Archive for the ‘Announcements’ Category

An alarming trend in K-12 math education: a guest post and an open letter

Friday, December 3rd, 2021

Update (Dec. 5): Our open letter just made the WSJ, and has been tweeted by Matt Yglesias and others; hopefully more coverage will follow soon! See also Boaz Barak’s thread, and a supportive tweet from Rep. Ro Khanna (D-Silicon Valley). If you’re just arriving here, try TodayMag for an overview of some of the issues at stake.


Today, I’m turning over Shtetl-Optimized to an extremely important guest post by theoretical computer scientists Boaz Barak of Harvard and Edith Cohen of Google (cross-posted on the windows on theory blog). In addition to the post below, please read—and if relevant, consider signing—our open letter about math education in the US, which now has over 150 now 535 746 signatories, including Fields Medalists, Turing Award winners, and Nobel laureates. Finally, check out our fuller analysis of what the California Mathematics Framework is poised to do and why it’s such an urgent crisis for math education. I’m particularly grateful to my colleagues for their writing efforts, since I would never have been able to discuss what’s happening in such relatively measured words. –Scott Aaronson


Mathematical education at the K-12 level is critical for preparation for STEM careers. An ongoing challenge to the US K-12 system is to improve the preparation of students for advanced mathematics courses and expand access and enrollment in these courses. As stated by a Department of Education report “taking Algebra I before high school … can set students up for a strong foundation of STEM education and open the door for various college and career options.” The report states that while 80% of all students have access to Algebra I in middle school, only 24% enroll. This is also why the goal of Bob Moses’ Algebra Project is to ensure that “every child must master algebra, preferably by eighth grade, for algebra is the gateway to the college-prep curriculum, which in turn is the path to higher education.”

The most significant potential for growth is among African American or Latino students, among whom only 12% enroll in Algebra before high school. This untapped potential has longer-term implications for both society and individuals. For example, although African Americans and Latinos comprise 13% and 18% (respectively) of the overall US population, they only account for 4% and 11% of engineering degrees. There is also a gap in access by income: Calculus is offered in 92% of schools serving the top income quartile but only in 77% of schools serving the bottom quartile (as measured by the share of students eligible for free or reduced-price lunch). Thus minority and low income students have less access to STEM jobs, which yield more than double the median salary of non-STEM jobs, and are projected to grow at a 50% higher rate over the next decade.

Given these disparities, we applaud efforts such as the Algebra Project, the Calculus Project, and Bridge to Enter Advanced Mathematics that increase access to advanced mathematical education to underserved students. However, we are concerned by recent approaches, such as the proposed California Math Framework (CMF) revisions,  that take the opposite direction.

See this document for a detailed analysis and critique of the CMF, but the bottom line is that rather than trying to elevate under-served students, such “reforms” reduce access and options for all students. In particular, the CMF encourages schools to stop offering Algebra I in middle school, while placing obstacles (such as doubling-up, compressed courses, or outside-of-school private courses) in the way of those who want to take advanced math in higher grades. When similar reforms were implemented in San Francisco, they resulted in an “inequitable patchwork scheme” of workarounds that affluent students could access but that their less privileged counterparts could not. The CMF also promotes trendy and shallow courses (such as a nearly math-free version of  “data science”) as recommended alternatives  to foundational mathematical courses such as Algebra and Calculus. These courses do not prepare students even for careers in data science itself!

As educators and practitioners, we have seen first-hand the value of solid foundations in mathematics for pursuing college-level STEM education and a productive STEM career. 

While well-intentioned, we believe that many of the changes proposed by the CMF are deeply misguided and will disproportionately harm under-resourced students. Adopting them would result in a student population that is less prepared to succeed in STEM and other 4-year quantitative degrees in college.  The CMF states that “many students, parents, and teachers encourage acceleration beginning in grade eight (or sooner) because of mistaken beliefs that Calculus is an important high school goal.” Students, parents, and teachers are not mistaken. Neither is the National Society of Black Engineers (NSBE), which set in 2015 a goal to double the number of African American students taking calculus by 2025. Calculus is not the only goal of K-12 math education, but it is important for students who wish to prepare for STEM in college and beyond. 

We agree that calculus is not the “be-all and end-all” of high-school mathematics education. In particular, we encourage introducing options such as logic, probability, discrete mathematics, and algorithms design in the K-12 curriculum, as they can be valuable foundations for STEM education in college. However, when taught beyond a superficial level (which unfortunately is not the case in the CMF “data science” proposals), these topics are not any easier  than calculus. They require the same foundations of logic, algebra, and functions, and fluency with numbers and calculations. Indeed, the career paths with the highest potential for growth require more and deeper mathematical preparation than ever before. Calculus and other mathematical foundations are not important because they are admission requirements for colleges, or because they are relics of the “Sputnik era”. They are important because they provide fundamental knowledge and ways of thinking that are necessary for success in these fast growing and in-demand fields.

We also fully support incorporating introductory data analysis and coding skills in the K-12 curriculum (and there are some good approaches for doing so).  But we strongly disagree with marketing such skills as replacing foundational skills in algebra and calculus when preparing for 4-year college degrees in STEM and other quantitative fields. These topics are important and build on basic math foundations but are not a replacement for such foundations any more than social media skills can replace reading and writing foundations. 

Given the above, we, together with more than 150 scientists, educators, and practitioners in STEM, have signed an open letter expressing our concerns with such trends. The signatories include STEM faculty in public and private universities and practitioners from industry. They include educators with decades of experience teaching students at all levels, as well as researchers that won the highest awards in their fields, including the Fields Medal and the Turing Award. Signers also include people vested in mathematical high-school education, such as Adrian Mims (founder of The Calculus Project) and Jelani Nelson (UC Berkeley EECS professor and founder of AddisCoder) who have spearheaded projects to increase access to underserved populations.

We encourage you to read the letter, and if you are a US-based STEM professional or educator, consider signing it as well: https://bit.ly/mathedletter

Unfortunately, in recent years, debates on US education have become politicized. The letter is not affiliated with any political organization, and we believe that the issues we highlight transcend current political debates. After all, expanding access to mathematical education is both socially just and economically wise.


Note: The above guest post reflects the views of its authors, Boaz Barak and Edith Cohen. Any comments below by them, me, or other signatories reflect their own views, not necessarily those of the entire group. –SA

Two new talks and an interview

Thursday, December 2nd, 2021
  1. A talk to UT Austin’s undergraduate math club (handwritten PDF notes) about Hao Huang’s proof of the Sensitivity Conjecture, and its implications for quantum query complexity and more. I’m still not satisfied that I’ve presented Huang’s beautiful proof as clearly and self-containedly as I possibly can, which probably just means I need to lecture on it a few more times.
  2. A Zoom talk at the QPQIS conference in Beijing (PowerPoint slides), setting out my most recent thoughts about Google’s and USTC’s quantum supremacy experiments and the continuing efforts to spoof them classically.
  3. An interview with me in Communications of the ACM, mostly about BosonSampling and the quantum lower bound for the collision problem.

Enjoy y’all!

Scott Aaronson, when reached for comment, said…

Tuesday, November 16th, 2021

About IBM’s new 127-qubit superconducting chip: As I told New Scientist, I look forward to seeing the actual details! As far as I could see, the marketing materials that IBM released yesterday take a lot of words to say absolutely nothing about what, to experts, is the single most important piece of information: namely, what are the gate fidelities? How deep of a quantum circuit can they apply? How have they benchmarked the chip? Right now, all I have to go on is a stats page for the new chip, which reports its average CNOT error as 0.9388—in other words, close to 1, or terrible! (But see also a tweet by James Wootton, which explains that such numbers are often highly misleading when a new chip is first rolled out.) Does anyone here have more information? Update (11/17): As of this morning, the average CNOT error has been updated to 2%. Thanks to multiple commenters for letting me know!

About the new simulation of Google’s 53-qubit Sycamore chip in 5 minutes on a Sunway supercomputer (see also here): This is an exciting step forward on the classical validation of quantum supremacy experiments, and—ironically, what currently amounts to almost the same thing—on the classical spoofing of those experiments. Congratulations to the team in China that achieved this! But there are two crucial things to understand. First, “5 minutes” refers to the time needed to calculate a single amplitude (or perhaps, several correlated amplitudes) using tensor network contraction. It doesn’t refer to the time needed to generate millions of independent noisy samples, which is what Google’s Sycamore chip does in 3 minutes. For the latter task, more like a week still seems to be needed on the supercomputer. (I’m grateful to Chu Guo, a coauthor of the new work who spoke in UT Austin’s weekly quantum Zoom meeting, for clarifying this point.) Second, the Sunway supercomputer has parallel processing power equivalent to approximately ten million of your laptop. Thus, even if we agreed that Google no longer had quantum supremacy as measured by time, it would still have quantum supremacy as measured by carbon footprint! (And this despite the fact that the quantum computer itself requires a noisy, closet-sized dilution fridge.) Even so, for me the new work underscores the point that quantum supremacy is not yet a done deal. Over the next few years, I hope that Google and USTC, as well as any new entrants to this race (IBM? IonQ? Harvard? Rigetti?), will push forward with more qubits and, even more importantly, better gate fidelities leading to higher Linear Cross-Entropy scores. Meanwhile, we theorists should try to do our part by inventing new and better protocols with which to demonstrate near-term quantum supremacy—especially protocols for which the classical verification is easier.

About the new anti-woke University of Austin (UATX): In general, I’m extremely happy for people to experiment with new and different institutions, and of course I’m happy for more intellectual activity in my adopted city of Austin. And, as Shtetl-Optimized readers will know, I’m probably more sympathetic than most to the reality of the problem that UATX is trying to solve—living, as we do, in an era when one academic after another has been cancelled for ideas that a mere decade ago would’ve been considered unexceptional, moderate, center-left. Having said all that, I wish I could feel more optimistic about UATX’s prospects. I found its website heavy on free-speech rhetoric but frustratingly light on what the new university is actually going to do: what courses it will offer, who will teach them, where the campus will be, etc. etc. Arguably this is all excusable for a university still in ramp-up mode, but had I been in their shoes, I might have held off on the public launch until I had at least some sample content to offer. Certainly, the fact that Steven Pinker has quit UATX’s advisory board is a discouraging sign. If UATX asks me to get involved—to lecture there, to give them advice about their CS program, etc.—I’ll consider it as I would any other request. So far, though, they haven’t.

About the Association for Mathematical Research: Last month, some colleagues invited me to join a brand-new society called the Association for Mathematical Research. Many of the other founders (Joel Hass, Abigail Thompson, Colin Adams, Richard Borcherds, Jeff Cheeger, Pavel Etingof, Tom Hales, Jeff Lagarias, Mark Lackenby, Cliff Taubes, …) were brilliant mathematicians who I admired, they seemed like they could use a bit of theoretical computer science representation, there was no time commitment, maybe they’d eventually do something good, so I figured why not? Alas, to say that AMR has proved unpopular on Twitter would be an understatement: it’s received the same contemptuous reception that UATX has. The argument seems to be: starting a new mathematical society, even an avowedly diverse and apolitical one, is really just an implicit claim that the existing societies, like the Mathematical Association of America (MAA) and the American Mathematical Society (AMS), have been co-opted by woke true-believers. But that’s paranoid and insane! I mean, it’s not as if an AMS blog has called for the mass resignation of white male mathematicians to make room for the marginalized, or the boycott of Israeli universities, or the abolition of the criminal justice system (what to do about Kyle Rittenhouse though?). Still, even though claims of that sort of co-option are obviously far-out, rabid fantasies, yeah, I did decide to give a new organization the benefit of the doubt. AMR might well fail or languish in obscurity, just like UATX might. On the other hand, the barriers to making a positive difference for the intellectual world, the world I love, the world under constant threat from the self-certain ideologues of every side, do strike me as orders of magnitude smaller for a new professional society than they do for a new university.

Q2B 2021

Monday, November 1st, 2021

This is a quick post to let people know that the 2021 Q2B (Quantum 2 Business) conference will be this December 7-9 at the Santa Clara Convention Center. (Full disclosure: Q2B is hosted by QC Ware, Inc., to which I’m the scientific adviser.) Barring a dramatic rise in cases or the like, I’m planning to attend to do my Ask-Me-Anything session, in what’s become an annual tradition. Notably, this will be my first in-person conference, and in fact my first professional travel of any kind, since before covid shut down the US in late March 2020. I hope to see many of you there! And if you won’t be at Q2B, but you’ll be in the Bay Area and would like to meet otherwise, let me know and we’ll try to work something out.

Welcome to scottaaronson.blog !

Thursday, October 21st, 2021

If you’ve visited Shtetl-Optimized lately — which, uh, I suppose you have — you may have noticed that your URL was redirected from www.scottaaronson.com/blog to scottaaronson.blog. That’s because Automattic, makers of WordPress.com, volunteered to move my blog there from Bluehost, free of charge. If all goes according to plan, you should notice faster loading times, less downtime, and hopefully nothing else different. Please let me know if you encounter any problems. And huge thanks to the WordPress.com Special Projects Team, especially Christopher Jones and Mark Drovdahl, for helping me out with this.

The Physics Nobel, Gaussian BosonSampling, and Dorian Abbot

Tuesday, October 5th, 2021

1. Huge congratulations to the winners of this year’s Nobel Prize in Physics: Syukuro Manabe and Klaus Hasselmann for climate modelling, and separately, Giorgio Parisi for statistical physics. While I don’t know the others, I had the great honor to get to know Parisi three years ago, when he was chair of the committee that awarded me the Tomassoni-Chisesi Prize in Physics, and when I visited Parisi’s department at Sapienza University of Rome to give the prize lecture and collect the award. I remember Parisi’s kindness, a lot of good food, and a lot of discussion of the interplay between theoretical computer science and physics. Note that, while much of Parisi’s work is beyond my competence to comment on, in computer science he’s very well-known for applying statistical physics methods to the analysis of survey propagation—an algorithm that revolutionized the study of random 3SAT when it was introduced two decades ago.


2. Two weeks ago, a group at Google put out a paper with a new efficient classical algorithm to simulate the recent Gaussian BosonSampling experiments from USTC in China. They argued that this algorithm called into question USTC’s claim of BosonSampling-based quantum supremacy. Since then, I’ve been in contact with Sergio Boixo from Google, Chaoyang Lu from USTC, and Jelmer Renema, a Dutch BosonSampling expert and friend of the blog, to try to get to the bottom of this. Very briefly, the situation seems to be that Google’s new algorithm outperforms the USTC experiment on one particular metric: namely, total variation distance from the ideal marginal distribution, if (crucially) you look at only a subset of the optical modes, say 14 modes out of 144 total. Meanwhile, though, if you look at the kth-order correlations for large values of k, then the USTC experiment continues to win. With the experiment, the correlations fall off exponentially with k but still have a meaningful, detectable signal even for (say) k=19, whereas with Google’s spoofing algorithm, you choose the k that you want to spoof (say, 2 or 3), and then the correlations become nonsense for larger k.

Now, given that you were only ever supposed to see a quantum advantage from BosonSampling if you looked at the kth-order correlations for large values of k, and given that we already knew, from the work of Leonid Gurvits, that very small marginals in BosonSampling experiments would be easy to reproduce on a classical computer, my inclination is to say that USTC’s claim of BosonSampling-based quantum supremacy still stands. On the other hand, it’s true that, with BosonSampling especially, more so than with qubit-based random circuit sampling, we currently lack an adequate theoretical understanding of what the target should be. That is, which numerical metric should an experiment aim to maximize, and how well does it have to score on that metric before it’s plausibly outperforming any fast classical algorithm? One thing I feel confident about is that, whichever metric is chosen—Linear Cross-Entropy or whatever else—it needs to capture the kth-order correlations for large values of k. No metric that’s insensitive to those correlations is good enough.


3. Like many others, I was outraged and depressed that MIT uninvited Dorian Abbot (see also here), a geophysicist at the University of Chicago, who was slated to give the Carlson Lecture in the Department of Earth, Atmospheric, and Planetary Sciences about the atmospheres of extrasolar planets. The reason for the cancellation was that, totally unrelatedly to his scheduled lecture, Abbot had argued in Newsweek and elsewhere that Diversity, Equity, and Inclusion initiatives should aim for equality for opportunity rather than equality of outcomes, a Twitter-mob decided to go after him in retaliation, and they succeeded. It should go without saying that it’s perfectly reasonable to disagree with Abbot’s stance, to counterargue—if those very concepts haven’t gone the way of floppy disks. It should also go without saying that the MIT EAPS department chair is free to bow to social-media pressure, as he did, rather than standing on principle … just like I’m free to criticize him for it. To my mind, though, cancelling a scientific talk because of the speaker’s centrist (!) political views completely, 100% validates the right’s narrative about academia, that it’s become a fanatically intolerant echo chamber. To my fellow progressive academics, I beseech thee in the bowels of Bertrand Russell: why would you commit such an unforced error?

Yes, one can imagine views (e.g., open Nazism) so hateful that they might justify the cancellation of unrelated scientific lectures by people who hold those views, as many physicists after WWII refused to speak to Werner Heisenberg. But it seems obvious to me—as it would’ve been obvious to everyone else not long ago—that no matter where a reasonable person draws the line, Abbot’s views as he expressed them in Newsweek don’t come within a hundred miles of it. To be more explicit still: if Abbot’s views justify deplatforming him as a planetary scientist, then all my quantum computing and theoretical computer science lectures deserve to be cancelled too, for the many attempts I’ve made on this blog over the past 16 years to share my honest thoughts and life experiences, to write like a vulnerable human being rather than like a university press office. While I’m sure some sneerers gleefully embrace that implication, I ask everyone else to consider how deeply they believe in the idea of academic freedom at all—keeping in mind that such a commitment only ever gets tested when there’s a chance someone might denounce you for it.

Update: Princeton’s James Madison Program has volunteered to host Abbot’s Zoom talk in place of MIT. The talk is entitled “Climate and the Potential for Life on Other Planets.” Like probably hundreds of others who heard about this only because of the attempted cancellation, I plan to attend!

Unrelated Bonus Update: Here’s a neat YouTube video put together by the ACM about me as well as David Silver of AlphaGo and AlphaZero, on the occasion of our ACM Prizes in Computing.

“Is China Ahead in the Quantum Computing Race?”

Sunday, September 26th, 2021

Please enjoy an hourlong panel discussion of that question on YouTube, featuring yours truly, my former MIT colleague Will Oliver, and political scientist and China scholar Elsa Kania. If you’re worried that the title sounds too sensationalistic, I hope my fellow panelists and I will pleasantly surprise you with our relative sobriety! Thanks so much to QC Ware for arranging the panel (full disclosure: I’m QC Ware’s scientific adviser).

Exciting opportunities at Kabul University!

Sunday, September 5th, 2021

Update (Sept. 6): Alright, as promised in this post, I’ve now matched a reader’s generosity by donating $2,000 to NARAL’s Avow fund, which is fighting for abortion rights for women in Texas. Woke people on Twitter, I invite you/youse/y’all to figure out some creative ways to condemn me for that.


Normally, early fall is the time when I’d use this blog to advertise positions in quantum information and theoretical computer science at the University of Texas at Austin, for prospective PhD students, postdocs, and faculty. This year, you might say, anyone trying to recruit academics to Texas has a … teensy bit of a PR problem. We already had PR problems, first over the “failure by design” of our electrical grid in the winter, second over Governor Abbott’s battle against local mask mandates, which has made Texas the second-most notoriously covid-friendly state after Florida.

Now, of course, Texas has effectively outlawed abortion—well, after the 6th week, which is before many women even realize they’re pregnant, and when the fetus is still the size of a grain of rice and looks like this.

There are no exceptions for rape or incest, and—this is the “novel” part—there’s a bounty system, with $10,000+ fines for anyone who helps in any way with an abortion, payable to anyone who snitches on them. Texas has openly defied Roe v. Wade and, for the first time in half a century, has gotten five Supreme Court justices (three appointed by Donald Trump) to go along with it. Roe v. Wade is de facto no longer the law of the United States.

With a 15-week cutoff, a right to abortion would still functionally exist. At 6 weeks, it no longer functionally exists.

And as for our recruiting at UT Austin … I fear we might as well now be trying to recruit colleagues to Kabul University. It’s like, imagine some department chair at Kabul U., this week, trying to woo a star female physicist from abroad: “Oh, don’t worry … you’ll get used to wearing a burqa in no time! And the ban on being alone with unrelated males is actually a plus for you; it just means you’ll be freed from onerous teaching and committee assignments. Best yet, I’ve received personal assurances from our local Taliban commander that you almost certainly won’t be stoned for your licentiousness and whoredom. Err … no offense, those were his words, not mine.”

For five years, my recruiting pitches for UT Austin have often involved stressing how Austin is a famously hip, tolerant, high-tech, educated city—a “blueberry in the tomato soup,” as Rick Perry put it—and how Texas itself might indeed turn blue any election cycle, given the explosive growth of its metropolitan population, and how the crazy state politics is unlikely to affect an Austinite’s personal life—at least, by noticeably more than the crazy national politics would affect their personal life. I can no longer make this pitch with a straight face, or certainly not to women.

Like, I’m lucky that none of the women in my close family have ever needed an abortion, and that if they did, it would be easy for them to travel out of Texas to get one. But having carried to term two healthy but difficult pregnancies, my wife Dana has often stressed to me how insane she finds the very idea of being forced by the government to go through with such an ordeal. If women considering moving to Texas feel likewise, I can’t argue with them. More than that: if Texas continues on what half the country sees as a journey back to the Middle Ages, with no opt-outs allowed for the residents of its left-leaning urban centers, Dana and I will not be able to remain here, and many of our friends won’t either.

So why aren’t we packing our bags already? Partly because the current situation is inherently, obviously unstable. SB8 can’t long remain the law of Texas while Roe v. Wade remains the law of the United States: one of them has to give. I confess to being confused about why some abortion provider in Texas, with funding from national pro-choice groups, hasn’t already broken the law, welcomed a lawsuit, and forced the courts to rule explicitly on whether Roe v. Wade still stands and why or why not, rather than gutting a core part of American jurisprudence literally under cover of night. I’m also confused about why some solid blue state, like Massachusetts or Hawaii, isn’t right now passing a law that would let any citizen sue any other for carrying a firearm—thereby forcing the five Supreme Hypocrites, in striking down that law, to admit that they don’t believe after all that state laws get to trample what the Supreme Court has held to be constitutional rights, merely by outsourcing the enforcement to random vigilantes.

My best guess is that Thomas, Alito, Gorsuch, Kavanaugh, and Barrett are already plotting to replace Roe by something much more restrictive, albeit probably not quite as shockingly draconian as Texas’s current ban on all abortions after six weeks, nor quite as breathtakingly insane as its bounty system for anyone who snitches about abortions. My best guess is that they saw last week’s ruling as a way to test the waters and soften the country up: if you’re going to rescind what multiple generations of Americans have grown up seeing as a fundamental right, best not to do it too suddenly. My best guess is that Democrats will respond by making abortion a central campaign issue in 2022 and 2024, and that given the public’s 58%-32% support for Roe, the Democrats will do pretty well with that—to the point where, like the proverbial dog that finally catches the car, Republicans might come to regret actually sinking their jaws into Roe, rather than just conspicuously chasing it down the street for half a century.

I have friends who are sincere, thoughtful pro-lifers. I admire, if nothing else, their principled dedication to a moral stance that regularly gets condemned in academia. But I’d also say to them: even if you think of abortion as murder, a solid majority of Americans don’t, and it’s hard to see a stable way of getting what you want that skips the step where you change those Americans’ minds. Indeed, there’s long been a pro-choice critique of Roe, which says that, by short-circuiting the political loosening of abortion restrictions that was already underway in the 70s, Roe fueled the growth of the radical right that’s now all but destroyed America. For Roe falsely convinced pro-lifers that all they needed to do was seize control of the Supreme Court, by any means fair or foul, when what they really needed to do was convince the public.

And, let’s be honest, convincing the public means convincing them to adopt a religious as opposed to secular framework for morality. (And not just any religious framework: Orthodox Jews, for example, while not exactly fans of abortion, are fine with it under many circumstances. In the Jewish view, so the old classic goes, the fetus attains full personhood only after graduating medical school.) Of the Americans who want abortion to be illegal in all or most cases, 94% are at least “fairly certain” that God exists, and 79% are “absolutely certain”—consistent with my experience of having met highly intelligent and articulate pro-lifers, but never secular ones. Modulo Lizardman’s Constant, virtually all pro-lifers have metaphysical commitments about God and the soul that presumably do some of the heavy lifting for them. If the case for a blanket abortion ban can be made in terms that are compelling to a secular, rationalist, tradeoffs-based morality, no one seems to have done it yet.

From the standpoint of secular moral philosophy, my own opinion is that no one has ever improved on the searching analysis of the abortion question that Carl Sagan and Ann Druyan published in 1990. After painstakingly laying out scientific facts, moral hypotheticals, and commonsense principles, Sagan and Druyan ultimately conclude that the right question to ask is when the fetus develops something that’s recognizably a human brain, processing thoughts and emotions. In practice, that probably means drawing a hard line at the end of the second trimester. Coincidentally, that’s almost exactly where Roe v. Wade drew the line, but Sagan and Druyan’s reasoning is completely different: they reject Roe‘s criterion of viability outside the womb, as both morally irrelevant and contingent on medical technology.

Reasonable people could disagree with the details of Sagan and Druyan’s analysis. But if we agree that

(1) a sperm and unfertizilied egg have a “personhood” of 0,

(2) a newborn baby has a “personhood” of 1, and

(3) whatever “personhood” is, it’s somehow tied to the gradual growth of neurons and dendrites in the physical universe, rather than to a mystical and discontinuous moment of ensoulment,

… then by the intermediate value theorem, for all p∈(0,1), there’s going to be some stage of fetal development where the fetus has a personhood of p. Which means that we’re going to be drawing a debatable line, making a compromise, just like the majority did in Roe. To me, one of the strangest aspects of the abortion debate is how both sides came to view Roe v. Wade as the “pro-choice maximalist position,” forgetting how it itself was an attempted compromise between conflicting moral intuitions.

Another strange aspect of the debate is how the most visible representatives of both sides seem to have given up, decades ago, on actually arguing for their positions. Maybe it’s because people simply threw up their hands in futility; or because all the ground had been covered with nothing left to say; or because the debate was so obviously entangled with religion, and we have a polite norm of not arguing about religion; or because both positions hardened into tribal identity markers, to be displayed rather than defended. Whatever the reason, though, by the mid-90s everything became about border skirmishes one or two steps removed from the actual question: e.g., if the woman is under 18, should her parents be notified? should she be shown pictures of her fetus and given a 24-hour waiting period in hopes she’ll reconsider? is this judicial nominee hiding his or her anti-abortion views?

Now that Texas and five Supreme Court justices have launched a frontal assault on Roe—it’s impossible to see it any other way—it seems to me that the long armistice is over. The pro-life side will have to make the case for its moral framework to a populace that will suddenly be paying more attention—and that includes tens of millions of Americans who hadn’t even been born the last time mainstream figures debated abortion head-on. The pro-choice side can then counterargue for its moral framework. If any pro-lifers are raring for this fight, I’ll point out that one of the most dramatic demographic changes, since the last time abortion was a “hot war,” has been a doubling in the percentage of Americans who are atheist, agnostic, or religiously unaffiliated.

Let me close this post with two things.

Firstly, if anyone is still unclear where I stand: over the next week, I will match Shtetl-Optimized readers’ donations to NARAL up to $2,000. If you’d like to participate, just leave a comment with the amount you donated. If I’ve argued with certain strains of feminism on this blog, that gives me all the more obligation to support the strains that I regard as fundamentally correct.

Secondly, come join us at the University of Kab … I mean Texas at Austin! For grad students, see here; for faculty, see here; for postdocs, email me a CV and recent publications and have two reference letters sent to me by December 31st. In the US, the east coast is now being ravaged beyond recognition by hurricanes and the west coast by wildfires. Here in Texas, all we have to deal with is extreme heat, a failing electrical grid, runaway covid, and now the ban on abortion. Hook ’em Hadamards!

Stephen Wiesner (1942-2021)

Friday, August 13th, 2021

Photo credit: Lev Vaidman

These have not been an auspicious few weeks for Jewish-American-born theoretical physicists named Steve who made epochal contributions to human knowledge in the late 1960s, and who I had the privilege to get to know a bit when they were old.

This morning, my friend and colleague Or Sattath brought me the terrible news that Stephen Wiesner has passed away in Israel. [Because people have asked: I’ve now also heard directly from Wiesner’s daughter Sarah.]

Decades ago, Wiesner left academia, embraced Orthodox Judaism, moved from the US to Israel, and took up work there as a construction laborer—believing (or so he told me) that manual labor was good for the soul. In the late 1960s, however, Wiesner was still a graduate student in physics at Columbia University, when he wrote Conjugate Coding: arguably the foundational document of the entire field of quantum information science. Famously, this paper was so far ahead of its time that it was rejected over and over from journals, taking nearly 15 years to get published. (Fascinatingly, Gilles Brassard tells me that this isn’t true: it was rejected once, from IEEE Transactions on Information Theory, and then Wiesner simply shelved it.) When it finally appeared, in 1983, it was in SIGACT News—a venue that I know and love, where I’ve published too, but that’s more like the house newsletter for theoretical computer scientists than an academic journal.

But it didn’t matter. By the early 1980s, Wiesner’s ideas had been successfully communicated to Charlie Bennett and Gilles Brassard, who refashioned them into the first scheme for quantum key distribution—what we now call BB84. Even as Bennett and Brassard received scientific acclaim for the invention of quantum cryptography—including, a few years ago, the Wolf Prize (often considered second only to the Nobel Prize), at a ceremony in the Knesset in Jerusalem that I attended—the two B’s were always careful to acknowledge their massive intellectual debt to Steve Wiesner.


Let me explain what Wiesner does in the Conjugate Coding paper. As far as I know, this is the first paper ever to propose that quantum information—what Wiesner called “polarized light” or “spin-1/2 particles” but we now simply call qubits—works differently than classical bits, in ways that could actually be useful for achieving cryptographic tasks that are impossible in a classical world. What could enable these cryptographic applications, wrote Wiesner, is the fact that there’s no physical means for an attacker or eavesdropper to copy an unknown qubit, to produce a second qubit in the same quantum state. This observation—now called the No-Cloning Theorem—would only be named and published in 1982, but Wiesner treats it in his late-1960s manuscript as just obvious background.

Wiesner went further than these general ideas, though, to propose an explicit scheme for quantum money that would be physically impossible to counterfeit—a scheme that’s still of enormous interest half a century later (I teach it every year in my undergraduate course). In what we now call the Wiesner money scheme, a central bank prints “quantum bills,” each of which contains a classical serial number as well as a long string of qubits. Each qubit is prepared in one of four possible quantum states:

  • |0⟩,
  • |1⟩,
  • |+⟩ = (|0⟩+|1⟩)/√2, or
  • |-⟩ = (|0⟩-|1⟩)/√2.

The bank, in a central database, stores the serial number of every bill in circulation, as well as the preparation instructions for each of the bill’s qubits. If you want to verify a bill as genuine—this, as Wiesner knew, is the big drawback—you have to bring it back to the bank. The bank, using its secret knowledge of how each qubit was prepared, measures each qubit in the appropriate basis—the {|0⟩,|1⟩} basis for |0⟩ or |1⟩ qubits, the {|+⟩,|-⟩} basis for |+⟩ or |-⟩ qubits—and checks that it gets the expected outcomes. If even one qubit yields the wrong outcome, the bill is rejected as counterfeit.

Now consider the situation of a counterfeiter, who holds a quantum bill but lacks access to the bank’s secret database. When the counterfeiter tries to copy the bill, they won’t know the right basis in which to measure each qubit—and if they make the wrong choice, then it’s not only that they fail to make a copy; it’s that the measurement destroys even the original copy! For example, measuring a |+⟩ or |-⟩ qubit in the {|0⟩,|1⟩} basis will randomly collapse the qubit to either |0⟩ or |1⟩—so that, when the bank later measures the same qubit in the correct {|+⟩,|-⟩} basis, it will see the wrong outcome, and realize that the bill has been compromised, with 1/2 probability (with the probability increasing to nearly 1 as we repeat across hundreds or thousands of qubits).

Admittedly, the handwavy argument above, which Wiesner offered, is far from a security proof by cryptographers’ standards. In 2011, I pointed that out on StackExchange. My post, I’m happy to say, spurred Molina, Vidick, and Watrous to write a beautiful 2012 paper, where they rigorously proved for the first time that in Wiesner’s money scheme, no counterfeiter consistent with the laws of quantum mechanics can turn a single n-qubit bill into two bills that both pass the bank’s verification with success probability greater than (3/4)n (and this is tight). But the intuition was already clear enough to Wiesner in the 1960s.

In 2003—when I was already a PhD student in quantum information, but incredibly, had never heard of Stephen Wiesner or his role in founding my field—I rediscovered the idea of quantum states |ψ⟩ that you could store, measure, and feed into a quantum computer, but that would be usefully uncopyable. (My main interest was in whether you could create “unpiratable quantum software programs.”) Only in 2006, at the University of Waterloo, did Michele Mosca and his students make the connection for me to quantum money, Stephen Wiesner, and his Conjugate Coding paper, which I then read with amazement—along with a comparably amazing followup work by Bennett, Brassard, Breidbart, and Wiesner.

But it was clear that there was still a great deal to do. Besides unpiratable software, Wiesner and his collaborators had lacked the tools in the early 1980s seriously to tackle the problem of secure quantum money that anybody could verify, not only the bank that had created the money. I realized that, if such a thing was possible at all, then just like unpiratable software, it would require cryptographic hardness assumptions, a restriction to polynomial-time counterfeiters, and (hence) ideas from quantum computational complexity. The No-Cloning Theorem couldn’t do the job on its own.

That realization led to my 2009 paper Quantum Copy-Protection and Quantum Money, and from there, to the “modern renaissance” of Wiesner’s old idea of quantum money, with well over a hundred papers (e.g., my 2012 paper with Paul Christiano, Farhi et al.’s quantum state restoration paper, their quantum money from knots paper, Mark Zhandry’s 2017 quantum lightning paper, Dmitry Gavinsky’s improvement of Wiesner’s scheme wherein the money is verified by classical communication with the bank, Broduch et al.’s adaptive attack on Wiesner’s original scheme, my shadow tomography paper proving the necessity for the bank to keep a giant database in information-theoretic quantum money schemes like Wiesner’s, Daniel Kane’s strange scheme based on modular forms…). The purpose of many of these papers was either to break the quantum money schemes proposed in previous papers, or to patch the schemes that were previously broken.

After all this back-and-forth, spanning more than a decade, I’d say that Wiesner’s old idea of quantum money is now in good enough theoretical shape that the main obstacle to its practical realization is merely the “engineering difficulty”—namely, how to get the qubits in a bill, sitting in your pocket or whatever, to maintain their quantum coherence for more than a few nanoseconds! (Or possibly a few hours, if you’re willing to schlep a cryogenic freezer everywhere you go.) It’s precisely because quantum key distribution doesn’t have this storage problem—because there the qubits are simply sent across a channel and then immediately measured on arrival—that QKD is actually practical today, although the market for it has proven to be extremely limited so far.

In the meantime, while the world waits for the quantum error-correction that could keep qubits alive indefinitely, there’s Bitcoin. The latter perversely illustrates just how immense the demand for quantum money might someday be: the staggering lengths to which people will go, diverting the electricity to power whole nations into mining rigs, to get around our current inability to realize Wiesner’s elegant quantum-mechanical solution to the same problem. When I first learned about Bitcoin, shortly after its invention, it was in the context of: “here’s something I’d better bring up in my lectures on quantum money, in order to explain how much better WiesnerCoin could eventually be, when it’s the year 2200 or whatever and we all have quantum computers wired up by a quantum Internet!” It never occurred to me that I should forget about the year 2200, liquidate my life savings, and immediately buy up all the Bitcoin I could. [Added: I’ve since learned that Wiesner’s daughter Sarah is a professional in the Bitcoin space.]


Photo credit: Or Sattath

In his decades as a construction laborer, Wiesner had (as far as I know) no Internet presence; many of my colleagues didn’t even realize he was still alive. Even then, though, Wiesner never turned his back so far on his previous life, his academic life, that the quantum information faculty at Hebrew University in Jerusalem couldn’t entice him to participate in some seminars there. Those seminars are where I had the privilege to meet and talk to him several times over the last decade. He was thoughtful and kind, listening with interest as I told him how I and others were trying to take quantum money into the modern era by making it publicly verifiable.

I also vividly remember a conversation in 2013 where Steve shared his fears about the American physics establishment and military-industrial complex, and passionately urged me to

  1. quit academia and get a “real job,” and
  2. flee the US immediately and move my family to Israel, because of a wave of fascism and antisemitism that was about to sweep the US, just like with Germany in the 1930s.

I politely nodded along, pointing out that my Israeli wife and I had considered living in Israel but the job opportunities were better in US, silently wondering when Steve had gone completely off his rocker. Today, Steve’s urgent warning about an impending fascist takeover of the US seems … uh, slightly less crazy than in 2013? Maybe, just like with quantum money, Wiesner was simply too far ahead of his time to sound sane.

Wiesner also talked to me about his father, Jerome Wiesner, who was a legendary president of MIT—still spoken about in reverent tones when I taught there—as well as the chief science advisor to John F. Kennedy. One of JFK’s most famous decisions was to override the elder Wiesner’s fervent opposition to sending humans to the moon (Wiesner thought it a waste of money, as robots could do the same science for vastly cheaper).

While I don’t know all the details (I hope someone someday researches it and writes a book), Steve Wiesner made it clear to me that he did not get along with his famous father at all—in fact they became estranged. Steve told me that his embrace of Orthodox Judaism was, at least in part, a reaction against everything his father had stood for, including militant scientific atheism. I suppose that in the 1960s, millions of young Americans defied their parents via sex, drugs, and acoustic guitar; only a tiny number did so by donning tzitzit and moving to Israel to pray and toil with their hands. The two groups of rebels did, however, share a tendency to grow long beards.

Wiesner’s unique, remarkable, uncloneable life trajectory raises the question: who are the young Stephen Wiesners of our time? Will we be faster to recognize their foresight than Wiesner’s contemporaries were to recognize his?


Feel free to share any other memories of Stephen Wiesner or his influence in the comments.


Update (Aug. 14): See also Or Sattath’s memorial post, which (among other things) points out something that my narrative missed: namely, besides quantum money, Wiesner also invented superdense coding in 1970, although he and Bennett only published the idea 22 years later (!).

And I have more photos! Here’s Wiesner with an invention of his and another photo (thanks to his daughter Sarah). Here’s another photo from 1970 and Charlie Bennett’s handwritten notes (!) after first meeting Wiesner in 1970 (thanks to Charlie Bennett).

Another Update: Stephen’s daughter Sarah gave me the following fascinating information to share.

In the 70’s he lived in California where he worked in various Silicon Valley startups while also working weekends as part of a produce (fruits and vegetables) distribution co-op. During this time he became devoted to the ideas of solar energy, clean energy and space migration and exploration. He also became interested in Judaism. He truly wanted to help and make our world more peaceful and safe with his focus being on clean energy and branching out into space. He also believed that instead of fighting over the temple mount in Jerusalem, the Third Temple should be built in outer-space or in a structure above the original spot, an idea he tried to promote to prevent wars over land.

Striking new Beeping Busy Beaver champion

Tuesday, July 27th, 2021

For the past few days, I was bummed about the sooner-than-expected loss of Steven Weinberg. Even after putting up my post, I spent hours just watching old interviews with Steve on YouTube and reading his old essays for gems of insight that I’d missed. (Someday, I’ll tackle Steve’s celebrated quantum field theory and general relativity textbooks … but that day is not today.)

Looking for something to cheer me up, I was delighted when Shtetl-Optimized reader Nick Drozd reported a significant new discovery in BusyBeaverology—one that, I’m proud to say, was directly inspired by my Busy Beaver survey article from last summer (see here for blog post).

Recall that BB(n), the nth Busy Beaver number (technically, “Busy Beaver shift number”), is defined as the maximum number of steps that an n-state Turing machine, with 1 tape and 2 symbols, can make on an initially all-0 tape before it invokes a Halt transition. Famously, BB(n) is not only uncomputable, it grows faster than any computable function of n—indeed, computing anything that grows as quickly as Busy Beaver is equivalent to solving the halting problem.

As of 2021, here is the extent of human knowledge about concrete values of this function:

  • BB(1) = 1 (trivial)
  • BB(2) = 6 (Lin 1963)
  • BB(3) = 21 (Lin 1963)
  • BB(4) = 107 (Brady 1983)
  • BB(5) ≥ 47,176,870 (Marxen and Buntrock 1990)
  • BB(6) > 7.4 × 1036,534 (Kropitz 2010)
  • BB(7) > 102×10^10^10^18,705,352 (“Wythagoras” 2014)

As you can see, the function is reasonably under control for n≤4, then “achieves liftoff” at n=5.

In my survey, inspired by a suggestion of Harvey Friedman, I defined a variant called Beeping Busy Beaver, or BBB. Define a beeping Turing machine to be a TM that has a single designated state where it emits a “beep.” The beeping number of such a machine M, denoted b(M), is the largest t such that M beeps on step t, or ∞ if there’s no finite maximum. Then BBB(n) is the largest finite value of b(M), among all n-state machines M.

I noted that the BBB function grows uncomputably even given an oracle for the ordinary BB function. In fact, computing anything that grows as quickly as BBB is equivalent to solving any problem in the second level of the arithmetical hierarchy (where the computable functions are in the zeroth level, and the halting problem is in the first level). Which means that pinning down the first few values of BBB should be even more breathtakingly fun than doing the same for BB!

In my survey, I noted the following four concrete results:

  • BBB(1) = 1 = BB(1)
  • BBB(2) = 6 = BB(2)
  • BBB(3) ≥ 55 > 21 = BB(3)
  • BBB(4) ≥ 2,819 > 107 = BB(4)

The first three of these, I managed to get on my own, with the help of a little program I wrote. The fourth one was communicated to me by Nick Drozd even before I finished my survey.

So as of last summer, we knew that BBB coincides with the ordinary Busy Beaver function for n=1 and n=2, then breaks away starting at n=3. We didn’t know how quickly BBB “achieves liftoff.”

But Nick continued plugging away at the problem all year, and he now claims to have resolved the question. More concretely, he claims the following two results:

  • BBB(3) = 55 (via exhaustive enumeration of cases)
  • BBB(4) ≥ 32,779,478 (via a newly-discovered machine)

For more, see Nick’s announcement on the Foundations of Mathematics email list, or his own blog post.

Nick actually writes in terms of yet another Busy Beaver variant, which he calls BLB, or “Blanking Beaver.” He defines BLB(n) to be the maximum finite number of steps that an n-state Turing machine can take before it first “wipes its tape clean”—that is, sets all the tape squares to 0, as they were at the very beginning of the computation, but as they were not at intermediate times. Nick has discovered a 4-state machine that takes 32,779,477 steps to blank out its tape, thereby proving that

  • BLB(4) ≥ 32,779,477.

Nick’s construction, when investigated, turns out to be based on a “Collatz-like” iterative process—exactly like the BB(5) champion and most of the other strong Busy Beaver contenders currently known. A simple modification of his construction yields the lower bound on BBB.

Note that the Blanking Beaver function does not have the same sort of super-uncomputable growth that Beeping Busy Beaver has: it merely grows “normally” uncomputably fast, like the original BB function did. Yet we see that BLB, just like BBB, already “achieves liftoff” by n=4, rather than n=5. So the real lesson here is that 4-state Turing machines can already do fantastically complicated things on blank tapes. It’s just that the usual definitions of the BB function artificially prevent us from seeing that; they hide the uncomputable insanity until we get to 5 states.