Archive for the ‘Announcements’ Category

Talk, be merry, and be rational

Monday, November 23rd, 2015

Yesterday I wrote a statement on behalf of a Scott Alexander SlateStarCodex/rationalist meetup, which happened last night at MIT (in the same room where I teach my graduate class), and which I’d really wanted to attend but couldn’t.  I figured I’d share the statement here:

I had been looking forward to attending tonight’s MIT SlateStarCodex meetup as I hardly ever look forward to anything. Alas, I’m now stuck in Chicago, with my flight cancelled due to snow, and with all flights for the next day booked up. But instead of continuing to be depressed about it, I’ve decided to be happy that this meetup is even happening at all—that there’s a community of people who can read, let’s say, a hypothetical debate moderator questioning Ben Carson about what it’s like to be a severed half-brain, and simply be amused, instead of silently trying to figure out who benefits from the post and which tribe the writer belongs to. (And yes, I know: the answer is the gray tribe.) And you can find this community anywhere—even in Cambridge, Massachusetts! Look, I spend a lot of time online, just getting more and more upset reading social justice debates that are full of people calling each other douchebags without even being able to state anything in the same galactic supercluster as the other side’s case. And then what gives me hope for humanity is to click over to the slatestarcodex tab, and to see all the hundreds of comments (way more than my blog gets) by people who disagree with each other but who all basically get it, who all have minds that don’t make me despair. And to realize that, when Scott Alexander calls an SSC meetup, he can fill a room just about anywhere … well, at least anywhere I would visit. So talk, be merry, and be rational.

I’m now back in town, and told by people who attended the meetup that it was crowded, disorganized, and great.  And now I’m off to Harvard, to attend the other Scott A.’s talk “How To Ruin A Perfectly Good Randomized Controlled Trial.”

Update (Nov. 24) Scott Alexander’s talk at Harvard last night was one of the finest talks I’ve ever attended. He was introduced to rapturous applause as simply “the best blogger on the Internet,” and as finally an important speaker, in a talk series that had previously wasted everyone’s time with the likes of Steven Pinker and Peter Singer. (Scott demurred that his most notable accomplishment in life was giving the talk at Harvard that he was just now giving.) The actual content, as Scott warned from the outset, was “just” a small subset of a basic statistics course, but Scott brought each point alive with numerous recent examples, from psychiatry, pharmacology, and social sciences, where bad statistics or misinterpretations of statistics were accepted by nearly everyone and used to set policy. (E.g., Alcoholics Anonymous groups that claimed an “over 95%” success rate, because the people who relapsed were kicked out partway through and not counted toward the total.) Most impressively, Scott leapt immediately into the meat, ended after 20 minutes, and then spent the next two hours just taking questions. Scott is publicity-shy, but I hope for others’ sake that video of the talk will eventually make its way online.

Then, after the talk, I had the honor of meeting two fellow Boston-area rationalist bloggers, Kate Donovan and Jesse Galef. Yes, I said “fellow”: for almost a decade, I’ve considered myself on the fringes of the “rationalist movement.” I’d hang out a lot with skeptic/effective-altruist/transhumanist/LessWrong/OvercomingBias people (who are increasingly now SlateStarCodex people), read their blogs, listen and respond to their arguments, answer their CS theory questions. But I was always vaguely uncomfortable identifying myself with any group that even seemed to define itself by how rational it was compared to everyone else (even if the rationalists constantly qualified their self-designation with “aspiring”!). Also, my rationalist friends seemed overly interested in questions like how to prevent malevolent AIs from taking over the world, which I tend to think we lack the tools to make much progress on right now (though, like with many other remote possibilities, I’m happy for some people to work on them and see if they find anything interesting).

So, what changed? Well, in the debates about social justice, public shaming, etc. that have swept across the Internet these past few years, it seems to me that my rationalist friends have proven themselves able to weigh opposing arguments, examine their own shortcomings, resist groupthink and hysteria from both sides, and attack ideas rather than people, in a way that the wider society—and most depressingly to me, the “enlightened, liberal” part of society—has often failed. In a real-world test (“real-world,” in this context, meaning social media…), the rationalists have walked the walk and rationaled the rational, and thus they’ve given me no choice but to stand up and be counted as one of them.

Have a great Thanksgiving, those of you in the US!

Another Update: Dana, Lily, and I had the honor of having Scott Alexander over for dinner tonight. I found this genius of human nature, who took so much flak last year for defending me, to be completely uninterested in discussing anything related to social justice or online shaming. Instead, his gaze was fixed on the eternal: he just wanted to grill me all evening about physics and math and epistemology. Having recently read this Nature News article by Ron Cowen, he kept asking me things like: “you say that in quantum gravity, spacetime itself is supposed to dissolve into some sort of network of qubits. Well then, how does each qubit know which other qubits it’s supposed to be connected to? Are there additional qubits to specify the connectivity pattern? If so, then doesn’t that cause an infinite regress?” I handwaved something about AdS/CFT, where a dynamic spacetime is supposed to emerge from an ordinary quantum theory on a fixed background specified in advance. But I added that, in some sense, he had rediscovered the whole problem of quantum gravity that’s confused everyone for almost a century: if quantum mechanics presupposes a causal structure on the qubits or whatever other objects it talks about, then how do you write down a quantum theory of the causal structures themselves?

I’m sure there’s a lesson in here somewhere about what I should spend my time on.

G. Phi. Fo. Fum.

Wednesday, November 4th, 2015

Update (Nov. 17): Video of Laci’s first talk is now available.

Breaking News (Nov. 12): Jeremy Kun has written up a phenomenal summary of Babai’s first lecture.  I haven’t carefully studied all of it, and in any case, there are many missing details to be filled in later (Babai told Kun that the preprint will be available “soon, soon!”).  But from the summary, four points stood out to me:

  1. Babai actually claims a quasipolynomial-time algorithm for an interestingly more general problem than graph isomorphism, called string isomorphism.  This was already in the abstract, but googling didn’t reveal what string isomorphism was.  So, OK, here’s what it is: you’re given two strings x and y over some finite alphabet, as well as the generators of a group G of permutations of the string indices.  The problem is to determine whether you can transform x to y by applying a permutation in G.  Or even more generally: given a string x, find a full set of generators for the subgroup of G that fixes x.  See Kun’s post for the straightforward reductions from GI to these group-theoretic problems.
  2. As was hinted in the abstract, in Babai’s analysis of his algorithm, there’s one step that relies on a statement whose only known proof depends on the Classification of Finite Simple Groups.  (Thus, it’s not the algorithm itself requires iterating through all the sporadic simple groups or anything like that; this only shows up in the correctness proof.)  This is not the first-ever computer-science application of the Classification of Finite Simple Groups (indeed, Babai himself has some previous ones), but it’s certainly the most dramatic.
  3. In previous work on GI, the Johnson graph emerged over and over as a forehead-bangingly hard case that caused numerous algorithms to fail.  In the new work, it looks like Babai’s central technical innovation is to show that, in some sense, the Johnson graph is the only obstruction to taking the divide-and-conquer approaches that people that had tried before, and making them run in quasipolynomial time.  I.e., in each step of the recursion, either you can find a Johnson graph on a large fraction of the vertices and handle it specially, or else you can do something that works whenever there’s not a Johnson graph on a large fraction of the vertices.  Babai calls this “split-or-Johnson.”
  4. Babai stressed that in some sense, his new algorithm is the culmination of a program laid out by Eugene Luks in 1982.  Now, the Classification of Finite Simple Groups was also more-or-less completed in the early 1980s.  To my mind, this raises a fascinating socio-mathematical question: which aspects of the new work, if any, could not have been done in the early 80s, possibly by Babai or Luks themselves?  what is it that needed another 30 years?  If the answer turns out to be “nothing,” then to me that’s an astounding illustration of the role of the individual in mathematical progress.  As in: Laci was nice enough to take a third-of-a-century break between his and Luks’ work in the early 80s, and the “natural next step” in their program … and still no one managed to use that break to beat him to the next step!

Earlier today, I was tipped off to what might be the theoretical computer science result of the decade.  My source asked me not to break the news on this blog—but since other theory bloggers (and twitterers) are now covering the story, I guess the graph is out of the Babai.

According to the University of Chicago’s theory seminar calendar, on Tuesday of next week (November 10), the legendary Laszlo Babai will be giving a talk about a new algorithm that solves the graph isomorphism problem in quasipolynomial time.  The previous fastest algorithm to decide whether two n-vertex graphs G and H are isomorphic—by Babai and Luks, back in 1983—ran in exp(√(n log n)) time.  If we credit the announcement, Babai has now gotten that down to exp(polylog(n)), putting one of the central problems of computer science “just barely above P.”  (For years, I’ve answered questions on this blog about the status of graph isomorphism—would I bet that it’s in BQP? in coNP? etc.—by saying that, as far as I and many others are concerned, it might as well just be in P.  Of course I’m happy to reaffirm that conjecture tonight.)

Next week, I assume, Laci will lecture to a packed house; then the experts will race to unpack the details.  Until then, we probably need to sit tight; I don’t know any more than what’s in the abstract.  For now, I’m delighted if commenters want to share general thoughts or questions about graph isomorphism (and I’ll try to answer what I can), but I won’t allow uninformed speculations or rumors about the details of the new result—not until Laci has had a chance to speak.

Update (Nov. 5): While we all wait with bated breath for more details, you can amuse yourself with the talk I gave at Laci’s 60th birthday conference five years ago.

Also, a comment of mine that I should probably promote to the main post:

Dana points out to me that non-native English speakers might not get the staggeringly clever pun in this post’s title (hey, it was the best I could do on a deadline).

So, alright, fee fi fo fum is what the approaching giant bellows in Jack and the Beanstalk. It means something big is on the horizon. Also, G is a graph, and Phi is an isomorphism.

Update (Nov. 12): So, Laci gave his talk. Video was made but does not appear to be available yet. However, Gabriel Gaster, who was in attendance, graciously live-tweeted everything. Here’s a Storify of the live-tweets. (What’s a “Storify”?)

Six announcements

Monday, September 21st, 2015
  1. I did a podcast interview with Julia Galef for her series “Rationally Speaking.”  See also here for the transcript (which I read rather than having to listen to myself stutter).  The interview is all about Aumann’s Theorem, and whether rational people can agree to disagree.  It covers a lot of the same ground as my recent post on the same topic, except with less technical detail about agreement theory and more … well, agreement.  At Julia’s suggestion, we’re planning to do a follow-up podcast about the particular intractability of online disagreements.  I feel confident that we’ll solve that problem once and for all.  (Update: Also check out this YouTube video, where Julia offers additional thoughts about what we discussed.)
  2. When Julia asked me to recommend a book at the end of the interview, I picked probably my favorite contemporary novel: The Mind-Body Problem by Rebecca Newberger Goldstein.  Embarrassingly, I hadn’t realized that Rebecca had already been on Julia’s show twice as a guest!  Anyway, one of the thrills of my life over the last year has been to get to know Rebecca a little, as well as her husband, who’s some guy named Steve Pinker.  Like, they both live right here in Boston!  You can talk to them!  I was especially pleased two weeks ago to learn that Rebecca won the National Humanities Medal—as I told Julia, Rebecca Goldstein getting a medal at the White House is the sort of thing I imagine happening in my ideal fantasy world, making it a pleasant surprise that it happened in this one.  Huge congratulations to Rebecca!
  3. The NSA has released probably its most explicit public statement so far about its plans to move to quantum-resistant cryptography.  For more see Bruce Schneier’s Crypto-Gram.  Hat tip for this item goes to reader Ole Aamot, one of the only people I’ve ever encountered whose name alphabetically precedes mine.
  4. Last Tuesday, I got to hear Ayaan Hirsi Ali speak at MIT about her new book, Heretic, and then spend almost an hour talking to students who had come to argue with her.  I found her clear, articulate, and courageous (as I guess one has to be in her line of work, even with armed cops on either side of the lecture hall).  After the shameful decision of Brandeis in caving in to pressure and cancelling Hirsi Ali’s commencement speech, I thought it spoke well of MIT that they let her speak at all.  The bar shouldn’t be that low, but it is.
  5. From far away on the political spectrum, I also heard Noam Chomsky talk last week (my first time hearing him live), about the current state of linguistics.  Much of the talk, it struck me, could have been given in the 1950s with essentially zero change (and I suspect Chomsky would agree), though a few parts of it were newer, such as the speculation that human languages have many of the features they do in order to minimize the amount of computation that the speaker needs to perform.  The talk was full of declarations that there had been no useful work whatsoever on various questions (e.g., about the evolutionary function of language), that they were total mysteries and would perhaps remain total mysteries forever.
  6. Many of you have surely heard by now that Terry Tao solved the Erdös Discrepancy Problem, by showing that for every infinite sequence of heads and tails and every positive integer C, there’s a positive integer k such that, if you look at the subsequence formed by every kth flip, there comes a point where the heads outnumber tails or vice versa by at least C.  This resolves a problem that’s been open for more than 80 years.  For more details, see this post by Timothy Gowers.  Notably, Tao’s proof builds, in part, on a recent Polymath collaborative online effort.  It was a big deal last year when Konev and Lisitsa used a SAT-solver to prove that there’s always a subsequence with discrepancy at least 3; Tao’s result now improves on that bound by ∞.

6-photon BosonSampling

Wednesday, August 19th, 2015

The news is more-or-less what the title says!

In Science, a group led by Anthony Laing at Bristol has now reported BosonSampling with 6 photons, beating their own previous record of 5 photons, as well as the earlier record of 4 photons achieved a few years ago by the Walmsley group at Oxford (as well as the 3-photon experiments done by groups around the world).  I only learned the big news from a commenter on this blog, after the paper was already published (protip: if you’ve pushed forward the BosonSampling frontier, feel free to shoot me an email about it).

As several people explain in the comments, the main advance in the paper is arguably not increasing the number of photons, but rather the fact that the device is completely reconfigurable: you can try hundreds of different unitary transformations with the same chip.  In addition, the 3-photon results have an unprecedentedly high fidelity (about 95%).

The 6-photon results are, of course, consistent with quantum mechanics: the transition amplitudes are indeed given by permanents of 6×6 complex matrices.  Key sentence:

After collecting 15 sixfold coincidence events, a confidence of P = 0.998 was determined that these are drawn from a quantum (not classical) distribution.

No one said scaling BosonSampling would be easy: I’m guessing that it took weeks of data-gathering to get those 15 coincidence events.  Scaling up further will probably require improvements to the sources.

There’s also a caveat: their initial state consisted of 2 modes with 3 photons each, as opposed to what we really want, which is 6 modes with 1 photon each.  (Likewise, in the Walmsley group’s 4-photon experiments, the initial state consisted of 2 modes with 2 photons each.)  If the number of modes stayed 2 forever, then the output distributions would remain easy to sample with a classical computer no matter how many photons we had, since we’d then get permanents of matrices with only 2 distinct rows.  So “scaling up” needs to mean increasing not only the number of photons, but also the number of sources.

Nevertheless, this is an obvious step forward, and it came sooner than I expected.  Huge congratulations to the authors on their accomplishment!

But you might ask: given that 6×6 permanents are still pretty easy for a classical computer (the more so when the matrices have only 2 distinct rows), why should anyone care?  Well, the new result has major implications for what I’ve always regarded as the central goal of quantum computing research, much more important than breaking RSA or Grover search or even quantum simulation: namely, getting Gil Kalai to admit he was wrong.  Gil is on record, repeatedly, on this blog as well as his (see for example here), as saying that he doesn’t think BosonSampling will ever be possible even with 7 or 8 photons.  I don’t know whether the 6-photon result is giving him second thoughts (or sixth thoughts?) about that prediction.

Jacob Bekenstein (1947-2015)

Tuesday, August 18th, 2015

Today I learned the sad news that Jacob Bekenstein, one of the great theoretical physicists of our time, passed away at the too-early age of 68.

Everyone knows what a big deal it was when Stephen Hawking discovered in 1975 that black holes radiate.  Bekenstein was the guy who, as a grad student in Princeton in the early 1970s, was already raving about black holes having nonzero entropy and temperature, and satisfying the Second Law of Thermodynamics—something just about everyone, including Hawking, considered nuts at the time.  It was, as I understand it, Hawking’s failed attempt to prove Bekenstein wrong that led to Hawking’s discovery of the Hawking radiation, and thence to the modern picture of black holes.

In the decades since, Bekenstein continued to prove ingenious physical inequalities, often using thought experiments involving black holes.  The most famous of these, the Bekenstein bound, says that the number of bits that can be stored in any bounded physical system is finite, and is upper-bounded by ~2.6×1043 MR, where M is the system’s mass in kilograms and R is its radius in meters.  (This bound is saturated by black holes, and only by black holes, which therefore emerge as the most compact possible storage medium—though probably not the best for retrieval!)  Bekenstein’s lectures were models of clarity and rigor: at conferences full of audacious speculations, he stood out to my non-expert eyes as someone who was simply trying to follow chains of logic from accepted physical principles, however mind-bogglingly far those chains led but no further.

I first met Bekenstein in 2003, when I was a grad student spending a semester at Hebrew University in Jerusalem.  I was struck by the kindness he showed a 21-year-old nobody, who wasn’t even a physics student, coming to bother him.  Not only did he listen patiently to my blather about applying computational complexity to physics, he said that of course physics should ultimately aim to understand everything as the output of some computer program, that he too was thinking in terms of computation when he studied black-hole entropy.  I remember pondering the fact that the greatest reductionist I’d ever met was wearing a yarmulke—and then scolding myself for wasting precious brain-cycles on such a trivial thought when there was science to discuss.  I met Bekenstein maybe four or five more times on visits to Israel, most recently a year and a half ago, when we shared walks to and from the hotel at a firewall workshop at the Weizmann Institute.  He was unfailingly warm, modest, and generous—totally devoid of the egotism that I’ve heard can occasionally afflict people of his stature.  Now, much like with the qubits hitting the event horizon, the information that comprised Jacob Bekenstein might seem to be gone, but it remains woven into the cosmos.

Introducing some British people to P vs. NP

Wednesday, July 22nd, 2015

Here’s a 5-minute interview that I did with The Naked Scientists (a radio show syndicated by the BBC, and no, I’m not sure why it’s called that), explaining the P vs. NP problem.  For readers of this blog, there won’t be anything new here, but, well … you might enjoy the rest of the hour-long programme [sic], which also includes segments about a few other Clay Millennium problems (the Riemann Hypothesis, Navier-Stokes, and Poincaré), as well as a segment about fat fish that live in caves and gorge themselves on food on the rare occasions when it becomes available, and which turn out to share a gene variant with humans with similar tendencies.

Quantum query complexity: the other shoe drops

Tuesday, June 30th, 2015

Two weeks ago I blogged about a breakthrough in query complexity: namely, the refutation by Ambainis et al. of a whole slew of conjectures that had stood for decades (and that I mostly believed, and that had helped draw me into theoretical computer science as a teenager) about the largest possible gaps between various complexity measures for total Boolean functions. Specifically, Ambainis et al. built on a recent example of Göös, Pitassi, and Watson to construct bizarre Boolean functions f with, among other things, near-quadratic gaps between D(f) and R0(f) (where D is deterministic query complexity and R0 is zero-error randomized query complexity), near-1.5th-power gaps between R0(f) and R(f) (where R is bounded-error randomized query complexity), and near-4th-power gaps between D(f) and Q(f) (where Q is bounded-error quantum query complexity). See my previous post for more about the definitions of these concepts and the significance of the results (and note also that Mukhopadhyay and Sanyal independently obtained weaker results).

Because my mental world was in such upheaval, in that earlier post I took pains to point out one thing that Ambainis et al. hadn’t done: namely, they still hadn’t shown any super-quadratic separation between R(f) and Q(f), for any total Boolean function f. (Recall that a total Boolean function, f:{0,1}n→{0,1}, is one that’s defined for all 2n possible input strings x∈{0,1}n. Meanwhile, a partial Boolean function is one where there’s some promise on x: for example, that x encodes a periodic sequence. When you phrase them in the query complexity model, Shor’s algorithm and other quantum algorithms achieving exponential speedups work only for partial functions, not for total ones. Indeed, a famous result of Beals et al. from 1998 says that D(f)=O(Q(f)6) for all total functions f.)

So, clinging to a slender reed of sanity, I said it “remains at least a plausible conjecture” that, if you insist on a fair comparison—i.e., bounded-error quantum versus bounded-error randomized—then the biggest speedup quantum algorithms can ever give you over classical ones, for total Boolean functions, is the square-root speedup that Grover’s algorithm easily achieves for the n-bit OR function.

Today, I can proudly report that my PhD student, Shalev Ben-David, has refuted that conjecture as well.  Building on the Göös et al. and Ambainis et al. work, but adding a new twist to it, Shalev has constructed a total Boolean function f such that R(f) grows roughly like Q(f)2.5 (yes, that’s Q(f) to the 2.5th power). Furthermore, if a conjecture that Ambainis and I made in our recent “Forrelation” paper is correct—namely, that a problem called “k-fold Forrelation” has randomized query complexity roughly Ω(n1-1/k)—then one would get nearly a cubic gap between R(f) and Q(f).

The reason I found this question so interesting is that it seemed obvious to me that, to produce a super-quadratic separation between R and Q, one would need a fundamentally new kind of quantum algorithm: one that was unlike Simon’s and Shor’s algorithms in that it worked for total functions, but also unlike Grover’s algorithm in that it didn’t hit some impassable barrier at the square root of the classical running time.

Flummoxing my expectations once again, Shalev produced the super-quadratic separation, but not by designing any new quantum algorithm. Instead, he cleverly engineered a Boolean function for which you can use a combination of Grover’s algorithm and the Forrelation algorithm (or any other quantum algorithm that gives a huge speedup for some partial Boolean function—Forrelation is just the maximal example), to get an overall speedup that’s a little more than quadratic, while still keeping your Boolean function total. I’ll let you read Shalev’s short paper for the details, but briefly, it once again uses the Göös et al. / Ambainis et al. trick of defining a Boolean function that equals 1 if and only if the input string contains some hidden substructure, and the hidden substructure also contains a pointer to a “certificate” that lets you quickly verify that the hidden substructure was indeed there. You can use a super-fast algorithm—let’s say, a quantum algorithm designed for partial functions—to find the hidden substructure assuming it’s there. If you don’t find it, you can simply output 0. But if you do find it (or think you found it), then you can use the certificate, together with Grover’s algorithm, to confirm that you weren’t somehow misled, and that the substructure really was there. This checking step ensures that the function remains total.

Are there further separations to be found this way? Almost certainly! Indeed, Shalev, Robin Kothari, and I have already found some more things (as well as different/simpler proofs of known separations), though nothing quite as exciting as the above.

Update (July 1): Ronald de Wolf points out in the comments that this “trust-but-verify” trick, for designing total Boolean functions with unexpectedly low quantum query complexities, was also used in a recent paper by himself and Ambainis (while Ashley Montanaro points out that a similar trick was used even earlier, in a different context, by Le Gall).  What’s surprising, you might say, is that it took as long as it did for people to realize how many applications this trick has.

Update (July 2): In conversation with Robin Kothari and Cedric Lin, I realized that Shalev’s superquadratic separation between R and Q, combined with a recent result of Lin and Lin, resolves another open problem that had bothered me since 2001 or so. Given a Boolean function f, define the “projective quantum query complexity,” or P(f), to be the minimum number of queries made by a bounded-error quantum algorithm, in which the answer register gets immediately measured after each query. This is a model of quantum algorithms that’s powerful enough to capture (for example) Simon’s and Shor’s algorithms, but not Grover’s algorithm. Indeed, one might wonder whether there’s any total Boolean function for which P(f) is asymptotically smaller than R(f)—that’s the question I wondered about around 2001, and that I discussed with Elham Kashefi. Now, by using an argument based on the “Vaidman bomb,” Lin and Lin recently proved the fascinating result that P(f)=O(Q(f)2) for all functions f, partial or total. But, combining with Shalev’s result that there exists a total f for which R(f)=Ω(Q(f)2.5), we get that there’s a total f for which R(f)=Ω(P(f)1.25). In the other direction, the best I know is that P(f)=Ω(bs(f)) and therefore R(f)=O(P(f)3).

Five announcements

Saturday, May 16th, 2015

1. Sanjeev Arora sent me a heads-up that there’s a discussion about the future of the STOC conference  at the Windows on Theory blog—in particular, about the idea of turning STOC into a longer “CS theory festival.”  If you have opinions about this, don’t miss the chance to make your voice heard.

2. Back in January, I blogged about a new quantum optimization algorithm by Farhi, Goldstone, and Gutmann, which was notable for being, as far as anyone could tell, the first quantum algorithm to achieve a provably better approximation ratio than the best-known classical algorithm for an NP-hard optimization problem.  Today, I report that a fearsome list of authors—Boaz Barak, Ankur Moitra, Ryan O’Donnell, Prasad Raghavendra, Oded Regev, David Steurer, Luca Trevisan, Aravindan Vijayaraghavan, David Witmer, and John Wright—has put out an eagerly-awaited paper that gives a classical algorithm for the same problem, with better performance than the quantum algorithm’s.  (They write that this “improves both qualitatively and quantitatively” on Farhi et al.’s work; I assume “qualitatively” refers to the fact that the new algorithm is classical.)  What happened, apparently, is that after I blogged (with enthusiasm) about the Farhi et al. result, a bunch of classical complexity theorists read my post and decided independently that they could match or beat the quantum algorithm’s performance classically; then they found out about each other and decided to merge their efforts.  I’m proud to say that this isn’t the first example of this blog catalyzing actual research progress, though it’s probably the best example so far.  [Update: Luca Trevisan now has a great post explaining what happened in much more detail, entitled “How Many Theoreticians Does It Take to Approximate Max 3Lin?”]

Another update: Farhi et al. have posted a new version of their paper, in which they can almost match the performance of the classical algorithm using their quantum algorithm.

3. Jennifer Ouellette has a wonderful article in Quanta magazine about recent progress in AdS/MERA (i.e., “the emergence of spacetime from entanglement”), centered around the ideas of Brian Swingle.  This is one of the main things that I’d love to understand better right now—if I succeed even partially, you’ll know because I’ll write a blog post trying to explain it to others.  See also this blog post by Sean Carroll (about this paper by Ning Bao et al.), and this paper by Pastawski, Yoshida, Harlow, and Preskill, which explicitly mines the AdS/CFT correspondence for examples of quantum error-correcting codes.

4. Celebrity rationalist Julia Galef, who I had the great honor of meeting recently, has a podcast interview with Sean Carroll about why Carroll accepts the many-worlds interpretation.  (Or if, like me, you prefer the written word to the spoken one, click here for a full transcript.)  Unfortunately, Sean is given the opportunity at the end of the interview to recommend one science book to his listeners—just one!—but he squanders it by plugging some weird, self-indulgent thing called Quantum Computing Since Democritus.  Julia also has a YouTube video about what she learned from the interview, but I haven’t yet watched it (is there a transcript?).

5. I came across an insightful if meandering essay about nerd culture by Meredith L. Patterson.  In particular, noticing how the term “nerd” has been co-opted by normal, socially-skilled people, who’ve quickly set about remaking nerd social norms to make them identical to the rest of the world’s norms, Patterson coins the term “weird-nerd” to describe people like herself, who are still nerds in the original sense and who don’t see nerd culture as something horribly, irreparably broken.  As she writes: “We’ll start to feel less defensive when we get some indication — any indication — that our critics understand what parts of our culture we don’t want to lose and why we don’t want to lose them.”  (But is this the start of a linguistic treadmill?  Will we eventually need to talk about weird-weird-nerds, etc.?)

Two papers

Tuesday, April 21st, 2015

Just to get myself back into the habit of blogging:

For those of you who don’t read Lance’s and Bill’s blog, there was a pretty significant breakthrough in complexity theory announced last week.  (And yes, I’m now spending one of the two or so uses of the word “breakthrough” that I allow myself per year—wait, did I just spend the second one with this sentence?)  Ben Rossman (a former MIT PhD student whose thesis committee I was honored to serve on), Rocco Servedio, and Li-Yang Tan have now shown that the polynomial hierarchy is infinite relative to a random oracle, thereby solving the main open problem from Johan Håstad’s 1986 PhD thesis.  While it feels silly even to mention it, the best previous result in this direction was to separate PNP from Σ2P relative to a random oracle, which I did in my Counterexample to the Generalized Linial-Nisan Conjecture paper.  In some sense Rossman et al. infinitely improve on that (using completely different techniques).  Proving their result boils down to proving a new lower bound on the sizes of constant-depth circuits.  Basically, they need to show that, for every k, there are problems that can be solved by small circuits with k layers of AND, OR, and NOT gates, but for which the answer can’t even be guessed, noticeably better than chance, by any small circuit with only k-1 layers of AND, OR, and NOT gates.  They achieve that using a new generalization of the method of random restrictions.  Congratulations to Ben, Rocco, and Li-Yang!

Meanwhile, if you want to know what I’ve been doing for the last couple months, one answer is contained in this 68-page labor of love preprint by me and my superb PhD students Daniel Grier and Luke Schaeffer.  There we give a full classification of all possible sets of classical reversible gates acting on bits (like the Fredkin, Toffoli, and CNOT gates), as well as a linear-time algorithm to decide whether one reversible gate generates another one (previously, that problem wasn’t even known to be decidable).  We thereby completely answer a question that basically no one was asking, although I don’t understand why not.

The Turing movie

Tuesday, 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.