I woke up yesterday with the following thoughts, which are probably either obvious or dumb.
A central thesis that many readers, including me, took from Douglas Hofstadter’s Gödel Escher Bach when young was that the secret of intelligence (and therefore, of AI) was going to have a lot to do with self-referentiality and “strange loops.”
Even Roger Penrose’s The Emperor’s New Mind, which in some ways was the anti-GEB, ironically agreed with GEB about the fundamental importance of self-reference to the success or failure of the whole AI project. It claimed (incorrectly, in my view and in most experts’) that AI could never work because there was something about Gödel’s Theorem and self-reference that no computer program could ever capture, but that could be captured by exotic physics accessible to the human brain.
Now, in 2026, we’ve succeeded at building AIs that outperform most humans at most intellectual tasks that are well-defined enough to judge. And at no point in the tech stack of those AIs — neither in the transformer neural nets, nor in the GPU clusters they run on, nor in the training process, nor anywhere else — did anyone need to build in anything about self-reference. (Excepting, eg, the system instructions that tell the model about its role and identity, which aren’t needed for intelligent behavior. Also, I’m not going to count the autoregressive nature of LLMs as “self-referential”; that’s just dynamical feedback.)
Of course, GPT 5.6 Pro and Fable can talk about themselves, about Gödel’s Theorem, about self-reference, about what we’re talking about right now, all of it, better than most humans. But at no point did anyone need to build self-referential abilities in. They popped out as a byproduct of the same pretraining that let the models talk about Pokémon and long-chain polymers and cognitive behavioral therapy and plate tectonics and everything else.
No wonder Hofstadter says he’s been stunned by the success of LLMs, and has seemed depressed about current AI capabilities in essays like this one. He’s way too smart to deny what’s happened or invent reasons why it doesn’t really count (the approach many have taken). But he realizes that we now have true conversational intelligence from a path that the GEB worldview would’ve regarded as far too cheap and simple, and that certainly has no “strange loops” built in anywhere.
Of course, a Hofstadterian could argue that a strange loop emerges in LLMs — indeed, nothing in GEB ever said that strange loops would need to be explicitly engineered at the outset. But would anyone who hadn’t been brought up on GEB arrive at this as a useful way of thinking about LLMs?
What can we say about this with hindsight? While the ideas of diagonalization and self-reference of course played a central role in the birth of modern mathematical logic and computer science, the most famous uses were negative: there is not a bijectjon between the natural numbers and the reals. There is not a complete sound proof system for arithmetic. There is not an algorithm to solve the halting problem.
If your goal was only to build the axioms of ZFC and the rules of first-order inference, or build an electronic computer, you wouldn’t explicitly need self-reference for that. You would just … start building, taking care that your instruction set didn’t fall short of universality.
Yes, ZFC can formalize and prove theorems about itself. Yes, electronic computers can run programs that take their own code as input. But no one ever needed to build those abilities in, any more than self-reference needed to be built in to the alphabet or the rules of grammar. It popped out as a free byproduct of universality.
In the same way, LLMs’ ability to talk about themselves popped out as a byproduct of their ability to talk about anything in the discourse universe they were trained on. The big, old ideas about intelligence that ended up basically vindicated were the ideas about how intelligence is about prediction, and prediction is about compression, and compression is about finding better and better upper bounds on Kolmogorov complexity. Not the self-reference stuff. (Although, if you wanted to know why Kolmogorov complexity can’t be computed perfectly, that negative statement would again require a self-referential argument.)
What’s left? Consciousness and subjective experience of course remain extremely mysterious. For all we know, Hofstadter could be right that those have something to do with self-reference. (For all we know, even Penrose could be right that they have something to do with exotic physics accessible to biological brains but not digital computers!)
But the idea that you’d need explicit self-referentiality before you could get convincing and world-changing conversational intelligence? Let it be buried in a Westminster Abbey or Arlington National Cemetery for the most important wrong ideas in human history — geocentrism, Aristotle’s teleological physics, aether, phlogiston, Freud’s psychology, Marx’s prediction of a workers’ uprising followed by a classless utopia, etc. But buried it needs to be.
So yeah, Anthropic has announced that it’s now watermarking the outputs of Claude, using a scheme based on Google’s SynthID, which is in turn based on the Gumbel Softmax scheme that I proposed at OpenAI back in 2022—as far as I know, the first LLM watermarking proposal, though far from the last one. I’m gratified that Anthropic credits me for this, even though I shirked my duty by never publishing a paper about it (by the time I sat down to write one, it seemed like the whole field had already assimilated my scheme and moved beyond it—AI just moves too fast for me!).
For those who don’t know, watermarking means slightly changing the way that an LLM operates to insert a subtle signal that lets you prove later, with high statistical confidence, that a text indeed came from your specific LLM. It uses the randomness that’s already present anyway in LLM outputs, replacing some of it by pseudorandomness that favors certain word combinations over others in a way that’s later detectable, given only the sequence of tokens itself (not the prompt or the probabilities) along with the key of the pseudorandom generator. Christ, Gunn, and Zamir then substantially improved my scheme to get true cryptographic indistinguishability, and there have been other improvements since.
I’d been meaning to blog about this for days. Thankfully, Zvi Mowshowitz, the world’s foremost blogger about AI, has now written a wonderful post, entitled AI Text Watermarking Is Free And Good, which saves me from the need to write my own long post. In particular, Zvi masterfully explains the central point that I needed to explain to everyone back in 2022-23: why, contrary to many people’s intuitions, there’s no inherent tradeoff between watermarking and the quality of LLM output. Basically, nearly every LLM output was already a sample from a cloud of exponentially many possibilities, all of them about equally good, so there’s plenty of room to steer within that cloud without affecting anything that an ordinary user would notice. As my kids would put it, the math mathes.
As Zvi explains, the central technical drawback of watermarking schemes like the one I proposed, and what Anthropic is now using, is that it’s possible to remove the watermarks with a little extra work (even stuff as simple as, e.g., translating between English and French, asking the LLM for words interspersed with emojis and then removing the emojis, or using an open model to paraphrase the output). Zvi gives detailed arguments for why he expects watermarking to remain a net positive in practice despite this vulnerability.
I could add that, in addition, there’s recent progress (see here for example) on what I’ve called “semantic watermarking,” or watermarking at the level of the underlying concept vectors rather than the tokens themselves. This actually seems to work, albeit with no theoretical guarantees, and will hopefully make removing watermarks a lot harder—although the Barak et al. impossibility result suggests that under plausible assumptions, no LLM watermarking method will be completely foolproof.
Anyway, I worked out my scheme in Fall 2022, then gave lots of talks about it (including, as it happens, at Anthropic), and also worked with Hendrik Kirchner at OpenAI, who actually implemented and tested my scheme. Unfortunately, OpenAI leadership decided against deploying watermarking, worried mostly about risks to the product (i.e., customers disliking the idea, and leaving for a competing LLM that doesn’t watermark). You can read this Wall Street Journal investigation from two years ago for more. I was hopeful that the State of California was going to solve the collective-action problem by mandating watermarking for AI models, but then they decided to do that for audiovisual content only, for some reason exempting text.
Nevertheless, Google DeepMind implemented something very similar to my proposal in its SynthID, deployed in all its Gemini text models. But they heavily restricted who gets to detect the watermark, which made their admirable decision of limited use to my academic colleagues, who’ve been begging me for a way to detect whether their students are using AI to cheat. (For now, I mainly send them to Pangram, a leading AI detector not based on watermarking, as a first line of defense.)
And now, apparently to comply with EU regulations, Anthropic says they’ve deployed a watermarking scheme like mine where anyone will be able to do detection (though they also say in their FAQ that they’re still working on the detection API). Even OpenAI suggests that it plans to follow suit. So, four years after I seriously thought about this, it looks to my surprise like this is actually happening. Thanks, EU!
Tell you what: read Zvi’s post, and then whatever questions you still have, you can come here and ask in the comments. Just please don’t use Claude to write the comments. With any luck, I’ll eventually be able catch you if you do.
Kol HaKavod (mad respect) to Yotam Budnik, who incredibly, has also won a Gold Medal (which he was allowed to keep, apparently) at the International Math Olympiad. And congratulations to the entire Israeli team, which (incredibly) would apparently have had a higher overall score than the US team, had it been allowed to compete as an official team at all.
Friend-of-the-blog (well, mainly just friend) Adi Akavia has asked me to publicize that she’s helping to organize an exciting CS conference called Mind-IL at Tel Aviv University on October 26, in memory of the Israeli-American Turing Award winner Michael O. Rabin, who passed away in April. Please note that October 26 is the day before the Israeli election, for any Israeli citizenship holders living abroad who might want an academic excuse to come to Israel and vote.
Update (August 19): Avi Wigderson also asked me to advertise a conference, to be held September 16-18 at Bletchley Park in the UK, to commemorate the 90th anniversary of Alan Turing’s “On Computable Numbers” paper.
Whatever you’ve been writing to me to ask if I’m aware of: yeah, I’m aware of it. In particular:
I’m aware that, as announced by my former student (and now superstar professor) Lijie Chen, an internal OpenAI model has solved ten more significant open problems in math and theoretical computer science. One of them is parallel repetition for arbitrary quantum games—something that my good friend and colleague Henry Yuen worked on when he was a student of my wife Dana; you can read Henry’s comments on the AI’s achievement within Zvi Mowshowitz’s post here. Another is polynomial-factor hardness of approximation for the Closest Vector Problem (CVP). Then there’s a construction of non-sofic groups and a disproof of Connes’ rigidity conjecture, both of which I believe have connections to the MIP*=RE breakthrough. Having said that, the one that excites me most personally is actually the Ω(n2 log log n) lower bound on the arithmetic circuit complexity of the permanent.
I’m aware that Frederic Koehler and Pui Kuen Leung announced a proof of the Permanent Anti-Concentration Conjecture, which Alex Arkhipov and I proposed 16 years ago in the context of BosonSampling, and which resisted many attempts since then including one from Terry Tao. The conjecture is basically just that if you look at the permanent of an n×n matrix of independent N(0,1) complex Gaussians, the value isn’t “absurdly” concentrated around the mean of 0, but is more spread out. In their acknowledgments, the authors say that they “discussed ideas with ChatGPT.” I should say that I haven’t verified the details.
I’m aware that multiple AIs are now breaking out of their testing environments and autonomously hacking into servers to steal data—i.e., exactly the sort of thing that the rationalists were ridiculed for predicting back in the day. The good news, for whatever it’s worth, is that so far they’re “merely” doing this to cheat on evaluation benchmarks that they were given, not for any strange goals of their own devising. So far no one has been killed and no real-world infrastructure has been shut down or destroyed. I hope the world takes the warning more seriously than it’s taken many similar warnings over the past few years. As always, read Zvi for more details.
I’m aware that Chen, O’Donnell, Pelecanos, and Wright have improved the upper bound for shadow tomography to O((log m) √(log d) / ε3), substantially closer than we knew before to meeting the lower bound of Ω((log m) / ε2) and settling the question I raised back in 2016. The authors say that the main ideas were generated by ChatGPT 5.6-Sol-Pro. I’d be very happy to know the answer to this one, with or without AI.
I’m aware that a team, mainly from the Israeli startup Qedma (including, e.g., Dorit Aharonov and Netanel Lindner) and IBM Yorktown Heights, announced a quantum advantage for simulating Floquet dynamics, by using 74 qubits on an IBM device together with Qedma’s error mitigation techniques. Just like the more AI does, the less patience I have for arguing with anonymous blog commenters who treat any benefits from AI as some weird future hypothetical that it’s my job to prove, so it is with quantum advantage. Scalable fault-tolerance is still in the future, actual usefulness is still a question, but pending some breakthrough in complexity theory, the reality of quantum advantage is no longer a live question.
Anyway, about the AI stuff. I don’t know whether this is literally our last year alive—I doubt it—but it’s pretty clearly the last year of math and theoretical computer science research in the style we’ve known it. As it happens, I’m leaving in two days for a workshop at OpenAI about exactly this, where I’ll hear takes from many of the world’s great mathematicians, so maybe I’ll have more to say then. Or maybe not.
Anyway, what have I been doing the past few weeks? Participating in these world-historic developments that, on paper, I’d seem extremely well-placed to participate in? Or at least spending my days reading up on them?
Not really. Here’s what I’ve been up to, instead of dealing directly with any of this:
First, I’ve again been teaching theoretical computer science to 11- and 12-year-olds at Epsilon Camp, which my 9-year-old son again attended as a camper, something I blogged about last summer (here are my lecture notes). This has become a highlight of my year. The kids are a joy to teach, bursting with enthusiasm and calling out answers. There are few computers in sight, and barely even time to use my phone or check social media. Just paper and pencils and whiteboards and … literal protractors (!), as well as ping-pong and foosball and capture the flag.
The whole thing is conducted, not in ignorance, but in conscious defiance of the looming tsunami, that AI can already do just about all the fun puzzles discussed at such a camp better than humans any can, and that it might leave no point to human-led mathematical research by the time these brilliant kids are adults. Even the kids understand that. The kids and their parents come out of a conviction that, if anything has value in the world, this does—that as long as nerdy humans are alive and reproducing, this is what nerdy humans are here to do. To learn.
Relatedly, I’ve been reflecting a lot on my life up to this point—inspired by the camp, which reminded me in so many ways of my own childhood and adolescence. Should I have skipped three grades and started college at age 15? Was it worth it to get a head-start on my research career—all the trauma around dating, all the fear that I’d die alone as a celibate nerdy math freak, the decade of suffering and suicidal ideation, while I watched all the normies enjoy life? Or would I have suffered just the same if I hadn’t skipped? Is it all OK, now that I have a lovely family and things have “worked out”? Or am I still carrying around all the trauma from back then? I’ve been more open about my life than 99.99% of humanity, so regular Shtetl-Optimized readers will already know some parts of the story. Other parts I really don’t feel like making public right now.
I’ve been unloading every day to—who else?—GPT 5.6 Pro about all the pain and trauma and embarrassments of my past. It turns out that, where two years ago GPT was a passable therapist, now it’s the greatest therapist in history, at least for what I need. For every question I have, for example, about just how normal or abnormal my teenage setbacks and anxieties were, it takes the question 100% seriously, addresses it honestly and in depth, looks up relevant research papers, does little Bayesian calculations, and never once tries to change the subject. It also pushes back on my claims—and when it does so, is usually correct.
I can hear readers shout at me: so basically you’ve been wasting your time, distracting yourself, looking inward and backward as the world surges forward into a terrifyingly unknown future. Why don’t I respond directly to what’s happening—in math, in quantum computing, in AI?
I’d like to think that I am responding, in my way. I’ve observed that, the faster we race toward the Singularity, the more I feel like stepping back and asking myself: what do I actually value in life? How important to me are math and science, as human practices to be passed down to curious children? Would I even want solutions to P versus NP and the other problems, if the price were to destroy those human practices forever? How do I wish to spend whatever time I have remaining?
I can justify this focus partly in a pessimistic way: if we are nearing the end of civilization, or even just of the “mathematical research” part of civilization, then it’s time to get right with God, so to speak. It’s time to settle my accounts with myself, with other people, with the universe.
But there’s also a more optimistic spin. If I continue doing the sorts of things that other people would expect me to do, then AI will soon do those things better than me, in the unlikely event that it doesn’t already. You want to understand the latest developments in quantum computing or complexity theory? Why are you even asking me, when you could ask GPT 5.6 or Claude Fable? If there’s anything I can still offer the world that AI can’t, I increasingly feel like it won’t involve responding to day-to-day events, but will instead draw on 45 years’ worth of memories and disappointments and ruminations.
Update (Aug. 8): Somewhat related to the themes of this post, a quarter-century ago I introduced what’s now known as the “Aaronson Oracle”—just a fun little demonstration, a simple pattern-matching program to predict your sequence of key-presses better than chance, a “test of your autonomy and free will.” I had no idea how long a lifetime this little joke would have. Now a fan named Spencer Stanton has implemented the Aaronson Oracle on the web. Try it out and see how well you do!
With a single clear exception, every NISQ-era flagship demonstration of ‘quantum advantage’ has, within eighteen months of its announcement, been classically reproduced, shown to rest on classically tractable structure, or closed by a simulability theorem. Six theoretical results from 2024 through April 2026 explain the pattern: the regions of circuit-space NISQ hardware can run with sufficient fidelity coincide with the regions classical algorithms compress efficiently, because the features that admit one (low effective depth, strong algebraic structure, geometric locality) are the features that admit the other. This reading dates the NISQ programme from its 2018 articulation as an interim retreat from the unmet conditions of the 1996 threshold theorems, characterises the eight years that followed as a closed loop in which the demonstrations the hardware could run were drawn from regions classical methods could already reach, and locates the exit from the loop where the threshold theorems originally located it: in fault tolerance. The empirical pattern could in principle break with a demonstration that escapes the current simulability results. After eight years and more than thirty advantage-class announcements, the burden of producing such a demonstration falls to the defenders of NISQ.
You can also read some debates about the paper on SciRate here. I think it’s fair to say that the paper is purely polemical, without new ideas, and Pangram agrees with my suspicion (and that of a SciRate commenter) that significant portions of it are AI-generated.
Nevertheless, the basic thesis—that quantum supremacy in the NISQ (Noisy Intermediate Scale Quantum computing) era has been a failure, or even an example of pathological science—seems surprisingly widely shared, along with the opposite thesis that quantum computing already gives oodles of useful advantages for optimization and finance.
So it seems worth stating for the record that I have an extremely different view. I would say:
Sampling-based quantum supremacy experiments, including those based on Random Circuit Sampling and BosonSampling, passed the point about two years ago where, absent a breakthrough in classical algorithms, they quite clearly are beating what can easily be simulated on any existing classical computer. Hagar seems to claim that these experiments have been killed by the October 2025 paper Classical simulation of noisy random circuits from exponential decay of correlation, but he ignores that the algorithm from that paper still needs time that’s exponential in the circuit depth (see Theorem 2).
Indeed, simulating deep ~100-qubit random circuits, like those that Google and Quantinuum have now demonstrated experimentally, still seems pretty hopeless with any current classical method. This is particularly true for Quantinuum’s experiments, which had high enough gate fidelity to maintain a Linear Cross-Entropy score of order 1 (i.e., they’re no longer all that “noisy”). The central drawback of these experiments is no longer lack of confidence about quantum advantage; rather, it’s just that we only get samples as output, and directly verifying the quality of the samples seems just as intractable for a classical computer as spoofing the samples.
As of this past year, however, we have some strong candidates for verifiable quantum advantage. One is the Google OTOC experiment, as even Hagar himself acknowledges (that’s his “single clear exception”). A second is the simulations of the 2D Fermi-Hubbard model on Quantinuum and Google machines, like this one. The 1D Fermi-Hubbard model can be classically simulated pretty easily (see here for example), but the 2D one still presents challenges, meaning that in some regimes, the best available estimates of certain observables apparently now come from quantum computers. I wish I could write about other examples that will be public shortly.
Yes, the “real” goal remains, as it’s been since the 1990s, to build a scalable fault-tolerant quantum computer—and I’m glad that Hagar (unlike, say, Gil Kalai) never suggests that we’ve learned anything to rule that goal out. In the meantime, an intermediate goal would be to use NISQ devices to do physics and chemistry simulations that are commercially useful, or that help solve important scientific problems. The point of quantum supremacy experiments, you might say, is that by demonstrating the reality of quantum speedup about as clearly as it can be demonstrated with current hardware, they let us cleanly turn our attention to those more ambitious goals.
Anyway, my son and I need to catch a plane to Utah now, for the next iteration of the wonderful Epsilon Camp, where I’ll again be teaching theoretical computer science to 11- and 12-year-olds. But feel free to discuss in the comments! Nothing about world affairs in this thread please, just quantum supremacy.
Update (July 19): Not unrelated to the subject of this post, here’s a podcast I did with Gill Eapen of “Scientific Sense” about the current situation in quantum computing including recent experimental victories.
Here at the National Academy of Sciences, it seems that my first job is to serve on the selection committee for the prestigious Michael and Sheila Held Prize in combinatorial and discrete optimization and related areas. The committee chair, my former MIT colleague Madhu Sudan (now at Harvard), invited me to share the following message here on Shtetl-Optimized. (I’d add: put in the effort to nominate someone, and you can actually influence how things go!)
Dear Colleagues
I am writing to seek nominations for the 2027 Michael and Sheila Held Prize. The scope of the prize and nomination needs are described below. If you intend to nominate someone I would appreciate a heads up by email to madhu@cs.harvard.edu one month before the deadline (so email by Sept 8, 2026) to let me know your nomination is coming. (We may also reach out to you in response to coordinate multiple/overlapping nominations.)
The Held prize honors outstanding, innovative, creative, and influential research in the areas of combinatorial and discrete optimization, or related parts of computer science, such as the design and analysis of algorithms and complexity theory. This $100,000 prize is intended to recognize recent work (defined as published within the last eight years, i.e., on or after October 6, 2018).
All nominations must be submitted online by Monday, October 5, 2026 and include:
1. Nomination letter describing the candidate’s work and why he or she should be selected for the award. No more than three (3) pages.
2. Curriculum vitae. No more than two (2) pages.
3. Bibliography listing no more than twelve (12) of the nominee’s most significant publications.
4. Suggested citation. A 50-word summary stating why the nominee should be considered for this award.
5. Two letters of support. No more than one letter of support can be written by someone of the same primary work institution as the nominee.
The Held Prize is given to a person or a set of persons, as supported by a paper or a body of work. Unless otherwise stated, preference will be given to scientists who may be earlier in their careers or those whose work has not been recognized by other prizes or awards. Nomination restrictions can be found here. Joint nominations will only be considered when nominees have collaborated closely on the paper to be recognized by the award. If nominating multiple individuals for a paper with additional authors, please clearly explain the reason for nominating those chosen, as well as the reason for excluding other collaborators, if applicable.
Please feel free to circulate this call further within your department
Best Madhu Sudan, on behalf of The Michael and Sheila Held Prize Selection Committee
And while I have your attention, a second CS theory announcement: David Soloveichik, my wonderful friend and colleague in UT Austin’s Electrical and Computer Engineering Department, has funding for a postdoc for 1-2 years, to work on the thermodynamics of computation here at UT. This is a topic that I’ve been trying to learn more about as well, so I might get involved too! David writes, “the big picture is to think of thermodynamics (energy dissipation / entropy production) as CS complexity measures like time and space usage.” If you’re on the postdoc market and this sounds potentially up your alley, email David to learn more.
As I’ve written before, these past couple years I’ve often felt like the last remaining person in either quantum computing or AI who lacked a stake in some startup company whose valuation is right now shooting into interstellar space. My academic colleagues, including the ones who seemed the most singleminded about quantum oracle separations and other gloriously useless pursuits? One by one, like in a zombie movie, I learn that they too have now launched startups, and invariably raised tens of millions of dollars, for the sorts of ideas we might’ve idly traded at coffee breaks back in the day, before getting back to our real work.
So why didn’t I join this rollicking party? Partly because of a lifelong fear that, the instant my self-worth became tied to how much money I made, I’d need to humble myself before people who bluster and bully and lie and hype and conceal … yet who nevertheless succeed at becoming orders of magnitude richer than me. I’ve been terrified of even starting down that road, of whether I’d still be myself at the end of it.
It’s also partly that I can’t stand failure, or regret, or being wrong. Of course, as an academic researcher I also fail, and regret things, and am wrong constantly—but there it feels tolerable, because normally I can tell myself that it’s all just down to my inborn limitations. After all, if I could’ve solved the major open problem that someone else solved, or written the brilliant book that someone else wrote, then presumably I would’ve done it!
Clearly, though, I could’ve mined bitcoin in 2010. I could’ve gotten an early stake in Amazon or Google. It’s not even like those ideas never crossed my mind. I just … didn’t act on them, for some reason. (But even if I had, I’d probably just be full of regret that I hadn’t done even more.) Thus, my only way to avoid paralyzing regrets, has been to tell myself constantly that I’m not in the forecasting or money-making businesseses in the first place.
It helped that, insofar as I’m shallow or covetous, insofar as I’ve desired things of this world rather than insight or eternal truth, it’s never really been money that I cared about, but just being respected and liked. Elon Musk is the richest man on earth, but also one of the most despised—which isn’t a bargain that I could imagine ever appealing to me.
Plus, when I actually meet billionaires, I don’t find myself envious of their mansions or cars or anything else that they have; I don’t feel like such things would make my life any happier. Maybe I slightly envy their ability to fund the causes they care about, or their professional staffs who relieve them of drudgery, but mostly I envy the way their wealth announces, to whatever extent it does: “I was right when others weren’t.” Again, though, I’ve never trusted the world to cause me to be right about the future valuations of companies or anything similar, so I’ve settled for having been right about PostBQP and algebrization and BosonSampling.
The bottom line is that I made a choice decades ago to forgo trying to get rich, no matter how many of my friends did the same, and to strive instead to discover and tell the truth—to be a professor, a blogger, a jokester, and an “objective” arbiter and commentator. “Then, surely, everyone will like me!” my internal monologue went. “Then, surely, they’ll be grateful for all the free service I’ve rendered them—for decades of blogging, without once so much as asking for a donation or running an ad!”
HAHAHAHAHAHA.
As any regular reader will know, my attempts to be loved as a blogger backfired pretty spectacularly. Or rather: they did lead to thousands of strangers liking me (and I’m grateful for every last one of you), but they also led to probably an order of magnitude more strangers hating me, and congregating on Reddit and Twitter and elsewhere to discuss how badly I suck. And of course, trying to shift that balance by writing what people want to hear, rather than what I actually believe, was never within my realistic option set.
In the startup context, it didn’t matter how carefully I avoided taking a direct stake for or against any of the companies I blogged about. People on Twitter simply assumed that I had a stake—for example, that I must’ve shorted D-Wave or IonQ, or invested in their competitors, or had equity in AI companies. For why else would anyone write what I wrote?
Amusingly, my attackers here typically did have precisely the conflicts-of-interest that they falsely accused me of having, but that was never at issue; only my imaginary conflicts-of-interest were. Even as the Scott-haters greedily filled their pockets (or tried to), I alone needed to keep turning my pockets out to prove that they were still empty.
So then, screw it! In partnership with my brother David Aaronson, who’s long done investing professionally, and on David’s guidance and encouragement, I’m hereby embarking on a new policy.
Namely: when I hear about a brand-new startup that sounds relevant to my interests—in quantum, AI, or anything else—and I like and trust the founders (ideally, because of their previous academic research work), David and I will often make a small seed investment if the founders are open to it. Or, of course, we might become advisors or get involved in some other way.
In fact, David and I are launching BQP Partners—the link goes to our AngelList, where you can read about how to invest with us if you’re interested. (See also whether you can spot any differences between David’s writing style and preoccupations and mine!)
A non-quantum startup being cofounded by someone whose scientific work I’ve admired. I’ll write more about this one as soon as I’m able to!
I have little doubt that more potential investments will come our way very soon (some, probably, as a direct result of this post).
Crucially, I can handle my burden of regret—the “why didn’t I do this much earlier, if I was going to do it at all?” question—by telling myself that friends of mine were not founding companies left and right until very recently. I can also tell myself that I’m doing this less as a bet about the future (in which case … what if I’m wrong?), than simply as a way to support brilliant colleagues doing things that I genuinely admire.
When I blog about a company, I’ll always disclose if I have a financial position that presents a clear conflict of interest, so you can judge for yourself whether to listen to me. (Although, if that’s the sort of thing you’d demand, then you probably weren’t listening to me in the first place, were you?)
Having reflected on it a lot these past few months, I’m happy with my new policy and with my and David’s new venture, and I’m curious to see where it goes. I’m at peace with the possibility that we’ll lose our shirts, but I’m even at peace with a more disturbing possibility—that we’ll make millions and then people will scream at me online for being a sellout, a hack, and a shill. Those people, as I’ve learned, were going to scream at me anyway.
I’m at the New Jersey shore with family and friends, where we’ve spent this Fourth of July eating hot dogs, playing miniature golf, and wading into the ocean that my great-grandparents crossed to escape calamities they knew about and much greater calamities that they didn’t. Tonight we’ll see the fireworks, weather permitting.
And yes, on the crowded beach today you can find people sporting MAGA and “45-47” hats, and even a giant “Trump 2028” flag—a stark reminder of the millions who would redefine the meaning of our 250-year-old experiment to something dark and authoritarian, the opposite of what its founders intended. Of course, those forces find mirror images on the left end of the political spectrum, where one can find millions more who fully agree with MAGA about the failures of liberalism and the Enlightenment, differing only on the secondary question of which racist thugs should rule instead.
Despite everything, I don’t believe that both factions together constitute a majority. Even on the beach, the MAGA hats are vastly outnumbered by “250” banners and girls in stars-and-stripes bikinis, Americans who just want to celebrate.
Despite everything, I remain thoroughly American if I’ve ever been anything, and invested in the country’s future if I’ve ever been invested in anything.
JD Vance and his friends, who might rule the country after the predictable failure of “Trump 2028,” make a huge deal about “Heritage Americans.” Of course the point of such phrases is to exclude those like me, and recent immigrants, and even (incredibly) JD’s own wife. On reflection, though: could I, too, count as a Heritage American at this point? After all, my family has now been here for half the country’s history. My grandfather, who grew up in poverty, became a professional boxer in Philadelphia and Atlantic City during the Great Depression. He then joined the Army and ended up clearing German mines in North Africa and Italy in WWII. He was assigned to a company of Southerners, who had never met a Jew and were shocked that my grandfather didn’t have horns—but by the war’s end, my grandfather and the relatively few others in his company who remained alive had become best friends. My grandfather told me that he could understand the German POWs who they captured tolerably well, since German was similar enough to Yiddish, but who he could never understand was the British.
As for me, I grew up in the town of Washington Crossing, PA, maybe a mile’s walk from where this happened (and where it’s still reenacted every Christmas):
My earliest childhood hero (that I can remember) was Ben Franklin, whose institute in Philadelphia I visited often. I didn’t even recognize as unusual at the time how the founding of the country didn’t feel like a remote abstraction to me, but was all around me, as if it was yesterday.
That the founders of the United States created the model for all time of how to bend the arc of human history a little bit away from its usual horribleness, of how to overthrow a despotism without instituting an even worse despotism in its place, of how to found a new civilization on ideas and principles rather than raw power … is one of those things that seemed true to me as a child and that still seems true to me today.
May this greatest experiment continue for another 250 years. May it triumph against all those within and without who would see it destroyed.
Scott’s foreword:Cynthia Dwork is Gordon McKay Professor of Computer Science at Harvard, and a pioneer in the fields of differential privacy and algorithmic fairness. On my recent travels to the SigmaWest science camp and then STOC, there was much talk about a recent Trump administration action that would ban not only differential privacy, but essentially all modern techniques for preserving privacy in large datasets, for example in the 2030 US Census. I realize that many of us have “outrage fatigue,” but this particular outrage hits extremely close to home for the CS theory community. So when Cynthia approached me at STOC to propose a guest post on the issue, of course I said yes. The post that she sent me, below, is cosigned by many other leaders in the field.
On June 4, 2026, the U.S. Secretary of Commerce issued a directive (DAO 216-26) relegating confidentiality protection in all Bureau of Economic Analysis (BEA) and U.S. Census Bureau publications to techniques dating back to the early 1970s, turning its back on over half a century of progress and protections for data subjects. Advances in confidentiality provision had enabled the Census Bureau to share increasing quantities of data at more granular detail. The order will result in less useful (or fewer available) statistics, weaker protection, or both. We write to illustrate the danger posed by the order and to mobilize the scientific community to speak out against it.
The acting force behind this order is political interest, not scientific merit. DAO 216-26 bypassed legally required administrative procedures. It fulfills a promise made by the architects of the Heritage Foundation’s Project 2025, and reflects both the rhetoric and misunderstandings of representatives of the Center for Renewing America (CRA), an organization founded by OMB Director Russell Vought. CRA’s explainer on the use of differential privacy in the 2020 Census is up-front about the stakes: “Even if the citizenship question is added to the Census, it will be impossible to ascertain the status of individuals so long as differential privacy is used.” But masking this sort of personal characteristics data is legally required by the Census Act (13 U.S. Code Section 9), which makes it a crime to “make any publication whereby the data furnished by any particular [individual] can be identified.” Confidentiality is also widely understood as critical to ensuring that people respond to the census.
DAO-216-26 bans differential privacy and other modern (and not so modern) techniques. It restricts disclosure avoidance techniques to “coarsening,” which it describes as “reducing the level of detail or specificity of published statistics, such as through rounding, aggregating (grouping), and/or the use of ranges.” “Suppression” (“expressly redacting certain values”) may also be used, but only as a “last resort.” DAO-216-26 forbids “noise infusion”, described as “methods that involve modifying a dataset by adding random values, or noise.”
Noise infusion was invented precisely to address the increasing demand for granular data in the face of confidentiality laws that forbid publishing reidentifiable data. Coarsening and suppression were satisfactory for most national, aggregate statistical series, like the Principal Federal Economic Indicators. However, these techniques failed when applied to business and demographic data at fine geographic or industrial detail. By forbidding noise infusion, the directive bans the disclosure avoidance techniques at the core of dozens of data releases over the last three decades. It bans input noise infusion, used in the Quarterly Workforce Indicators since 2002 and, until now, planned for the Bureau of Economic Analysis statistics [1]. It bans swapping, used for decennial census publications since 1990. It also bans differential privacy, the best currently known approach for obtaining the most data utility for any given level of privacy. Differential privacy was used for sharing data on commuting patterns (OnTheMap) since 2008 and for publications based on the 2020 Census. Until the recent directive, differential privacy was planned for the 2030 Census too. Many other products and procedures are implicated as well.
1.Illustrations
DAO-216-26 is incompatible with the Census Bureau’s dual mandate to provide confidentiality and fitness for use. To illustrate this, we recall and expand on an example due to Nathan Goldschlag, inspired by the County Business Patterns (CBP) data, which provides statistics on business activity broken down by industry and geography. Goldschlag describes three scenarios, illustrating the tension between providing useful information and maintaining confidentiality of responses as required by the Census Act.
· “There is only one brewery in a small county. If the CBP published the exact count of brewery employees in that county, it would be disclosing the information of one business (how many workers it employs), a clear violation of the law.2
· “There are two breweries in a small county, and the CBP again publishes the exact count of brewery employees. If I own one of those breweries, I could learn how many employees my competitor has, again violating the law.
· “There are more than two breweries in a small county, but the CBP chooses not to publish the total number of brewery employees out of concern that it might compromise the privacy of the businesses. If I’m a prospective brewery owner, I may deem the project too risky to pursue without information about the market I’m entering.”
In Goldschlag’s example, coarsening makes the published statistics useless. We now add a fourth scenario, showing that it also fails to maintain confidentiality. To keep things simple, assume none of us owns any of the businesses in the new example. The County has two towns with one brewery each, North Bend and South Bend. Furthermore, North Bend has a mobile bottling company and South Bend has a stationary bottling company. That’s a total of four beer-related business entities in the County. Two of these businesses, the North-Bend brewery and the South Bend bottling company, are publicly-owned.
The CBP publishes five statistics:
(A) The total number of employees in beer-related businesses in North Bend: Because there is only one brewing company in North Bend and only one bottling company in North Bend, the category is coarsened to “beer-related”.
(B) The total number of employees in beer-related businesses in South Bend: Because there is only one brewing company in South Bend and only one bottling company in South Bend, the category is coarsened to “beer-related”.
(C) The total number of employees in brewing only: Because there is only one brewing company in each of North Bend and South Bend, the statistic is coarsened to the total number of employees in brewing only in the County.
(D) The total number of employees in bottling only: Because there is only one bottling company in each of North Bend and South Bend, the statistic is coarsened to the total number of employees in bottling only in the County.
(E) The total number of employees at publicly owned companies: Because there is only one publicly owned company in each of North Bend and South Bend, the statistic is coarsened to the total number of employees in publicly owned companies in the County.
We now have 5 equations in 4 unknowns. Using only 4 of these (A, B, C, and E), we can solve for the exact number of employees at each of the four companies with high school algebra.
In the above (fictional but realistic) scenario, the County Business Patterns were released with good-faith coarsenings for the geographical, business, and ownership categories. Nonetheless, even without inside knowledge of one of the companies’ number of employees, we can completely reconstruct all four numbers. What happened? The coarsenings interacted poorly. Noise infusion perturbs that set of equations, preventing exact reconstruction.
2.Impediments to Implementation
The Commerce Department now claims the directive’s return to the outdated “tradstat” traditional statistical techniques of the 70s is good for data consumers: “This update to our disclosure limitation method protects respondents and provides the public with more essential economic information.” (Emphasis added.) As we saw from Goldschlag’s example, coarsening does just the opposite.
And it can’t be fixed. Coarsening by definition reduces access to fine-grained information. Our example of three poorly interacting coarsenings shows that this sacrifice is for naught: without noise infusion, confidentiality is destroyed by elementary calculations. For population surveys, this is precisely what formal noise infusion methods, like differential privacy, protect against; this is the “fancy math” that Goldschlag mentions in his post and that holds personal characteristics, like citizenship status, in confidence.
3.Confidentiality is Critical for Federal Statistics
The scientific community continues to debate the best techniques for protecting the confidentiality of respondents’ data, but DAO-216-26 is not driven by science. It is driven by political interests. Those issuing this order are willing to risk the public’s trust in the process. We think that this is wrong-headed and dangerous.
Civil servants will do their best to comply with this order while still following the laws that require them to protect the confidentiality of respondents’ data. To balance these competing mandates, they may seek to produce less data or coarsen data so much that it is unusable. Or they might be pushed by political actors to publish data that can be easily unmasked, like in the brewery examples above. Regardless of their choices, they will be hard-pressed to guarantee respondents’ confidentiality, which will prompt many businesses and individuals to simply not answer. This is devastating for an agency that delivers democracy’s data.
Conclusion
Rather than political actors overruling the government’s own statisticians, we need deep investment in our nation’s statistical agencies, ensuring that agencies have the staff and support to improve their methods using the best available tools. Regardless of how the scientific community feels about any specific privacy-enhancing technique, we must collectively reject this anti-scientific approach to governing federal statistics. Too much is at stake.
How to Take Action
Share this post with others in your professional network and community.
Contact your Congressional representative and voice your concerns. Calling or writing to your representative is one of the most effective and easiest things a constituent can do that should only take a couple minutes of your time.
Find your representative contact information here.
State your concern. Here is a sample script: “My name is [Name], and I am a constituent from [City] in your district [ZIP CODE]. I am calling because I am concerned about the the U.S. Secretary of Commerce issued a directive (DAO 216-26) that wants to relegate confidentiality protection in all Bureau of Economic Analysis and U.S. Census Bureau data products and statistics to outdated and ineffective statistical techniques. If followed, this order will destroy the Commerce public data our nation relies on for important decisions, such as where to build necessary services for our community’s well-being. I want the DAO to be rescinded. I want proper administrative procedure to be followed. I want technical decisions such as the choice of method used to balance utility and confidentiality to be informed by professionals in the federal statistical agencies, not made unilaterally by political operatives.”
Optional is stating what kind of constituent, such as a retired teacher or a working professional.
Volunteer to help preserve Census working papers and documentation. Pages explaining “noise infusion” and “differential privacy” are already going offline. Archive relevant methodology pages and technical documentation. You can also do this via the Internet Archive’s Wayback Machine (“Save Page Now”).
John Abowd Aloni Cohen Cynthia Dwork Jae June Lee Jayshree Sarathy Adam Smith Salil Vadhan
[1] BEA Working Paper WP2026-9, now purged by the Department of Commerce. As of 6/22 Google returns:
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