Happy Second Birthday Lily

January 21st, 2015

cat2

Two years ago, I blogged when Lily was born.  Today I can blog that she runs, climbs, swims (sort of), constructs 3-word sentences, demands chocolate cake, counts to 10 in both English and Hebrew, and knows colors, letters, shapes, animals, friends, relatives, the sun, and the moon.  To all external appearances she’s now conscious as you and I are (and considerably more so than the cat in the photo).

But the most impressive thing Lily does—the thing that puts her far beyond where her parents were at the same age, in a few areas—is her use of the iPad.  There she does phonics exercises, plays puzzle games that aren’t always trivial for me to win, and watches educational videos on YouTube (skipping past the ads, and complaining if the Internet connection goes down).  She chooses the apps and videos herself, easily switching between them when she gets bored.  It’s a sight to behold, and definitely something to try with your own toddler if you have one.  (There’s a movement these days that encourages parents to ban kids from using touch-screen devices, fearful that too much screen time will distract them from the real world.  To which I reply: for better or worse, this is the real world that our kids will grow up into.)

People often ask whether Dana and I will steer Lily into becoming a theoretical computer scientist like us.  My answer is “hell no”: I’ll support Lily in whatever she wants to do, whether that means logic, combinatorics, algebraic geometry, or even something further afield like theoretical neuroscience or physics.

As recent events illustrated, the world is not always the kindest place for nerds (male or female), with our normal ways of thinking, talking, and interacting sometimes misunderstood by others in the cruelest ways imaginable.  Yet despite everything, nerds do sometimes manage to meet, get married, and even produce offspring with nerd potential of their own.  We’re here, we’re sometimes inappropriately clear, and we’re not going anywhere.

So to life!  And happy birthday Lily!

BQP/LHC collision

January 15th, 2015

cms

This afternoon, I gave my usual spiel about Quantum Computing and the Limits of the Efficiently Computable at the CERN Colloquium.  (If you watched the webcast of the Higgs boson discovery announcement a couple years ago, it was in the same auditorium they used for that, except this time it was less packed.)  Beforehand, Dana and I got to join a tour of the CMS detector at the Large Hadron Collider—one of the very last tours, before CMS shuts down (as ATLAS already has) to get ready for collisions at the LHC’s new, higher energy.

Considered as eye candy, I’d say that the CMS detector holds its own against the Taj Mahal, Machu Picchu, the Great Wall of China, or any of the other engineering marvels of the world.  So, OK, let me describe what it’s like to visit it.  The first step is to take a tram from downtown Geneva to CERN, which is headquartered in the town of Meyrin.  This is easier than you’d imagine: a tram actually arrives in Geneva every few minutes with “CERN” (its final stop) written right on it!  Next you take a 20-minute bus ride from the CERN reception hall to the CMS building, which is across the French border.  You don’t really think about it until you’re here, but:

(a) The Large Hadron Collider is large—it’s, like, a whole drive through the countryside to get from the main CERN buildings to CMS.

(b) All inside the LHC ring is just a normal rural/suburban area, with restaurants, roads, gas stations, cows, etc.

Anyway, then you arrive at CMS, which looks from the outside like just a big warehouse-type building.

outside

And you go inside, wondering if now you’re going to see the detector.  But no, there’s just a giant tarp hanging from the ceiling with a picture of the detector on it.  Maybe this tour won’t include the detector?

tarp

But then you go outside, back in through some back entrance, then into a staging area where you get hard hats to wear.  Then you get into an elevator that goes about 150 feet down.  Meanwhile, your tour guide is carrying a geiger counter to make sure you’re not exposed to too much radiation.  Now will you see the detector?  No, just a bunch of dark corridors.  You pass through a room full of computers on racks—cool, this must be where they analyze the collision data!  (Actually, according to Panflutist in the comments section, these computers are only for control and for the trigger system, which decides which events to store for later analysis.)

computers

Then, after that room, there’s a door with a sign indicating that beyond it is the LHC ring.  Cool!

lhcenter

Of course, you’re not actually going into the ring.  But then you turn a different way, and emerge onto a platform where you to get to the “big reveal”: the detector, two giant circular pieces that obviously screw together but are now separated, and engineers making final tweaks to them before they’re reunited for the next collider run.  (I forgot to mention: the whole tour is being conducted in French.  That’s why you sort of need to guess what’s happening.)

Anyway, thanks so much to Wolfgang Lerche and everyone else at CERN for an awesome visit.

Quantum computing news items (by reader request)

January 12th, 2015

Within the last couple months, there was a major milestone in the quest to build a scalable quantum computer, and also a major milestone in the quest to figure out what you would do with a quantum computer if you had one.  As I’ve admitted many times, neither of those two quests is really the reason why I got into quantum computing—I’m one of the people who would still want to study this field, even if there were no serious prospect either of building a quantum computer or of doing anything useful with it for a thousand years—but for some reason that I don’t fully understand, both of those goals do seem to excite other people.

So, OK, the experimental breakthrough was the Martinis group’s use of quantum error-correction with superconducting qubits, to preserve a logical bit for several times longer than the underlying physical qubits survived for.  Shortly before this came out, I heard Krysta Svore give a talk at Yale in which she argued that preserving a logical qubit for longer than the physical qubits was the next experimental milestone (the fourth, out of seven she listed) along the way to a scalable, fault-tolerant quantum computer.  Well, it looks like that milestone may have been crossed.  (update: I’ve since learned from Graeme Smith, in the comments section, that the milestone crossed should really be considered the “3.5th,” since even though quantum error-correction was used, the information that was being protected was classical.  I also learned from commenter Jacob that the seven milestones Krysta listed came from a Science paper by Schoelkopf and Devorret.  She cited the paper; the forgetfulness was entirely mine.)

In more detail, the Martinis group used a linear array of 9 qubits: 5 data qubits interleaved with 4 measurement qubits. The authors describe this setup as a “precursor” to Kitaev’s surface code (which would involve a 2-dimensional array).  They report that, after 8 cycles of error detection and correction, they were able to suppress the effective error rate compared to the physical qubits by a factor of 8.5.  They also use quantum state tomography to verify that their qubits were indeed in entangled states as they did this.

Of course, this is not yet a demonstration of any nontrivial fault-tolerant computation, let alone of scaling such a computation up to where it’s hard to simulate with a classical computer.  But it pretty clearly lies along the “critical path” to that.

As I blogged back in September, Google recently hired Martinis’s group away from UC Santa Barbara, where they’ll work on superconducting quantum annealing, as a step along the way to full universal QC.  As I mentioned then, the Martinis group’s “Xmon” qubits have maybe 10,000 times the coherence times of D-Wave’s qubits, at least when you measure coherence in the usual ways.  The fact that Martinis et al. are carefully doing quantum state tomography and demonstrating beneficial error-correction before scaling up are further indications of the differences between their approach and D-Wave’s.  Of course, even if you do everything right, there’s still no guarantee that you’ll outperform a classical computer anytime soon: it might simply be that the things you can do in the near future (e.g., quantum annealing for NP-complete problems) are not things where you’re going to outperform the best classical algorithms.  But it’s certainly worth watching closely.

Meanwhile, the quantum algorithms breakthrough came in a paper last month by an extremely well-known trio down the Infinite Corridor from me: Farhi, Goldstone, and Gutmann.  In slightly earlier work, Farhi et al. proposed a new quantum algorithm for NP-hard optimization problems.  Their algorithm badly needs a name; right now they’re just calling it the “QAOA,” or Quantum Approximate Optimization Algorithm.  But here’s what you need to know: their new algorithm is different from their famous adiabatic algorithm, although it does become equivalent to the adiabatic algorithm in a certain infinite limit.  Rather than staying in the ground state of some Hamiltonian, the QAOA simply

  1. starts with a uniform superposition over all n-bit strings,
  2. applies a set of unitary transformations, one for each variable and constraint of the NP-hard instance,
  3. repeats the set some number of times p (the case p=1 is already interesting), and then
  4. measures the state in the computational basis to see what solution was obtained.

The unitary transformations have adjustable real parameters, and a big part of the game is figuring out how to set the parameters to get a good solution.

The original, hyper-ambitious goal of the QAOA was to solve the Unique Games problem in quantum polynomial time—thereby disproving the Unique Games Conjecture (which I previously blogged about here), unless NP⊆BQP.  It hasn’t yet succeeded at that goal.  In their earlier work, Farhi et al. managed to show that the QAOA solves the MAX-CUT problem on 3-regular graphs with approximation ratio 0.6924, which is better than random guessing, but not as good as the best-known classical algorithms (Goemans-Williamson, or for the degree-3 case, Halperin-Livnat-Zwick), let alone better than those algorithms (which is what would be needed to refute the UGC).

In their new work, Farhi et al. apply the QAOA to a different problem: the poetically-named MAX E3LIN2.  Here you’re given a collection of linear equations mod 2 in n Boolean variables, where each equation involves exactly 3 variables, and each variable appears in at most D equations.  The goal is to satisfy as many of the equations as possible, assuming that they’re not all satisfiable (if they were then the problem would be trivial).  If you just guess a solution randomly, you’ll satisfy a 1/2 fraction of the equations.  Håstad gave a polynomial-time classical algorithm that satisfies a 1/2+c/D fraction of the maximum number of satisfiable equations, for some constant c.  This remains the best approximation ratio that we know how to achieve classically.  Meanwhile, Trevisan showed that if there’s a polynomial-time classical algorithm that satisfies a 1/2+c/√D fraction of the max number of satisfiable equations, for a sufficiently large constant c, then P=NP.

OK, so what do Farhi et al. do?  They show that the QAOA, with suitably tuned parameters, is able to satisfy a 1/2+c/D3/4 fraction of the total number of equations in polynomial time, for some constant c.  (In particular, this implies that a 1/2+c/D3/4 fraction of the equations are satisfiable—assuming, as Farhi et al. do, that two equations directly contradicting each other, like x+y+z=0 and x+y+z=1, never appear in the same instance.)

Now, the above is a bigger fraction than the best-known classical algorithm satisfies!  (And not only that, but here the fraction is of the total number of equations, rather than the number of satisfiable equations.)  Farhi et al. also show that, if the constraint hypergraph doesn’t contain any small cycles, then QAOA can satisfy a 1/2+c/√D fraction of the equations in polynomial time, which is essentially the best possible unless NP⊆BQP.

The importance of this result is not that anyone cares about the MAX E3LIN2 problem for its own sake.  Rather it’s that, as far as I know, this is the first time that a quantum algorithm has been proved to achieve a better approximation ratio for a natural NP-hard optimization problem than the best known classical algorithm achieves.  People have discussed that as a hypothetical possibility for 20 years, but (again, unless I’m missing something) we never had a good example until now.  The big question now is whether the 1/2+c/D3/4 performance can be matched classically, or whether there truly is an NP-intermediate region of this optimization problem where quantum outperforms classical.  (The third possibility, that doing as well as the quantum algorithm is already NP-hard, is one that I won’t even speculate about.  For, as Boaz Barak rightly points out in the comments section, the quantum algorithm is still being analyzed only in the regime where solutions are combinatorially guaranteed to exist—and that regime can’t possibly be NP-hard, unless NP=coNP.)

[Above, I corrected some errors that appeared in the original version of this post—thanks to Ed Farhi and to the commenters for bringing them to my attention.]


Update (Feb. 3, 2015): Boaz Barak has left the following comment:

in a work with Ankur Moitra, Oded Regev, David Stuerer and Aravindan Vijayaraghavan we were able to match (in fact exceed) the guarantees of the Farhi et al paper via a classical efficient algorithm. (Namely satisfy 1/2 + C/√D fraction of the equations). p.s. we hope to post this on the arxiv soon

What I believe

December 30th, 2014

Two weeks ago, prompted by a commenter named Amy, I wrote by far the most personal thing I’ve ever made public—what’s now being referred to in some places as just “comment 171.”  My thinking was: I’m giving up a privacy that I won’t regain for as long as I live, opening myself to ridicule, doing the blog equivalent of a queen-and-two-rook sacrifice.  But at least—and this is what matters—no one will ever again be able to question the depth of my feminist ideals.  Not after they understand how I clung to those ideals through a decade when I wanted to die.  And any teenage male nerds who read this blog, and who find themselves in a similar hole, will know that they too can get out without giving up on feminism. Surely that’s a message any decent person could get behind?

Alas, I was overoptimistic.  Twitter is now abuzz with people accusing me of holding precisely the barbaric attitudes that my story was all about resisting, defeating, and escaping, even when life throws you into those nasty attitudes’ gravity well, even when it tests you as most of your critics will never be tested.  Many of the tweets are full of the courageous clucks of those who speak for justice as long as they’re pretty sure their friends will agree with them: wow just wow, so sad how he totes doesn’t get it, expletives in place of arguments.  This whole affair makes me despair of the power of language to convey human reality—or at least, of my own ability to use language for that end.  I took the most dramatic, almost self-immolating step I could to get people to see me as I was, rather than according to some preexisting mental template of a “privileged, entitled, elite male scientist.”  And many responded by pressing down the template all the more firmly, twisting my words until they fit, and then congratulating each other for their bravery in doing so.

Here, of course, these twitterers (and redditors and facebookers) inadvertently helped make my argument for me.  Does anyone still not understand the sort of paralyzing fear that I endured as a teenager, that millions of other nerds endure, and that I tried to explain in the comment—the fear that civilized people will condemn you as soon as they find out who you really are (even if the truth seems far from uncommonly bad), that your only escape is to hide or lie?

Thankfully, not everyone responded with snarls.  Throughout the past two weeks, I’ve been getting regular emails from shy nerds who thanked me profusely for sharing as I did, for giving them hope for their own lives, and for articulating a life-crushing problem that anyone who’s spent a day among STEM nerds knows perfectly well, but that no one acknowledges in polite company.  I owe the writers of those emails more than they owe me, since they’re the ones who convinced me that on balance, I did the right thing.

I’m equally grateful to have gotten some interesting, compassionate responses from feminist women.  The most striking was that of Laurie Penny in the New Statesman—a response that others of Penny’s views should study, if they want to understand how to win hearts and change minds.

I do not intend for a moment to minimise Aaronson’s suffering. Having been a lonely, anxious, horny young person who hated herself and was bullied I can categorically say that it is an awful place to be. I have seen responses to nerd anti-feminism along the lines of ‘being bullied at school doesn’t make you oppressed.’ Maybe it’s not a vector of oppression in the same way, but it’s not nothing. It burns. It takes a long time to heal.

Feminism, however, is not to blame for making life hell for ‘shy, nerdy men.’ Patriarchy is to blame for that. It is a real shame that Aaronson picked up Dworkin rather than any of the many feminist theorists and writers who manage to combine raw rage with refusal to resort to sexual shame as an instructive tool. Weaponised shame- male, female or other- has no place in any feminism I subscribe to. Ironically, Aronson [sic] actually writes a lot like Dworkin- he writes from pain felt and relived and wrenched from the intimate core of himself, and because of that his writing is powerfully honest, but also flawed …

What fascinates me about Aaronson’s piece, in which there was such raw, honest suffering, was that there was not one mention of women in any respect other than how they might relieve him from his pain by taking pity, or educating him differently. And Aaronson is not a misogynist. Aaronson is obviously a compassionate, well-meaning and highly intelligent man [damn straight—SA]

I’ll have more to say about Penny’s arguments in a later post—where I agree and where I part ways from her—but there’s one factual point I should clear up now.  When I started writing comment 171, I filled it with anecdotes from the happier part of my life (roughly, from age 24 onward): the part where I finally became able to ask; where women, with a frequency that I couldn’t have imagined as a teenager, actually answered ‘yes'; and where I got to learn about their own fears and insecurities and quirks.  In the earlier draft, I also wrote about my wife’s experiences as a woman in computer science, which differed from Amy’s in some crucial ways.  But then I removed it all, for a simple reason: because while I have the right to bare my own soul on my blog, I don’t have the right to bare other people’s unless they want me to.

Without further ado, and for the benefit of the world’s Twitterariat, I’m now just going to state nine of my core beliefs.

1. I believe that women are authors of their own stories, that they don’t exist merely to please men, that they are not homogeneous, that they’re not slot machines that ‘pay out’ but only if you say the right things.  I don’t want my two-year-old daughter to grow up to be anyone else’s property, and I’m happy that she won’t.  And I’d hope all this would no more need to be said, than (say) that Gentiles shouldn’t be slaughtered to use their blood in making matzo.

2. I believe everyone’s story should be listened to—and concretely, that everyone should feel 300% welcome to participate in my comments section.  I don’t promise to agree with you, but I promise to try to engage your ideas thoughtfully, whether you’re a man, woman, child, AI-bot, or unusually-bright keyboard-pecking chicken.  Indeed, I spend a nontrivial fraction of my life doing exactly that (well, not so much with chickens).

3. I believe no one has the right to anyone else’s sexual affections.  I believe establishing this principle was one of the triumphs of modern civilization.

4. I believe women who go into male-dominated fields like math, CS, and physics deserve praise, encouragement, and support.  But that’s putting the point too tepidly: if I get to pick 100 people (unrelated to me) to put onto a spaceship as the earth is being destroyed, I start thinking immediately about six or seven of my female colleagues in complexity and quantum computing.  And no, Twitter: not because being female, they could help repopulate the species.  Just because they’re great people.

5. I believe there still exist men who think women are inferior, that they have no business in science, that they’re good only for sandwich-making and sex.  Though I don’t consider it legally practicable, as a moral matter I’d be fine if every such man were thrown in prison for life.

6. I believe that even if they don’t hold views anything like the above (as, overwhelmingly, they don’t), there might be nerdy males who unintentionally behave in ways that tend to drive some women away from science.  I believe this is a complicated problem best approached with charity: we want win-win solutions, where no one is made to feel despised because of who they are.  Toward that end, I believe open, honest communication (as I’ve been trying to foster on this blog) is essential.

7. I believe that no one should be ashamed of inborn sexual desires: not straight men, not straight women, not gays, not lesbians, not even pedophiles (though in the last case, there might really be no moral solution other than a lifetime of unfulfilled longing).  Indeed, I’ve always felt a special kinship with gays and lesbians, precisely because the sense of having to hide from the world, of being hissed at for a sexual makeup that you never chose, is one that I can relate to on a visceral level.  This is one reason why I’ve staunchly supported gay marriage since adolescence, when it was still radical.  It’s also why the tragedy of Alan Turing, of his court-ordered chemical castration and subsequent suicide, was one of the formative influences of my life.

8. I believe that “the problem of the nerdy heterosexual male” is surely one of the worst social problems today that you can’t even acknowledge as being a problem—the more so, if you weight the problems by how likely academics like me are to know the sufferers and to feel a personal stake in helping them. How to help all the young male nerds I meet who suffer from this problem, in a way that passes feminist muster, and that triggers the world’s sympathy rather than outrage, is a problem that interests me as much as P vs. NP, and that right now seems about equally hard.

9. I believe that, just as there are shy, nerdy men, there are also shy, nerdy women, who likewise suffer from feeling unwanted, sexually invisible, or ashamed to express their desires.  On top of that, these women also have additional difficulties that come with being women!  At the same time, I also think there are crucial differences between the two cases—at least in the world as it currently exists—which might make the shy-nerdy-male problem vastly harder to solve than the shy-nerdy-female one.  Those differences, and my advice for shy nerdy females, will be the subject of another post.  (That’s the thing about blogging: in for a penny, in for a post.)


Update (Dec. 31): I struggle always to be ready to change my views in light of new arguments and evidence. After reflecting on the many thoughtful comments here, there are two concessions that I’m now willing to make.

The first concession is that, as Laurie Penny maintained, my problems weren’t caused by feminism, but rather by the Patriarchy. One thing I’ve learned these last few days is that, as many people use it, the notion of “Patriarchy” is sufficiently elastic as to encompass almost anything about the relations between the sexes that is, or has ever been, bad or messed up—regardless of who benefits, who’s hurt, or who instigated it. So if you tell such a person that your problem was not caused by the Patriarchy, it’s as if you’ve told a pious person that a certain evil wasn’t the Devil’s handiwork: the person has trouble even parsing what you said, since within her framework, “evil” and “Devil-caused” are close to synonymous. If you want to be understood, far better just to agree that it was Beelzebub and be done with it. This might sound facetious, but it’s really not: I believe in the principle of always adopting the other side’s terms of reference, whenever doing so will facilitate understanding and not sacrifice what actually matters to you.

Smash the Patriarchy!

The second concession is that, all my life, I’ve benefited from male privilege, white privilege, and straight privilege. I would only add that, for some time, I was about as miserable as it’s possible for a person to be, so that in an instant, I would’ve traded all three privileges for the privilege of not being miserable. And if, as some suggested, there are many women, blacks, and gays who would’ve gladly accepted the other side of that trade—well then, so much the better for all of us, I guess. “Privilege” simply struck me as a pompous, cumbersome way to describe such situations: why not just say that person A’s life stinks in this way, and person B’s stinks in that way? If they’re not actively bothering each other, then why do we also need to spread person A’s stink over to person B and vice versa, by claiming they’re each “privileged” by not having the other one’s?

However, I now understand why so many people became so attached to that word: if I won’t use it, they think it means I think that sexism, racism, and homophobia don’t exist, rather than just that I think people fixated on a really bad way to talk about these problems.


Update (Jan. 1): Yesterday I gave a seminar at the Hebrew University of Jerusalem. Since I’d been spending all my time dealing with comment-171-gate, I showed up with no slides, no notes, no anything—just me and the whiteboard. But for an hour and a half, I got to forget entirely about the thousands of people on the Internet I’d never met who were now calling me an asshole because of wild, “postmodernist” misreadings of a blog comment, which twisted what I said (and meant) into its exact opposite, building up a fake-Scott-Aaronson onto whom the ax-grinders could project all of their own bogeymen. For 90 minutes I got to forget all that, and just throw myself into separations between randomized and quantum query complexity. It was the most cathartic lecture of my life. And in the near future, I’d like more such catharses. Someday I’ll say more about the inexhaustibly-fascinating topic of nerds and sex—and in particular, I’ll write the promised post about shy female nerds—but not now. This will be my last post on the subject for a while.

On balance, I don’t regret having shared my story—because it prompted an epic discussion; because I learned so much from the dozens of other nerd coming-of-age stories that it drew out, similar to mine but also different; because what I learned will change the way I talk about these issues in the future; and most of all, because so many people, men and also some women, emailed me to say how my speaking out gave them hope for their own lives. But I do regret a few rhetorical flourishes, which I should have known might be misread maliciously, though I could never have guessed how maliciously. I never meant to minimize the suffering of other people, nor to deny that many others have had things as bad or worse than I did (again, how does one even compare?). I meant only that, if we’re going to discuss how to change the culture of STEM fields, or design sexual-conduct policies to minimize suffering, then I request a seat at the table not as the “white male powerful oppressor figure,” but as someone who also suffered something atypically extreme, overcame it, and gained relevant knowledge that way. I never meant to suggest that anyone else should leave the table.

To the people who tweeted that female MIT students should now be afraid to take classes with me: please check out the beautiful blog post by Yan, a female student who did take 6.045 with me. See also this by Lisa Danz and this by Chelsea Voss.

More broadly: thank you to everyone who sent me messages of support, but especially to all the female mathematicians and scientists who did so.  I take great solace from the fact that, of all the women and men whose contributions to the world I had respected beforehand, not one (to my knowledge) reacted to this affair in a mean-spirited way.

Happy New Year, everyone. May 2015 be a year of compassion and understanding.


Update (Jan. 2): If you’ve been following this at all, then please, please, please read Scott Alexander’s tour-de-force post. To understand what it was like for me to read this, after all I’ve been through the past few days, try to imagine Galileo’s Dialogue Concerning the Two Chief World Systems, the American Declaration of Independence, John Stuart Mill’s The Subjection of Women, and Clarence Darrow’s closing arguments in the Scopes trial all rolled into one, except with you as the protagonist. Reason and emotion are traditionally imagined as opposites, but that’s never seemed entirely right to me: while, yes, part of reason is learning how to separate out emotion, I never experience such intense emotion as when, like with Alexander’s piece, I see reason finally taking a stand, reason used to face down a thousand bullies and as a fulcrum to move the world.


Update (Jan. 13): Please check out this beautiful Quora answer by Jean Yang, a PhD student in MIT CSAIL. She’s answering the question: “What do you think of Scott Aaronson’s comment #171 and the subsequent posts?”

More generally, I’ve been thrilled by the almost-unanimously positive reactions that I’ve been getting these past two weeks from women in STEM fields, even as so many people outside STEM have responded with incomprehension and cruelty.  Witnessing that pattern has—if possible—made me even more of a supporter and admirer of STEM women than I was before this thing started.


Update (Jan. 17): See this comment on Lavinia Collins’s blog for my final response to the various criticisms that have been leveled at me.

Quantum Complexity Theory Student Project Showcase 3

December 26th, 2014

Merry Christmas (belatedly)!  This year Quanta Claus has brought us eight fascinating final project reports from students in my 6.845 Quantum Complexity Theory class, covering everything from interactive proofs to query and communication complexity to quantum algorithms to quantum gates (and one project even includes a web-based demo you can try!).  Continuing in the tradition of the two previous showcases, I’m sharing the reports here; some of these works might also be posted to the arXiv and/or submitted to journals.  Thanks so much to the students who volunteered to participate in the showcase, and to all the students for making this such a great class.

The Turing movie

December 16th, 2014

Last week I finally saw The Imitation Game, the movie with Benedict Cumberbatch as Alan Turing.

OK, so for those who haven’t yet seen it: should you?  Here’s my one paragraph summary: imagine that you told the story of Alan Turing—one of the greatest triumphs and tragedies of human history, needing no embellishment whatsoever—to someone who only sort-of understood it, and who filled in the gaps with weird fabrications and Hollywood clichés.  And imagine that person retold the story to a second person, who understood even less, and that that person retold it to a third, who understood least of all, but who was charged with making the movie that would bring Turing’s story before the largest audience it’s ever had.  And yet, imagine that enough of the enormity of the original story made it through this noisy channel, that the final product was still pretty good.  (Except, imagine how much better it could’ve been!)

The fabrications were especially frustrating to me, because we know it’s possible to bring Alan Turing’s story to life in a way that fully honors the true science and history.  We know that, because Hugh Whitemore’s 1986 play Breaking the Code did it.  The producers of The Imitation Game would’ve done better just to junk their script, and remake Breaking the Code into a Hollywood blockbuster.  (Note that there is a 1996 BBC adaptation of Breaking the Code, with Derek Jacobi as Turing.)

Anyway, the movie focuses mostly on Turing’s codebreaking work at Bletchley Park, but also jumps around in time to his childhood at Sherborne School, and to his arrest for “homosexual indecency” and its aftermath.  Turing’s two world-changing papers—On Computable Numbers and Computing Machinery and Intelligence—are both mentioned, though strangely, his paper about computing zeroes of the Riemann zeta function is entirely overlooked.

Here are my miscellaneous comments:

  • The boastful, trash-talking, humor-impaired badass-nerd of the movie seems a lot closer to The Big Bang Theory‘s Sheldon Cooper, or to some other Hollywood concept of “why smart people are so annoying,” than to the historical Alan Turing.  (At least in Sheldon’s case, the archetype is used for laughs, not drama or veracity.)  As portrayed in the definitive biography (Andrew Hodges’ Alan Turing: The Enigma), Turing was eccentric, sure, and fiercely individualistic (e.g., holding up his pants with pieces of string), but he didn’t get off on insulting the intelligence of the people around him.
  • In the movie, Turing is pretty much singlehandedly responsible for designing, building, and operating the Bombes (the codebreaking machines), which he does over the strenuous objections of his superiors.  This, of course, is absurd: Bletchley employed about 10,000 people at its height.  Turing may have been the single most important cog in the operation, but he was still a cog.  And by November 1942, the operation was already running smoothly enough that Turing could set sail for the US (in waters that were now much safer, thanks to Bletchley!), to consult on other cryptographic projects at Bell Labs.
  • But perhaps the movie’s zaniest conceit is that Turing was also in charge of deciding what to do with Bletchley’s intelligence (!).  In the movie, it falls to him, not the military, to decide which ship convoys will be saved, and which sacrificed to prevent spilling Bletchley’s secret.  If that had any historicity to it, it would surely be the most military and political power ever entrusted to a mathematician (update: see the comments section for potential counterexamples).
  • It’s true that Turing (along with three other codebreakers) wrote a letter directly to Winston Churchill, pleading for more funding for Bletchley Park—and that Churchill saw the letter, and ordered “Action this day! Make sure they have all they want on extreme priority.”  However, the letter was not a power play to elevate Turing over Hugh Alexander and his other colleagues: in fact, Alexander co-signed the letter.  More broadly, the fierce infighting between Turing and everyone else at Bletchley Park, central to the movie’s plot, seems to have been almost entirely invented for dramatic purposes.
  • The movie actually deserves a lot of credit for getting right that the major technical problem of Bletchley Park was how to get the Bombes to search through keys fast enough—and that speeding things up is where Turing made a central contribution.  As a result, The Imitation Game might be the first Hollywood movie ever made whose plot revolves around computational efficiency.  (Counterexamples, anyone?)  Unfortunately, the movie presents Turing’s great insight as being that one can speed up the search by guessing common phrases, like “HEIL HITLER,” that are likely to be in the plaintext.  That was, I believe, obvious to everyone from the beginning.
  • Turing never built a computer in his own home, and he never named a computer “Christopher,” after his childhood crush Christopher Morcom.  (On the other hand, Christopher Morcom existed, and his early death from tuberculosis really did devastate Turing, sending him into morbid-yet-prescient ruminations about whether a mind could exist separately from a brain.)
  • I found it ironic that The Imitation Game, produced in 2014, is far more squeamish about on-screen homosexuality than Breaking the Code, produced in 1986.  Turing talks about being gay (which is an improvement over 2001’s Enigma, which made Turing straight!), but is never shown embracing another man.  However, the more important problem is that the movie botches the story of the burglary of Turing’s house (i.e., the event that led to Turing’s arrest and conviction for homosexual indecency), omitting the role of Turing’s own naiveté in revealing his homosexuality to the police, and substituting some cloak-and-dagger spy stuff.  Once again, Breaking the Code handled this perfectly.
  • In one scene, Euler is pronounced “Yooler.”

For more, see an excellent piece in Slate, How Accurate Is The Imitation Game?.  And for other science bloggers’ reactions, see this review by Christos Papadimitriou (which I thought was extremely kind, though it focuses more on Turing himself than on the movie), this reaction by Peter Woit, which largely echoes mine, and this by Clifford Johnson.

Walter Lewin

December 10th, 2014

Yesterday I heard the sad news that Prof. Walter Lewin, age 78—perhaps the most celebrated physics teacher in MIT’s history—has been stripped of his emeritus status and barred from campus, and all of his physics lectures removed from OpenCourseWare, because an internal investigation found that he had been sexually harassing students online.  I don’t know anything about what happened beyond the terse public announcements, but those who do know tell me that the charges were extremely serious, and that “this wasn’t a borderline case.”

I’m someone who feels that sexual harassment must never be tolerated, neither here nor anywhere else.  But I also feel that, if a public figure is going to be publicly brought down like this (yes, even by a private university), then the detailed findings of the investigation should likewise be made public, regardless of how embarrassing they are.  I know others differ, but I think the need of the world to see that justice was done overrides MIT’s internal administrative needs, and even Prof. Lewin’s privacy (the names of any victims could, of course, be kept secret).

More importantly, I wish to register that I disagree in the strongest possible terms with MIT’s decision to remove Prof. Lewin’s lectures from OpenCourseWare—thereby forcing the tens of thousands of students around the world who were watching these legendary lectures to hunt for ripped copies on BitTorrent.  (Imagine that: physics lectures as prized contraband!)  By all means, punish Prof. Lewin as harshly as he deserves, but—as students have been pleading on Reddit, in the MIT Tech comments section, and elsewhere—don’t also punish the countless students of both sexes who continue to benefit from his work.  (For godsakes, I’d regard taking down the lectures as a tough call if Prof. Lewin had gone on a murder spree.)  Doing this sends the wrong message about MIT’s values, and is a gift to those who like to compare modern American college campuses to the Soviet Union.

Update: For those who are interested, while the comment section starts out with a discussion of whether Walter Lewin’s physics lectures should’ve been removed from OCW, it’s now broadened to include essentially all aspects of the human condition.

PostBQP Postscripts: A Confession of Mathematical Errors

November 30th, 2014

tl;dr: This post reveals two errors in one of my most-cited papers, and also explains how to fix them.  Thanks to Piotr Achinger, Michael Cohen, Greg Kuperberg, Ciaran Lee, Ryan O’Donnell, Julian Rosen, Will Sawin, Cem Say, and others for their contributions to this post.


If you look at my Wikipedia page, apparently one of the two things in the world that I’m “known for” (along with algebrization) is “quantum Turing with postselection.”  By this, Wikipedia means my 2004 definition of the complexity class PostBQP—that is, the class of decision problems solvable in bounded-error quantum polynomial time, assuming the ability to postselect (or condition) on certain measurement outcomes—and my proof that PostBQP coincides with the classical complexity PP (that is, the class of decision problems expressible in terms of whether the number of inputs that cause a given polynomial-time Turing machine to accept does or doesn’t exceed some threshold).

To explain this a bit: even without quantum mechanics, it’s pretty obvious that, if you could “postselect” on exponentially-unlikely events, then you’d get huge, unrealistic amounts of computational power.  For example (and apologies in advance for the macabre imagery), you could “solve” NP-complete problems in polynomial time by simply guessing a random solution, then checking whether the solution is right, and shooting yourself if it happened to be wrong!  Conditioned on still being alive (and if you like, appealing to the “anthropic principle”), you must find yourself having guessed a valid solution—assuming, of course, that there were any valid solutions to be found.  If there weren’t any, then you’d seem to be out of luck!  (Exercise for the reader: generalize this “algorithm,” so that it still works even if you don’t know in advance whether your NP-complete problem instance has any valid solutions.)

So with the PostBQP=PP theorem, the surprise was not that postselection gives you lots of computational power, but rather that postselection combined with quantum mechanics gives you much more power even than postselection by itself (or quantum mechanics by itself, for that matter).  Since PPP=P#P, the class PP basically captures the full difficulty of #P-complete counting problems—that is, not just solving an NP-complete problem, but counting how many solutions it has.  It’s not obvious that a quantum computer with postselection can solve counting problems, but that’s what the theorem shows.  That, in turn, has implications for other things: for example, I showed it can be used to prove classical facts about PP, like the fact that PP is closed under intersection (the Beigel-Reingold-Spielman Theorem), in a straightforward way; and it’s also used to show the hardness of quantum sampling problems, in the work of Bremner-Jozsa-Shepherd as well as my BosonSampling work with Arkhipov.

I’m diffident about being “known for” something so simple; once I had asked the question, the proof of PostBQP=PP took me all of an hour to work out.  Yet PostBQP ended up being a hundred times more influential for quantum computing theory than things on which I expended a thousand times more effort.  So on balance, I guess I’m happy to call PostBQP my own.

That’s why today’s post comes with a special sense of intellectual responsibility.  Within the last month, it’s come to my attention that there are at least two embarrassing oversights in my PostBQP paper from a decade ago, one of them concerning the very definition of PostBQP.  I hasten to clarify: once one fixes up the definition, the PostBQP=PP theorem remains perfectly valid, and all the applications of PostBQP that I mentioned above—for example, to reproving Beigel-Reingold-Spielman, and to the hardness of quantum sampling problems—go through just fine.  But if you think I have nothing to be embarrassed about: well, read on.


The definitional subtlety came clearly to my attention a few weeks ago, when I was lecturing about PostBQP in my 6.845 Quantum Complexity Theory graduate class.  I defined PostBQP as the class of languages L⊆{0,1}* for which there exists a polynomial-time quantum Turing machine M such that, for all inputs x∈{0,1}*,

  • M(x) “succeeds” (determined, say, by measuring its first output qubit in the {|0>,|1>} basis) with nonzero probability.
  • If x∈L, then conditioned on M(x) succeeding, M(x) “accepts” (determined, say, by measuring its second output qubit in the {|0>,|1>} basis) with probability at least 2/3.
  • If x∉L, then conditioned on M(x) succeeding, M(x) accepts with probability at most 1/3.

I then had to reassure the students that PostBQP, so defined, was a “robust” class: that is, that the definition doesn’t depend on stupid things like which set of quantum gates we allow. I argued that, even though we’re postselecting on exponentially-unlikely events, it’s still OK, because the Solovay-Kitaev Theorem lets us approximate any desired unitary to within exponentially-small error, with only a polynomial increase in the size of our quantum circuit. (Here we actually need the full power of the Solovay-Kitaev Theorem, in contrast to ordinary BQP, where we only need part of the power.)

A student in the class, Michael Cohen, immediately jumped in with a difficulty: what if M(x) succeeded, not with exponentially-small probability, but with doubly-exponentially-small probability—say, exp(-2n)?  In that case, one could no longer use the Solovay-Kitaev Theorem to show the irrelevance of the gate set.  It would no longer even be clear that PostBQP⊆PP, since the PP simulation might not be able to keep track of such tiny probabilities.

Thinking on my feet, I replied that we could presumably choose a set of gates—for example, gates involving rational numbers only—for which doubly-exponentially-small probabilities would never arise.  Or if all else failed, we could simply add to the definition of PostBQP that M(x) had to “succeed” with probability at least 1/exp(n): after all, that was the only situation I ever cared about anyway, and the only one that ever arose in the applications of PostBQP.

But the question still gnawed at me: was there a problem with my original, unamended definition of PostBQP?  If we weren’t careful in choosing our gate set, could we have cancellations that produced doubly-exponentially-small probabilities?  I promised I’d think about it more.

By a funny coincidence, just a couple weeks later, Ciaran Lee, a student at Oxford, emailed me the exact same question.  So on a train ride from Princeton to Boston, I decided to think about it for real.  It wasn’t hard to show that, if the gates involved square roots of rational numbers only—for example, if we’re dealing with the Hadamard and Toffoli gates, or the cos(π/8) and CNOT gates, or other standard gate sets—then every measurement outcome has at least 1/exp(n) probability, so there’s no problem with the definition of PostBQP.  But I didn’t know what might happen with stranger gate sets.

As is my wont these days—when parenting, teaching, and so forth leave me with almost no time to concentrate on math—I posted the problem to MathOverflow.  Almost immediately, I got incisive responses.  First, Piotr Achinger pointed out that, if we allow arbitrary gates, then it’s easy to get massive cancellations.  In more detail, let {an} be extremely-rapidly growing sequence of integers, say with an+1 > exp(an).  Then define

$$ \alpha = \sum_{n=1}^{\infty} 0.1^{a_n}. $$

If we write out α in decimal notation, it will consist of mostly 0’s, but with 1’s spaced further and further apart, like so: 0.1101000000000001000….  Now consider a gate set that involves α as well as 0.1 and -0.1 as matrix entries.  Given n qubits, it’s not hard to see that we can set up an interference experiment in which one of the paths leading to a given outcome E has amplitude α, and the other paths have amplitudes $$ -(0.1^{a_1}), -(0.1^{a_2}), \ldots, -(0.1^{a_k}), $$ where k is the largest integer such that ak≤n. In that case, the total amplitude of E will be about $$0.1^{a_{k+1}},$$ which for most values of n is doubly-exponentially small in n. Of course, by simply choosing a faster-growing sequence {an}, we can cause an even more severe cancellation.

Furthermore, by modifying the above construction to involve two crazy transcendental numbers α and β, I claim that we can set up a PostBQP computation such that deciding what happens is arbitrarily harder than PP (though still computable)—say, outside of exponential space, or even triple-exponential space. Moreover, we can do this despite the fact that the first n digits of α and β remain computable in O(n) time. The details are left as an exercise for the interested reader.

Yet even though we can engineer massive cancellations with crazy gates, I still conjectured that nothing would go wrong with “normal” gates: for example, gates involving algebraic amplitudes only. More formally, I conjectured that any finite set A=(a1,…,ak) of algebraic numbers is “tame,” in the sense that, if p is any degree-n polynomial with integer coefficients at most exp(n) in absolute value, then p(a1,…,ak)≠0 implies |p(a1,…,ak)|≥1/exp(n). And indeed, Julian Rosen on MathOverflow found an elegant proof of this fact. I’ll let you read it over there if you’re interested, but briefly, it interprets the amplitude we want as one particular Archimedean valuation of a certain element of a number field, and then lower-bounds the amplitude by considering the product of all Archimedean and non-Archimedean valuations (the latter of which involves the p-adic numbers). Since this was a bit heavy-duty for me, I was grateful when Will Sawin reformulated the proof in linear-algebraic terms that I understood.

And then came the embarrassing part. A few days ago, I was chatting with Greg Kuperberg, the renowned mathematician and author of our climate-change parable. I thought he’d be interested in this PostBQP progress, so I mentioned it to him. Delicately, Greg let me know that he had recently proved the exact same results, for the exact same reason (namely, fixing the definition of PostBQP), for the latest revision of his paper How Hard Is It to Approximate the Jones Polynomial?. Moreover, he actually wrote to me in June to tell me about this! At the time, however, I regarded it as “pointless mathematical hairsplitting” (who cares about these low-level gate-set issues anyway?). So I didn’t pay it any attention—and then I’d completely forgotten about Greg’s work when the question resurfaced a few months later. This is truly a just punishment for looking down on “mathematical hairsplitting,” and not a lesson I’ll soon forget.

Anyway, Greg’s paper provides yet a third proof that the algebraic numbers are tame, this one using Galois conjugates (though it turns out that, from a sufficiently refined perspective, Greg’s proof is equivalent to the other two).

There remains one obvious open problem here, one that I noted in the MathOverflow post and in which Greg is also extremely interested. Namely, we now know that it’s possible to screw up PostBQP using gates with amplitudes that are crazy transcendental numbers (closely related to the Liouville numbers). And we also know that, if the gates have algebraic amplitudes, then everything is fine: all events have at least 1/exp(n) probability. But what if the gates have not-so-crazy transcendental amplitudes, like 1/e, or (a bit more realistically) cos(2)?  I conjecture that everything is still fine, but the proof techniques that worked for the algebraic case seem useless here.

Stepping back, how great are the consequences of all this for our understanding of PostBQP? Fortunately, I claim that they’re not that great, for the following reason. As Adleman, DeMarrais, and Huang already noted in 1997—in the same paper that proved BQP⊆PP—we can screw up the definition even of BQP, let alone PostBQP, using a bizarre enough gate set. For example, suppose we had a gate G that mapped |0> to x|0>+y|1>, where y was a real number whose binary expansion encoded the halting problem (for example, y might equal Chaitin’s Ω).  Then by applying G more and more times, we could learn more and more bits of y, and thereby solve an uncomputable problem in the limit n→∞.

Faced with this observation, most quantum computing experts would say something like: “OK, but this is silly! It has no physical relevance, since we’ll never come across a magical gate like G—if only we did! And at any rate, it has nothing to do with quantum computing specifically: even classically, one could imagine a coin that landed heads with probability equal to Chaitin’s Ω. Therefore, the right way to deal with this is simply to define BQP in such a way as to disallow such absurd gates.” And indeed, that is what’s done today—usually without even remarking on it.

Now, it turns out that even gates that are “perfectly safe” for defining BQP, can turn “unsafe” when it comes to defining PostBQP. To screw up the definition of PostBQP, it’s not necessary that a gate involve uncomputable (or extremely hard-to-compute) amplitudes: the amplitudes could all be easily computable, but they could still be “unsafe” because of massive cancellations, as in the example above involving α. But one could think of this as a difference of degree, rather than of kind. It’s still true that there’s a large set of gates, including virtually all the gates anyone has ever cared about in practice (Toffoli, Hadamard, π/8, etc. etc.), that are perfectly safe for defining the complexity class; it’s just that the set is slightly smaller than it was for BQP.


The other issue with the PostBQP=PP paper was discovered by Ryan O’Donnell and Cem Say.  In Proposition 3 of the paper, I claim that PostBQP = BQPPostBQP||,classical, where the latter is the class of problems solvable by a BQP machine that’s allowed to make poly(n) parallel, classical queries to a PostBQP oracle.  As Ryan pointed out to me, nothing in my brief argument for this depended on quantum mechanics, so it would equally well show that PostBPP = BPPPostBPP||, where PostBPP (also known as BPPpath) is the classical analogue of PostBQP, and BPPPostBPP|| is the class of problems solvable by a BPP machine that can make poly(n) parallel queries to a PostBPP oracle.  But BPPPostBPP|| clearly contains BPPNP||, which in turn contains AM—so we would get AM in PostBPP, and therefore AM in PostBQP=PP.  But Vereshchagin gave an oracle relative to which AM is not contained in PP.  Since there was no nonrelativizing ingredient anywhere in my argument, the only possible conclusion is that my argument was wrong.  (This, incidentally, provides a nice illustration of the value of oracle results.)

In retrospect, it’s easy to pinpoint what went wrong.  If we try to simulate BPPPostBPP|| in PostBPP, our random bits will be playing a dual role: in choosing the queries to be submitted to the PostBPP oracle, and in providing the “raw material for postselection,” in computing the responses to those queries.  But in PostBPP, we only get to postselect once.  When we do, the two sets of random bits that we’d wanted to keep separate will get hopelessly mixed up, with the postselection acting on the “BPP” random bits, not just on the “PostBPP” ones.

How can we fix this problem?  Well, when defining the class BQPPostBQP||,classical, suppose we require the queries to the PostBQP oracle to be not only “classical,” but deterministic: that is, they have to be generated in advance by a P machine, and can’t depend on any random bits whatsoever.  And suppose we define BPPPostBPP||,classical similarly.  In that case, it’s not hard to see that the equalities BQPPostBQP||,classical = PostBQP and BPPPostBPP||,classical = PostBPP both go through.  You don’t actually care about this, do you?  But Ryan O’Donnell and Cem Say did, and that’s good enough for me.


I wish I could say that these are the only cases of mistakes recently being found in decade-old papers of mine, but alas, such is not the case.  In the near future, my student Adam Bouland, MIT undergrad Mitchell Lee, and Singapore’s Joe Fitzsimons will post to the arXiv a paper that grew out of an error in my 2005 paper Quantum Computing and Hidden Variables. In that paper, I introduced a hypothetical generalization of the quantum computing model, in which one gets to see the entire trajectory of a hidden variable, rather than just a single measurement outcome. I showed that this generalization would let us solve problems somewhat beyond what we think we can do with a “standard” quantum computer. In particular, we could solve the collision problem in O(1) queries, efficiently solve Graph Isomorphism (and all other problems in the Statistical Zero-Knowledge class), and search an N-element list in only ~N1/3 steps, rather than the ~N1/2 steps of Grover’s search algorithm. That part of the paper remains fine!

On the other hand, at the end of the paper, I also gave a brief argument to show that, even in the hidden-variable model, ~N1/3 steps are required to search an N-element list. But Mitchell Lee and Adam Bouland discovered that that argument is wrong: it fails to account for all the possible ways that an algorithm could exploit the correlations between the hidden variable’s values at different moments in time. (I’ve previously discussed this error in other blog posts, as well as in the latest edition of Quantum Computing Since Democritus.)

If we suitably restrict the hidden-variable theory, then we can correctly prove a lower bound of ~N1/4, or even (with strong enough assumptions) ~N1/3; and we do that in the forthcoming paper. Even with no restrictions, as far as we know an ~N1/3 lower bound for search with hidden variables remains true. But it now looks like proving it will require a major advance in our understanding of hidden-variable theories: for example, a proof that the “Schrödinger theory” is robust to small perturbations, which I’d given as the main open problem in my 2005 paper.

As if that weren’t enough, in my 2003 paper Quantum Certificate Complexity, I claimed (as a side remark) that one could get a recursive Boolean function f with an asymptotic gap between the block sensitivity bs(f) and the randomized certificate complexity RC(f). However, two and a half years ago, Avishay Tal discovered that this didn’t work, because block sensitivity doesn’t behave nicely under composition.  (In assuming it did, I was propagating an error introduced earlier by Wegener and Zádori.)  More broadly, Avishay showed that there is no recursively-defined Boolean function with an asymptotic gap between bs(f) and RC(f). On the other hand, if we just want some Boolean function with an asymptotic gap between bs(f) and RC(f), then Raghav Kulkarni observed that we can use a non-recursive function introduced by Xiaoming Sun, which yields bs(f)≈N3/7 and RC(f)≈N4/7. This is actually a larger separation than the one I’d wrongly claimed.

Now that I’ve come clean about all these things, hopefully the healing can begin at last.

Lens of Computation on the Sciences

November 25th, 2014

This weekend, the Institute for Advanced Study in Princeton hosted a workshop on the “Lens of Computation in the Sciences,” which was organized by Avi Wigderson, and was meant to showcase theoretical computer science’s imperialistic ambitions to transform every other field.  I was proud to speak at the workshop, representing CS theory’s designs on physics.  But videos of all four of the talks are now available, and all are worth checking out:

Unfortunately, the videos were slow to buffer when I last tried it.  While you’re waiting, you could also check my PowerPoint slides, though they overlap considerably with my previous talks.  (As always, if you can’t read PowerPoint, then go ask another reader of this blog to convert the file into a format you like.)

Thanks so much to Avi, and everyone else at IAS, for organizing an awesome workshop!

Kuperberg’s parable

November 23rd, 2014

Recently, longtime friend-of-the-blog Greg Kuperberg wrote a Facebook post that, with Greg’s kind permission, I’m sharing here.


A parable about pseudo-skepticism in response to climate science, and science in general.

Doctor: You ought to stop smoking, among other reasons because smoking causes lung cancer.
Patient: Are you sure? I like to smoke. It also creates jobs.
D: Yes, the science is settled.
P: All right, if the science is settled, can you tell me when I will get lung cancer if I continue to smoke?
D: No, of course not, it’s not that precise.
P: Okay, how many cigarettes can I safely smoke?
D: I can’t tell you that, although I wouldn’t recommend smoking at all.
P: Do you know that I will get lung cancer at all no matter how much I smoke?
D: No, it’s a statistical risk. But smoking also causes heart disease.
P: I certainly know smokers with heart disease, but I also know non-smokers with heart disease. Even if I do get heart disease, would you really know that it’s because I smoke?
D: No, not necessarily; it’s a statistical effect.
P: If it’s statistical, then you do know that correlation is not causation, right?
D: Yes, but you can also see the direct effect of smoking on lungs of smokers in autopsies.
P: Some of whom lived a long time, you already admitted.
D: Yes, but there is a lot of research to back this up.
P: Look, I’m not a research scientist, I’m interested in my case. You have an extended medical record for me with X-rays, CAT scans, blood tests, you name it. You can gather more data about me if you like. Yet you’re hedging everything you have to say.
D: Of course, there’s always more to learn about the human body. But it’s a settled recommendation that smoking is bad for you.
P: It sounds like the science is anything but settled. I’m not interested in hypothetical recommendations. Why don’t you get back to me when you actually know what you’re talking about. In the meantime, I will continue to smoke, because as I said, I enjoy it. And by the way, since you’re so concerned about my health, I believe in healthy skepticism.