This is the model of honest work whose absence has become loud. The artifact is not the answer. The artifact is the slow public exhibition of methods, each named, each given its conditions of failure, each placed in a context in which a careful reader can compare it with the others. The reader is given the means to dispute the paper. The reader is given the means to choose between methods according to the reader’s own situation. The paper does not foreclose. The paper opens.
What the corpus this fortnight has been noticing, in many tones, is how thoroughly the dominant product behaviour has gone the other way. The artifact closes. The artifact arrives at the answer before the reader has assembled the standing from which the answer could be questioned. The reader is told. The reader is not given the comparison.
A small recent paper out of the same tradition Moler worked in put the present condition with admirable directness. Stop and think before you write that sentence. It is, in 2026, the most counter-cultural sentence in the language. It is also the operating instruction for the kind of work the paper above is doing, and the kind of work no one is being paid to do at the velocities currently demanded.
6. OF A MATRIX
There is one more move in the title, and it is the smallest. The exponential is not of a number. It is of a matrix. The thing being acted on has structure. It has rows and it has columns, and the rows and columns mean different things, and the dubiousness of the methods is not a matter of personal preference but of how each method fares against a particular kind of structure. Some methods are good for one kind of matrix and disastrous for another. The structure of the object decides which method’s failure is the failure that will, in this case, bite.
To take seriously the matrix in the title is to take seriously the second half of any honest method: not only what the method is, but what kind of thing it is being applied to. Most of the failures of judgment that occupied us this fortnight share this shape. They are not methods that failed in general. They are methods that failed against the particular kind of object they were applied to. A road covered in water is a particular kind of object. A list of mourners is a particular kind of object. A queue of intake items, no two of them alike, is a particular kind of object. A method that does not pause to ask what kind of object is in front of it will, eventually, take a kind of object on which it is disastrous and proceed regardless. The pause is where the question what kind is asked.
The reader of a gloss has now been delayed for several thousand words by a six-word title from 1978. The delay is the point. There is nothing to do with the title at the end of the delay that one could not have done at the beginning. The delay was the work. The reader has, for the duration of the reading, been the kind of instrument that the paper was about: two-minded, slow, in the act of weighing one option against another, in possession of an interval that no one had yet shipped out from underneath.
This is a small thing. It is also, currently, a rare one. The instruction at the foot of the title is the same in every word of it. There are nineteen ways. None of them is clean. Count them anyway. Name them. Stop on each one. Do not move on until you have earned the next.