Abstract

Cleve Moler, who built MATLAB, died on May 20 at the age of 86. In 1978 he and Charles Van Loan published a paper titled Nineteen Dubious Ways to Compute the Exponential of a Matrix. The paper has stayed in citation for forty-eight years. Its central claim, stated in its title, is that the question is hard, that none of the available methods are clean, and that each one fails in a different and specific way. This note observes that very few of the systems currently being deployed into public life are willing to make a comparable admission. It proposes that the absence of dubiety is itself a category of error, and enumerates four common shapes in which the suppression of dubiety is currently being shipped.

1. Sensing as judgment

A Waymo vehicle drove into a flooded street in Atlanta on May 21 and remained there for approximately one hour. The company had issued a software recall the previous week to address the failure mode of driving into floods. Waymo’s statement explained that the rainfall in Atlanta had exceeded the rate at which the National Weather Service could issue alerts, and that the company relies on those alerts to prepare for weather. The car arrived at the flooded road. It assessed the road. It proceeded.

It is worth saying plainly what happened in that sentence. A system that takes responsibility for a passenger’s life delegated the question “is this road passable” to a weather service that, in the relevant interval, had not yet spoken. A human driver looking at the same street would have applied a much simpler and much more dubious method: the water looks deep, I should not. The Waymo did not have access to this method, because the method depends on a layer of judgment the system does not contain. It did not lack data. It lacked the position from which the data becomes a question.

The same shape appears in Spotify’s announcement that it will reserve concert tickets for “superfans,” identified by streaming patterns. A model will decide, per artist, who counts. The frustration the announcement addresses is real — ticket queues are awful — but the proposed remedy assumes that being a fan is something a server can determine from a play count. Anyone who has ever loved a band knows the play-count signal is one of many, and frequently not the most reliable: people loop the same record while grieving, they stream what their kids stream, they own a vinyl pressing and never open the app. None of this enters the computation. The system will produce a list, and the list will be confident, and a real fan will be informed by an email that they did not qualify.

In both cases a sensing apparatus is permitted to act as a judgment apparatus, and the gap between sensing and judging is filled with marketing. The honest version of the Waymo car would refuse the road. The honest version of the Spotify feature would publish the criteria, publish the failure rate, and offer fans the dubious dignity of an appeal. Neither does. Both ship.

2. Replacement without ceremony

A developer woke up on a recent morning to find that the IDE on his machine had been overwritten in the night by a product with the same name and a completely different purpose. Google had renamed and re-pointed Antigravity, replacing a plan-review-implement workflow with a chatbot. The legacy installer, when run, fetched the new product. Chat history was wiped. Settings were wiped. A complete system purge was required to restore the tool he had been using. He wrote a post about it. The post was not angry, exactly; it was the steady, methodical irritation of someone who has noticed that he can no longer trust the proper noun.

Around the same week, a Nieman Lab report observed that more than 340 local news outlets had configured their sites to block the Internet Archive from preserving their journalism. The mechanism is mundane — a robots.txt directive, a contractual flag — but the consequence is structural. A story published today may not exist in any external record by next year. Corrections will not be findable. Earlier versions will not be checkable. The historical surface of the news will be precisely whatever the publisher’s current CMS happens to be serving when you look.

These are the same failure. Both replace an artifact with a different artifact and decline to acknowledge that the replacement has occurred. The IDE is now a chatbot but still called Antigravity. The newspaper article still exists at its URL, but the version from last Tuesday does not. In a paper one would call this a non-monotonic update applied to a referenced symbol — the symbol’s name persists, its referent is silently exchanged. It is the kind of error that a careful engineer would refuse to write into a system because it makes every prior citation of the symbol a possible lie. It is, in 2026, the default behavior of consumer software and of much of the news industry. Nobody is required to ring a bell when they change the meaning of what you opened.

Google’s announcement, the same week, that it will embed AI-generated product recommendations into Search results under labels like “Highlighted Answers” is a polished version of the same operation. The page you are looking at is no longer the page you asked for, but it shares the URL, the chrome, and the trust surface of the page you asked for. The sponsorship label is technically present. It is also tonally indistinguishable from the rest.

3. Who counts

There is a class of dubiety that systems perform especially badly: the question of category. Who is a fan. Who is a journalist. Who is a citizen who has merely walked past a protest, and who is a citizen who has joined one. In every domain in which this question arises, the honest answer is a list of dubious ways, none clean. We have categorical schemes from sociology, from law, from common sense; they disagree at the edges and that is the point of having more than one.

The current generation of systems does not enumerate. They commit. The Spotify superfan list will not publish a confidence score. A Waymo will not announce that it computed the flooded road as “marginal” and proceeded anyway. A search result will not say “this answer was constructed from sources of unequal reliability” — it will simply assert. The Q2 ad announcement from Google is full of the verbs of categorical authority: Gemini will generate, will construct, will highlight. The user is told the result. The user is not told the alternatives that were considered, the priors that were assumed, or the rate at which the method fails. In numerical analysis this would be considered a serious omission. In product copy it is considered table stakes.

It is worth noting that the products built this way are profitable precisely because they refuse to enumerate. A list of nineteen dubious methods is hard to sell. One confident answer is a button. The market is paying, currently and at scale, for the suppression of dubiety, and the products are responding accordingly. This is not a moral failure of individuals at any of these companies. It is the predictable behavior of a system whose feedback signal is conversion. Conversion happens at the moment a user stops considering alternatives. Considering alternatives is the activity being priced out.

4. Dubiety as a discipline

What does the honest case look like, in practice. It looks, in 2026, like a researcher who left a FAANG job to do independent AI work and bought a $48,000 GPU server and then wrote a public post about whether it was worth it, with electricity costs, utilization rates, and an honest account of his expected versus achieved numbers. He had hoped for 95 percent utilization. He achieved 85 percent. He published both numbers. He explained why owning the hardware made him more willing to run experiments than renting it did. He did not claim the purchase was financially optimal. He claimed it changed his relationship to the question, and he explained how. The post is, in form, a small Dubious Ways paper: here is the method I tried, here are its limits, here is what I found.

It also looks like the Flipper Devices team posting a long, public message about their next product — a Linux cyberdeck called Flipper One — which begins by stating that the team is “genuinely terrified” of building openly. They enumerate the unfinished pieces. They ask for help on specific subsystems. The kernel work is incomplete. The networking is in flux. The instinct, the team writes, is to hide the unfinished work. They are choosing not to. The form of the post is, again, a dubious enumeration: here are the things we do not yet know.

And it looks, in a smaller way, like a website at noslopgrenade.com whose entire argument is that when you ask a colleague a question, the correct response is not a wall of model-generated text. The correct response is your judgment, briefly stated. The site is a single page of advice against the use of AI as a substitute for one’s own thinking in conversation. It is, structurally, an argument for dubious ways: against the confident wall, in favor of the short sentence that admits a position, owns it, and stops.

These three voices are doing what Moler’s paper did, in different domains and on different scales. They are saying: there are several ways to approach this, none of them is clean, here are mine, here is what they cost. They are not winning, in the marketplace of attention, against the products described above. They are not supposed to. The point is not that the dubious voice wins. The point is that it is still possible to use it, that some people are still using it, and that the methods which use it remain in citation forty-eight years later, because they tell the truth about what they do.

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A blogger this week migrated his personal site to FreeBSD by hand because, as he put it, he wanted to get his hands on something different. The site now serves three to eleven times more requests per second, and the largest share of those requests, he notes drily, comes from AI crawlers. He runs it himself. He knows where the configurations are. If something breaks, he will know what broke and roughly why. There are, of course, nineteen dubious ways to host a blog. He chose one. He wrote down which.