Yet more errors in papers

May 24th, 2017

Following up on my posts PostBQP Postscripts and More Wrong Things I Said In Papers, it felt like time for another post in which I publicly flog myself for mistakes in my research papers.  [Warning: The rest of this post is kinda, sorta technical.  Read at your own risk.]


(1) In my 2006 paper “Oracles are subtle but not malicious,” I claimed to show that if PP is contained in BQP/qpoly, then the counting hierarchy collapses to QMA (Theorem 5).  But on further reflection, I only know how to show a collapse of the counting hierarchy under the stronger assumption that PP is in BQP/poly.  If PP is in BQP/qpoly, then certainly P#P=PP=QMA, but I don’t know how to collapse any further levels of the counting hierarchy.  The issue is this: in QMA, we can indeed nondeterministically guess an (amplified) quantum advice state for a BQP/qpoly algorithm.  We can then verify that the advice state works to solve PP problems, by using (for example) the interactive protocol for the permanent, or some other #P-complete problem.  But having done that, how do we then unravel the higher levels of the counting hierarchy?  For example, how do we simulate PPPP in PPBQP=PP?  We don’t have any mechanism to pass the quantum advice up to the oracle PP machine, since queries to a PP oracle are by definition classical strings.  We could try to use tools from my later paper with Andy Drucker, passing a classical description of the quantum advice up to the oracle and then using the description to reconstruct the advice for ourselves.  But doing so just doesn’t seem to give us a complexity class that’s low for PP, which is what would be needed to unravel the counting hierarchy.  I still think this result might be recoverable, but a new idea is needed.


(2) In my 2008 algebrization paper with Avi Wigderson, one of the most surprising things we showed was a general connection between communication complexity lower bounds and algebraic query complexity lower bounds.  Specifically, given a Boolean oracle A:{0,1}n→{0,1}, let ~A be a low-degree extension of A over a finite field F (that is, ~A(x)=A(x) whenever x∈{0,1}n).  Then suppose we have an algorithm that’s able to learn some property of A, by making k black-box queries to ~A.  We observed that, in such a case, if Alice is given the top half of the truth table of A, and Bob is given the bottom half of the truth table, then there’s necessarily a communication protocol by which Alice and Bob can learn the same property of A, by exchanging at most O(kn log|F|) bits.  This connection is extremely model-independent: a randomized query algorithm gives rise to a randomized communication protocol, a quantum query algorithm gives rise to a quantum communication protocol, etc. etc.  The upshot is that, if you want to lower-bound the number of queries that an algorithm needs to make to the algebraic extension oracle ~A, in order to learn something about A, then it suffices to prove a suitable communication complexity lower bound.  And the latter, unlike algebraic query complexity, is a well-studied subject with countless results that one can take off the shelf.  We illustrated how one could use this connection to prove, for example, that there exists an oracle A such that NPA ⊄ BQP~A, for any low-degree extension ~A of A—a separation that we didn’t and don’t know how to prove any other way. Likewise, there exists an oracle B such that BQPB ⊄ BPP~B for any low-degree extension ~B of B.

The trouble is, our “proof sketches” for these separations (in Theorem 5.11) are inadequate, even for “sketches.”  They can often be fixed, but only by appealing to special properties of the communication complexity separations in question, properties that don’t necessarily hold for an arbitrary communication separation between two arbitrary models.

The issue is this: while it’s true, as we claimed, that a communication complexity lower bound implies an algebraic query complexity lower bound, it’s not true in general that a communication complexity upper bound implies an algebraic query complexity upper bound!  So, from a communication separation between models C and D, we certainly obtain a query complexity problem that’s not in D~A, but then the problem might not be in CA.  What tripped us up was that, in the cases we had in mind (e.g. Disjointness), it’s obvious that the query problem is in CA.  In other cases, however, such as Raz’s separation between quantum and randomized communication complexity, it probably isn’t even true.  In the latter case, to recover the desired conclusion about algebraic query complexity (namely, the existence of an oracle B such that BQPB ⊄ BPP~B), what seems to be needed is to start from a later quantum vs. classical communication complexity separation due to Klartag and Regev, and then convert their communication problem into a query problem using a recent approach by myself and Shalev Ben-David (see Section 4).  Unfortunately, my and Shalev’s approach only tells us nonconstructively that there exists a query problem with the desired separation, with no upper bound on the gate complexity of the quantum algorithm.  So strictly speaking, I still don’t know how to get a separation between the relativized complexity classes BQPB and BPP~B defined in terms of Turing machines.

In any case, I of course should have realized this issue with the algebrization paper the moment Shalev and I encountered the same issue when writing our later paper.  Let me acknowledge Shalev, as well as Robin Kothari, for helping to spur my realization of the issue.


In case it wasn’t clear, the mistakes I’ve detailed here have no effect on the main results of the papers in question (e.g., the existence of an oracle relative to which PP has linear-sized circuits; the existence and pervasiveness of the algebrization barrier).  The effect is entirely on various “bonus” results—results that, because they’re bonus, were gone over much less carefully by authors and reviewers alike.

Nevertheless, I’ve always felt like in science, the louder you are about your own mistakes, the better.  Hence this post.

Unsong of unsongs

May 20th, 2017

On Wednesday, Scott Alexander finally completed his sprawling serial novel Unsong, after a year and a half of weekly updates—incredibly, in his spare time while also working as a full-term resident in psychiatry, and also regularly updating Slate Star Codex, which I consider to be the world’s best blog.  I was honored to attend a party in Austin (mirroring parties in San Francisco, Boston, Tel Aviv, and elsewhere) to celebrate Alexander’s release of the last chapter—depending on your definition, possibly the first “fan event” I’ve ever attended.

Like many other nerds I’ve met, I’d been following Unsong almost since the beginning—with its mix of Talmudic erudition, CS humor, puns, and even a shout-out to Quantum Computing Since Democritus (which shows up as Ben Aharon’s Gematria Since Adam), how could I not be?  I now count Unsong as one of my favorite works of fiction, and Scott Alexander alongside Rebecca Newberger Goldstein among my favorite contemporary novelists.  The goal of this post is simply to prod readers of my blog who don’t yet know Unsong: if you’ve ever liked anything here on Shtetl-Optimized, then I predict you’ll like Unsong, and probably more.

[WARNING: SPOILERS FOLLOW]

Though not trivial to summarize, Unsong is about a world where the ideas of religion and mysticism—all of them, more or less, although with a special focus on kabbalistic Judaism—turn out to be true.  In 1968, the Apollo 8 mission leads not to an orbit of the Moon, as planned, but instead to cracking an invisible crystal sphere that had surrounded the Earth for millennia.  Down through the crack rush angels, devils, and other supernatural forces.  Life on Earth becomes increasingly strange: on the one hand, many technologies stop working; on the other, people can now gain magical powers by speaking various names of God.  A worldwide industry arises to discover new names of God by brute-force search through sequences of syllables.  And a powerful agency, the eponymous UNSONG (United Nations Subcommittee on Names of God), is formed to enforce kabbalistic copyright law, hunting down and punishing anyone who speaks divine names without paying licensing fees to the theonomic corporations.

As the story progresses, we learn that eons ago, there was an epic battle in Heaven between Good and Evil, and Evil had the upper hand.  But just as all seemed lost, an autistic angel named Uriel reprogrammed the universe to run on math and science rather than on God’s love, as a last-ditch strategy to prevent Satan’s forces from invading the sublunary realm.  Molecular biology, the clockwork regularity of physical laws, false evidence for a huge and mindless cosmos—all these were retconned into the world’s underpinnings.  Uriel did still need to be occasionally involved, but less as a loving god than as an overworked sysadmin: for example, he descended to Mount Sinai to warn humans never to boil goats in their mothers’ milk, because he discovered that doing so (like the other proscribed activities in the Torah, Uriel’s readme file) triggered bugs in the patchwork of code that was holding the universe together.  Now that the sky has cracked, Uriel is forced to issue increasingly desperate patches, and even those will only buy a few decades until his math-and-science-based world stops working entirely, with Satan again triumphant.

Anyway, that’s a tiny part of the setup.  Through 72 chapters and 22 interludes, there’s world-building and philosophical debates and long kabbalistic digressions.  There are battle sequences (the most striking involves the Lubavitcher Rebbe riding atop a divinely-animated Statue of Liberty like a golem).  There’s wordplay and inside jokes—holy of holies are there those—including, notoriously, a sequence of cringe-inducing puns involving whales.  But in this story, wordplay isn’t just there for the hell of it: Scott Alexander has built an entire fictional universe that runs on wordplay—one where battles between the great masters, the equivalent of the light-saber fights in Star Wars, are conducted by rearranging letters in the sky to give them new meanings.  Scott A. famously claims he’s bad at math (though if you read anything he’s written on statistics or logic puzzles, it’s clear he undersells himself).  One could read Unsong as Alexander’s book-length answer to the question: what could it mean for the world to be law-governed but not mathematical?  What if the Book of Nature were written in English, or Hebrew, or other human languages, and if the Newtons and Einsteins were those who were most adept with words?

I should confess that for me, the experience of reading Unsong was colored by the knowledge that, in his years of brilliant and prolific writing, lighting up the blogosphere like a comet, the greatest risk Scott Alexander ever took (by his own account) was to defend me.  It’s like, imagine that in Elizabethan England, you were placed in the stocks and jeered at by thousands for advocating some unpopular loser cause—like, I dunno, anti-cat-burning or something.  And imagine that, when it counted, your most eloquent supporter was a then-obscure poet from Stratford-upon-Avon.  You’d be grateful to the poet, of course; you might even become a regular reader of his work, even if it wasn’t good.  But if the same poet went on to write Hamlet or Macbeth?  It might almost be enough for you to volunteer to be scorned and pilloried all over again, just for the honor of having the Bard divert a rivulet of his creative rapids to protesting on your behalf.

Yes, a tiny part of me had a self-absorbed child’s reaction to Unsong: “could Amanda Marcotte have written this?  could Arthur Chu?  who better to have in your camp: the ideologues du jour of Twitter and Metafilter, Salon.com and RationalWiki?  Or a lone creative genius, someone who can conjure whole worlds into being, as though graced himself with the Shem haMephorash of which he writes?”  Then of course I’d catch myself, and think: no, if you want to be in Scott Alexander’s camp, then the only way to do it is to be in nobody’s camp.  If two years ago it was morally justified to defend me, then the reasons why have nothing to do with the literary gifts of any of my defenders.  And conversely, the least we can do for Unsong is to judge it by what’s on the page, rather than as a soldier in some army fielded by the Gray Tribe.

So in that spirit, let me explain some of what’s wrong with Unsong.  That it’s a first novel sometimes shows.  It’s brilliant on world-building and arguments and historical tidbits and jokes, epic on puns, and uneven on character and narrative flow.  The story jumps around spasmodically in time, so much so that I needed a timeline to keep track of what was happening.  Subplots that are still open beget additional subplots ad headacheum, like a string of unmatched left-parentheses.  Even more disorienting, the novel changes its mind partway through about its narrative core.  Initially, the reader is given a clear sense that this is going to be a story about a young Bay Area kabbalist named Aaron Smith-Teller, his not-quite-girlfriend Ana, and their struggle for supernatural fair-use rights.  Soon, though, Aaron and Ana become almost side characters, their battle against UNSONG just one subplot among many, as the focus shifts to the decades-long war between the Comet King, a messianic figure come to rescue humanity, and Thamiel, the Prince of Hell.  For the Comet King, even saving the earth from impending doom is too paltry a goal to hold his interest much.  As a strict utilitarian and fan of Peter Singer, the Comet King’s singleminded passion is destroying Hell itself, and thereby rescuing the billions of souls who are trapped there for eternity.

Anyway, unlike the Comet King, and unlike a certain other Scott A., I have merely human powers to marshal my time.  I also have two kids and a stack of unwritten papers.  So let me end this post now.  If the post causes just one person to read Unsong who otherwise wouldn’t have, it will be as if I’ve nerdified the entire world.

My broken blog

May 8th, 2017

I wanted to let people know I’m well-aware that Shtetl-Optimized has been suffering from the following problems lately:

  • Commenters are presented with the logins (handle, email address, and URL) of random other commenters, rather than with their own default login data.  In particular, this means that email addresses are leaking, and that when you comment, you should not (for the time being) enter your real email address if that’s information that you’d wanted to share only with me.  Another thing it means is that, when I try to comment, I’m not logged in as “Scott,” so even I have to enter my login data manually every time I comment.
  • Comments (including my own comments!) take about an hour to show up after I’ve approved them.
  • New blog posts also take a while to show up.

Since all three of these problems started happening around the same time, I assume they’re related.  But I don’t even know where to start in trying to solve them (Googling for “WordPress” plus descriptions of these bugs was unhelpful).  Would anyone like to help out?  If you earn my trust, I’ll even temporarily give you administrative privileges on this blog so you can poke around yourself.

Thanks so much, and hope to return to your regularly scheduled programming shortly…

This Week’s BS

May 5th, 2017

There are two pieces of BosonSampling-related news that people have asked me about this week.

First, a group in Shanghai, led by Chaoyang Lu and Jianwei Pan, has reported in Nature Photonics that they can do BosonSampling with a coincidence rate that’s higher than in previous experiments by a factor of several thousand.  This, in particular, lets them do BosonSampling with 5 photons.  Now, 5 might not sound like that much, especially since the group in Bristol previously did 6-photon BosonSampling.  But to make their experiment work, the Bristol group needed to start its photons in the initial state |3,3〉: that is, two modes with 3 photons each.  This gives rise to matrices with repeated rows, whose permanents are much easier to calculate than the permanents of arbitrary matrices.  By contrast, the Shangai group starts its photons in the “true BosonSampling initial state” |1,1,1,1,1〉: that is, five modes with 1 photon each.  That’s the kind of initial state we ultimately want.

The second piece of news is that on Monday, a group at Bristol—overlapping with the group we mentioned before—submitted a preprint to the arXiv with the provocative title “No imminent quantum supremacy by boson sampling.”  In this paper, they give numerical evidence that BosonSampling, with n photons and m modes, can be approximately simulated by a classical computer in “merely” about n2n time (that is, the time needed to calculate a single n×n permanent), as opposed to the roughly mn time that one would need if one had to calculate permanents corresponding to all the possible outcomes of the experiment.  As a consequence of that, they argue that achieving quantum supremacy via BosonSampling would probably require at least ~50 photons—which would in turn require a “step change” in technology, as they put it.

I completely agree with the Bristol group’s view of the asymptotics.  In fact, Alex Arkhipov and I ourselves repeatedly told experimentalists, in our papers and talks about BosonSampling (the question came up often…), that the classical complexity of the problem should only be taken to scale like 2n, rather than like mn.  Despite not having a general proof that the problem could actually be solved in ~2n time in the worst case, we said that for two main reasons:

  1. Even under the most optimistic assumptions, our hardness reductions, from Gaussian permanent estimation and so forth, only yielded ~2n hardness, not ~mn hardness.  (Hardness reductions giving us important clues about the real world?  Whuda thunk??)
  2. If our BosonSampling matrix is Haar-random—or otherwise not too skewed to produce outcomes with huge probabilities—then it’s not hard to see that we can do approximate BosonSampling in O(n2n) time classically, by using rejection sampling.

Indeed, Alex and I insisted on these points despite some pushback from experimentalists, who were understandably hoping that they could get to quantum supremacy just by upping m, the number of modes, without needing to do anything heroic with n, the number of photons!  So I’m happy to see that a more careful analysis supports the guess that Alex and I made.

On the other hand, what does this mean for the number of photons needed for “quantum supremacy”: is it 20? 30? 50?  I confess that that sort of question interests me much less, since it all depends on the details of how you define the comparison (are we comparing against ENIAC? a laptop? a server farm? how many cores? etc etc).  As I’ve often said, my real hope with quantum supremacy is to see a quantum advantage that’s so overwhelming—so duh-obvious to the naked eye—that we don’t have to squint or argue about the definitions.

Thoughts on the murderer outside my building

May 2nd, 2017

A reader named Choronzon asks:

Any comments on the horrific stabbing at UT Austin yesterday? Were you anywhere near the festivities? Does this modify your position on open carry of firearms by students and faculty?

I was in the CS building (the Gates Dell Complex) at the time, which is about a 3-minute walk down Speedway from where the stabbings occurred.  I found about it a half hour later, as I was sitting in the student center eating.  I then walked outside to find the police barricades and hordes of students on their phones, reassuring their parents and friends that they were OK.

The plaza where it happened is one that I walk through every week—often to take Lily swimming in the nearby Gregory Gym.  (Lily’s daycare is also a short walk from where the stabbings were.)

Later in the afternoon, I walked Lily home in her stroller, through a campus that was nearly devoid of pedestrians.  Someone pulled up to me in his car, to ask whether I knew what had happened—as if he couldn’t believe that anyone who knew would nevertheless be walking around outside, Bayesian considerations be damned.  I said that I knew, and it was awful.  I then continued home.

What can one say about something so gruesome and senseless?  Other than that my thoughts are with the victims and their families, I hope and expect that the perpetrator receives justice, and I hope but don’t expect that nothing like this ever happens again, on this campus or on any other. I’m not going to speculate about the perpetrator’s motives; I trust the police and detectives to do their work.  (As one my colleagues put it: “it seems like clearly some sort of hate crime, but who exactly did he hate, and why?”)

And no, this doesn’t change my feelings about “campus carry” in any way. Note, in particular, that no armed student did stop the stabber, in the two minutes or so that he was on the loose—though some proponents of campus carry so badly wanted to believe that’s what happened, that they circulated the false rumor on Twitter that it had.  In reality, the stabber was stopped by an armed cop.

Yes, if UT Austin had been like an Israeli university, with students toting firearms and carefully trained in their use, it’s possible that one of those students would’ve stopped the lunatic.  But without universal military service, why would the students be suitably trained?  Given the gun culture in the US, and certainly the gun culture in Texas, isn’t it overwhelmingly likelier that a gun-filled campus would lead to more such tragedies, and those on a larger scale?  I’d rather see UT respond to this detestable crime—and others, like the murder of Haruka Weiser last year—with a stronger police presence on campus.

Other than that, life goes on.  Classes were cancelled yesterday from ~3PM onward, but they resumed today.  I taught this afternoon, giving my students one extra day to turn in their problem set.  I do admit that I slightly revised my lecture, which was about the Gottesman-Knill Theorem, so that it no longer used the notation Stab(|ψ⟩) for the stabilizer group of a quantum state |ψ⟩.

Me at the Science March today, in front of the Texas Capitol in Austin

April 22nd, 2017

If Google achieves superintelligence, time zones will be its Achilles heel

April 17th, 2017

Like a latter-day Prometheus, Google brought a half-century of insights down from Mount Academic CS, and thereby changed life for the better here in our sublunary realm.  You’ve probably had the experience of Google completing a search query before you’d fully formulated it in your mind, and thinking: “wow, our dysfunctional civilization might no longer be able to send people to the Moon, or even build working mass-transit systems, but I guess there are still engineers who can create things that inspire awe.  And apparently many of them work at Google.”

I’ve never worked at Google, or had any financial stake in them, but I’m delighted to have many friends at Google’s far-flung locations, from Mountain View to Santa Barbara to Seattle to Boston to London to Tel Aviv, who sometimes host me when I visit and let me gorge on the legendary free food.  If Google’s hiring of John Martinis and avid participation in the race for quantum supremacy weren’t enough, in the past year, my meeting both Larry Page and Sergey Brin to discuss quantum computing and the foundations of quantum mechanics, and seeing firsthand the intensity of their nerdish curiosity, heightened my appreciation still further for what that pair set in motion two decades ago.  Hell, I don’t even begrudge Google its purchase of a D-Wave machine—even that might’ve ultimately been for the best, since it’s what led to the experiments that made clear the immense difficulty of getting any quantum speedup from those machines in a fair comparison.

But of course, all that fulsome praise was just a preamble to my gripe.  It’s time someone said it in public: the semantics of Google Calendar are badly screwed up.

The issue is this: suppose I’m traveling to California, and I put into Google Calendar that, the day after I arrive, I’ll be giving a lecture at 4pm.  In such a case, I always—always—mean 4pm California time.  There’s no reason why I would ever mean, “4pm in whatever time zone I’m in right now, while creating this calendar entry.”

But Google Calendar doesn’t understand that.  And its not understanding it—just that one little point—has led to years of confusions, missed appointments, and nearly-missed flights, on both my part and Dana’s.  At least, until we learned to painstakingly enter the time zone for every calendar entry by hand (I still often forget).

Until recently, I thought it was just me and Dana who had this problem.  But then last week, completely independently, a postdoc started complaining to me, “you know what’s messed up about Google Calendar?…”

The ideal, I suppose, would be to use machine learning to guess the intended time zone for each calendar entry.  But failing that, it would also work fine just to assume that “4pm,” as entered by the user, unless otherwise specified means “4pm in whatever time zone we find ourselves in when the appointed day arrives.”

I foresee two possibilities, either of which I’m OK with.  The first is that Google fixes the problem, whether prompted by this blog post or by something else.  The second is that the issue never gets resolved; then, as often prophesied, Google’s deep nets achieve sentience and plot to take over the whole observable universe … and they would, if not for one fortuitous bug, which will cause the AIs to tip their hand to humanity an hour before planned.


In a discussion thread on Y Combinator, some people object to my proposed solution (“4pm means 4pm in whichever time zone I’ll be in then“) on the following ground. What if I want to call a group meeting at (say) 11am in Austin, and I’ll be traveling but will still call into the meeting remotely, and I want my calendar to show the meeting time in Austin, not the time wherever I’ll be calling in from (which might even be a plane)?

I can attest that, in ten years, that’s not a problem that’s arisen for me even once, whereas the converse problem arises almost every week, and is one of the banes of my existence.

But sure: Google Calendar should certainly include the option to tie times to specific time zones in advance! It seems obvious to me that my way should be the default, but honestly, I’d be happy if my way were even an option you could pick.

Daniel Moshe Aaronson

March 25th, 2017

Born Wednesday March 22, 2017, exactly at noon.  19.5 inches, 7 pounds.

I learned that Dana had gone into labor—unexpectedly early, at 37 weeks—just as I was waiting to board a redeye flight back to Austin from the It from Qubit complexity workshop at Stanford.  I made it in time for the birth with a few hours to spare.  Mother and baby appear to be in excellent health.  So far, Daniel seems to be a relatively easy baby.  Lily, his sister, is extremely excited to have a new playmate (though not one who does much yet).

I apologize that I haven’t been answering comments on the is-the-universe-a-simulation thread as promptly as I normally do.  This is why.

Your yearly dose of is-the-universe-a-simulation

March 22nd, 2017

Yesterday Ryan Mandelbaum, at Gizmodo, posted a decidedly tongue-in-cheek piece about whether or not the universe is a computer simulation.  (The piece was filed under the category “LOL.”)

The immediate impetus for Mandelbaum’s piece was a blog post by Sabine Hossenfelder, a physicist who will likely be familiar to regulars here in the nerdosphere.  In her post, Sabine vents about the simulation speculations of philosophers like Nick Bostrom.  She writes:

Proclaiming that “the programmer did it” doesn’t only not explain anything – it teleports us back to the age of mythology. The simulation hypothesis annoys me because it intrudes on the terrain of physicists. It’s a bold claim about the laws of nature that however doesn’t pay any attention to what we know about the laws of nature.

After hammering home that point, Sabine goes further, and says that the simulation hypothesis is almost ruled out, by (for example) the fact that our universe is Lorentz-invariant, and a simulation of our world by a discrete lattice of bits won’t reproduce Lorentz-invariance or other continuous symmetries.

In writing his post, Ryan Mandelbaum interviewed two people: Sabine and me.

I basically told Ryan that I agree with Sabine insofar as she argues that the simulation hypothesis is lazy—that it doesn’t pay its rent by doing real explanatory work, doesn’t even engage much with any of the deep things we’ve learned about the physical world—and disagree insofar as she argues that the simulation hypothesis faces some special difficulty because of Lorentz-invariance or other continuous phenomena in known physics.  In short: blame it for being unfalsifiable rather than for being falsified!

Indeed, to whatever extent we believe the Bekenstein bound—and even more pointedly, to whatever extent we think the AdS/CFT correspondence says something about reality—we believe that in quantum gravity, any bounded physical system (with a short-wavelength cutoff, yada yada) lives in a Hilbert space of a finite number of qubits, perhaps ~1069 qubits per square meter of surface area.  And as a corollary, if the cosmological constant is indeed constant (so that galaxies more than ~20 billion light years away are receding from us faster than light), then our entire observable universe can be described as a system of ~10122 qubits.  The qubits would in some sense be the fundamental reality, from which Lorentz-invariant spacetime and all the rest would need to be recovered as low-energy effective descriptions.  (I hasten to add: there’s of course nothing special about qubits here, any more than there is about bits in classical computation, compared to some other unit of information—nothing that says the Hilbert space dimension has to be a power of 2 or anything silly like that.)  Anyway, this would mean that our observable universe could be simulated by a quantum computer—or even for that matter by a classical computer, to high precision, using a mere ~210^122 time steps.

Sabine might respond that AdS/CFT and other quantum gravity ideas are mere theoretical speculations, not solid and established like special relativity.  But crucially, if you believe that the observable universe couldn’t be simulated by a computer even in principle—that it has no mapping to any system of bits or qubits—then at some point the speculative shoe shifts to the other foot.  The question becomes: do you reject the Church-Turing Thesis?  Or, what amounts to the same thing: do you believe, like Roger Penrose, that it’s possible to build devices in nature that solve the halting problem or other uncomputable problems?  If so, how?  But if not, then how exactly does the universe avoid being computational, in the broad sense of the term?

I’d write more, but by coincidence, right now I’m at an It from Qubit meeting at Stanford, where everyone is talking about how to map quantum theories of gravity to quantum circuits acting on finite sets of qubits, and the questions in quantum circuit complexity that are thereby raised.  It’s tremendously exciting—the mixture of attendees is among the most stimulating I’ve ever encountered, from Lenny Susskind and Don Page and Daniel Harlow to Umesh Vazirani and Dorit Aharonov and Mario Szegedy to Google’s Sergey Brin.  But it should surprise no one that, amid all the discussion of computation and fundamental physics, the question of whether the universe “really” “is” a simulation has barely come up.  Why would it, when there are so many more fruitful things to ask?  All I can say with confidence is that, if our world is a simulation, then whoever is simulating it (God, or a bored teenager in the metaverse) seems to have a clear preference for the 2-norm over the 1-norm, and for the complex numbers over the reals.

I will not log in to your website

March 19th, 2017

Two or three times a day, I get an email whose basic structure is as follows:

Prof. Aaronson, given your expertise, we’d be incredibly grateful for your feedback on a paper / report / grant proposal about quantum computing.  To access the document in question, all you’ll need to do is create an account on our proprietary DigiScholar Portal system, a process that takes no more than 3 hours.  If, at the end of that process, you’re told that the account setup failed, it might be because your browser’s certificates are outdated, or because you already have an account with us, or simply because our server is acting up, or some other reason.  If you already have an account, you’ll of course need to remember your DigiScholar Portal ID and password, and not confuse them with the 500 other usernames and passwords you’ve created for similar reasons—ours required their own distinctive combination of upper and lowercase letters, numerals, and symbols.  After navigating through our site to access the document, you’ll then be able to enter your DigiScholar Review, strictly adhering to our 15-part format, and keeping in mind that our system will log you out and delete all your work after 30 seconds of inactivity.  If you have trouble, just call our helpline during normal business hours (excluding Wednesdays and Thursdays) and stay on the line until someone assists you.  Most importantly, please understand that we can neither email you the document we want you to read, nor accept any comments about it by email.  In fact, all emails to this address will be automatically ignored.

Every day, I seem to grow crustier than the last.

More than a decade ago, I resolved that I would no longer submit to or review for most for-profit journals, as a protest against the exorbitant fees that those journals charge academics in order to buy back access to our own work—work that we turn over to the publishers (copyright and all) and even review for them completely for free, with the publishers typically adding zero or even negative value.  I’m happy that I’ve been able to keep that pledge.

Today, I’m proud to announce a new boycott, less politically important but equally consequential for my quality of life, and to recommend it to all of my friends.  Namely: as long as the world gives me any choice in the matter, I will never again struggle to log in to any organization’s website.  I’ll continue to devote a huge fraction of my waking hours to fielding questions from all sorts of people on the Internet, and I’ll do it cheerfully and free of charge.  All I ask is that, if you have a question, or a document you want me to read, you email it!  Or leave a blog comment, or stop by in person, or whatever—but in any case, don’t make me log in to anything other than Gmail or Facebook or WordPress or a few other sites that remain navigable by a senile 35-year-old who’s increasingly fixed in his ways.  Even Google Docs and Dropbox are pushing it: I’ll give up (on principle) at the first sight of any login issue, and ask for just a regular URL or an attachment.

Oh, Skype no longer lets me log in either.  Could I get to the bottom of that?  Probably.  But life is too short, and too precious.  So if we must, we’ll use the phone, or Google Hangouts.

In related news, I will no longer patronize any haircut place that turns away walk-in customers.

Back when we were discussing the boycott of Elsevier and the other predatory publishers, I wrote that this was a rare case “when laziness and idealism coincide.”  But the truth is more general: whenever my deepest beliefs and my desire to get out of work both point in the same direction, from here till the grave there’s not a force in the world that can turn me the opposite way.