The Turing movie

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.

87 Responses to “The Turing movie”

  1. randomnumber53 Says:

    When ever I hear somebody correcting somebody else’s pronunciation of nuclear from “nuke-yooler” to “nu-clear,” I always point out that it is actually pronounced “nuke-Euler.”

  2. Gerben Says:

    Would you agree that the amount of influence von Neumann had on US military strategy is an example of “political and military power” entrusted to a mathematician that trumps that of what the movie makes us believe that Turing had?

  3. Raoul Ohio Says:

    The writers probably had a list of famous papers, and they could deal with the words: “On Computable Numbers” and “Computing Machinery and Intelligence”, but “Riemann zeta function” sounded too far over the edge!

    I am also in that boat. While I enjoy learning about the famous functions of mathematical physics (Mathieu, generalized hypergeometric, etc.), every time I try to understand the RZF I think I better try again later, with stronger coffee.

  4. Ashley Says:

    I winced at “Euler” too. But for me the most egregious problem with the film was the point you mention about his naming the computer “Christopher”: Turing is presented as a sad, lonely obsessive whose life is essentially over after his brief moment to shine during the war. This seems ridiculously far from the truth, and conforms to the rule that scientists and mathematicians in film can’t be portrayed as having happy, fulfilling lives, but only as either evil, or tortured, geniuses. I suppose we should be glad that the director didn’t go for the former option…

  5. Scott Says:

    Gerben #2: That’s a good point; von Neumann is possibly history’s best candidate for a counterexample. Even then, though, von Neumann’s “power” was indirect and conceptual, not direct and operational (he wouldn’t be deciding whether to launch missiles or not launch them). And of course, if we’re going to count mathematicians with indirect influence, there’s also Stanislaw Ulam who co-designed the hydrogen bomb, etc. Showing Alan Turing entrusted with operational power was sufficiently fantastical as to break me out of the movie.

  6. Alex Says:

    “Counterexamples, anyone?”

    Well clearly the film Antitrust.

  7. Michael Dixon Says:

    Another counter example:

    Travelling Salesman (2012 film)

  8. AfterMath Says:

    Thanks for this writeup. I still intend to see this movie as Turing has been a hero of mine since learning about the power of Turing machines way way back. It wasn’t until recently that I learned about the sequence of events that led to his death. Knowing of the inaccuracies in the film will help me from giving it too much weight, but I’ve always thought it a good rule of action to not put too much faith in Hollywood.

    But it is a good thing that a mathematician is receiving this much national attention.

  9. Rahul Says:

    Wasn’t there a French head of state, who was earlier in life, an academic mathematician?

    Perhaps he had had “the most military and political power ever entrusted to a mathematician.”

  10. Scott Says:

    Rahul #9: Yes, Paul Painlevé. I guess he’s another good contender.

  11. Fred Says:

    There’s also a documentary on Alan Turing on Netflix streaming called CODEBREAKER (they focus quite a bit on his childhood and homosexuality conviction).

  12. Narad Says:

    Another powerful mathematician: Lazare Carnot.

  13. GASARCH Says:

    1) Analog to Broadchurch/Gracepoint: A perfectly good British mystery,
    Broadchurch, redone as an american mystery Gracepoint. Why not just get the original? We are in the globalization age! Why even make The Imitation Game if there is already a good Turing Movie out there? I ask non rhetorically . (Note- David Tennant played the same role in both Broadchurch and Gracepoint. He didn’t have to memorize new lines, but he had to have to switch accents.)

    2) The story “the people on the ground know whats going on and have a conflict with the suits” is often told even when its not true. Same thing in the TV show Masters of Sex- their college DID support them to some extent.

    3) Its been said that History is written by the winners and that is true. But another powerful force is that history is SIMPLIFIED— there are conflicts where its clear who was right, fictional quotes (Patrick Henry never said `Give me liberty or give me death’) and fictional stories (Charles Drew, the black Doctor that helped make Blood transfusions possible did not die in a hospital that would not give blacks such transfusions) become true. The timing on Turing’s Suicide does make you wonder about the connection to his treatment.

    4) Angela Merkel has a PhD in Physical Chemistry.

  14. vzn Says:

    tried to see it weeks ago on release but this movie is currently hard to find in theatres, it was in limited release in only some cities & last I heard it wasnt going to expand until around xmas. its on my must-see list at the theatre which is usually not a very long list.
    great to see a lot of historical knowledge by anyone to rebut any “inaccuracies” in the movie (and ofc a hardcore/ pro well-educated/informed CS type is even better) although of course hollywood is not interested exactly in getting all the historical details right, because obviously it would be far more boring in many ways… as it seems many hardcore science geeks fail to grasp (and sometimes even hollywood workers fail to grasp it, eg recently read wired article on how intense verisimilitude to the black hole was the goal for some scenes in Interstellar). to me its a small miracle this Turing story finally made it to the big screen, have been waiting a long time, always thought it was highly worthy. similar to other great math movies in theme eg “beautiful mind”, “goodwill hunting” etc… also across the pond, the story of Feynman et al working on the atom bomb surely deserves some hollywood treatment some day. cant wait to see how they botch that also. lol. thx for compiling the other links on reactions. see also imitation game/ joy of code 2014 TMachine blog

  15. eitan bachmat Says:

    Ever since Archimedes and perhaps earlier, mathematicians and other scientists were essential in the development of useful war related technology, and many scientific and technological innovations are war related, for example, WWII crypto efforts in the US were instrumental in Shannon’s development of information and communication theopry.
    However, politicians and other social leaders/illusionists always made sure that they control things, and I doubt that Turing’s story is any different, so essential? certainly, powerful? I doubt it.

  16. Nick Read Says:

    Hi Scott,

    Thanks for this post. Turing has become one of my heroes. I saw the movie a few weeks back, and while I found its portrayal moving purely as a movie I worried about its accuracy on all but the big events I already knew about. But I can’t comment further on most of it as I am still doing the homework—i.e. reading Hodges’ biography.

    I too noticed the mispronunciation “yoo-ler”, of course. But I had a different reaction. Memory may be failing, and I have no way to check, but if I recall correctly when I came through the British education system (including Cambridge) we may actually have pronounced Euler as “yoo-ler”. (The influence of the classics, Euclid, and all Greek words beginning with eu- may have had something to do with it, as I’m sure readers of this blog will have realized. And no, we did not have to know Greek or Latin to go to Cambridge in my day.)

    It is possible that this error was just a mistake by the film-makers, but it is also possible that, whether inadvertently or not, the film is correct on this, and Keira Knightley’s character would have actually said it.

    On moving to the United States after my PhD I discovered that many received pronunciations in Britain of foreign names are simply wrong, and perhaps surprisingly (to Brits), that American usage is often much more accurate in this respect. As an egregious example of mispronunciation of a foreign scientist’s name in Britain, I will hereby put on the internet my best anecdote of this kind.

    I was once at a semiconductor conference in England, at which an audience member after a talk asked a question about the “whiner crystal”. After several seconds I realized he meant Wigner crystal. (No-one else seemed noticeably puzzled or corrected him; the speaker answered the question.) I presume the analogy is with “sign” (unless he confused Eugene W. with Norbert Wiener).

  17. PeterM Says:

    “Counterexamples anyone?”

    I think Dr Strangelove could also be mentioned. A slight SPOILER alert may be appropriate here, before going on.
    At some point it is relevant in the movie that they cannot search through effectively a number of possible codewords to abort a mission (they even elaborate on this).

  18. Raoul Ohio Says:

    Influential mathematicians: Painleve was Prime Minister of France twice, the first time (briefly) was in WW1.

    The concepts associated with the name “Painleve” are still vibrant and productive 100+ years later. In addition to the Painleve equations, he was among the first to study general relativity and deduced some preliminary ideas about black holes.

    Also in France, Napoleon liked to think he was a mathematician. Leplace is reported to have given him the first copy (five volume?) of “Celestial Mechanics”, and Napoleon promised to get back quick with comments. However, I think that report is from “Men of Mathematics”, so it is probably more E.T Bell embellishment.

  19. vzn Says:


    As a result, The Imitation Game might be the first Hollywood movie ever made whose plot revolves around computational efficiency.

    indeed a rare phenomenon although for another possibility/ datapoint see Sneakers (1992) which had some algorithmic conceit starting at the beginning with a lecturer describing fast factoring for breaking codes, starring redford etc…. but dont remember the movie much!

  20. asdf Says:

    Other influential math dudes:

    Ahmad Chalabi (PhD in math, U. of Chicago 1969) was a powerful politician in Iran, and according to some, he manipulated the US into starting the 2003 Iraq war.

    Louis Tordella (actual working mathematician who did codebreaking stuff) was deputy director of the NSA for decades. NSA directors are military types swapped in and out every few years, so the #2 person is the one with the real behind-the-scenes power. We may never know how much national influence he had (think J. Edgar Hoover). James Bamford’s book Body of Secrets has much more info.

  21. Ian Says:

    Did you catch the brief Easter Egg where they had Turing inventing RSA in 1942?

  22. Jay Gischer Says:

    Yes, “Sneakers” is about computational complexity, no question about it. The mcguffin for the plot is a device that can do fast factoring, and the plot implications revolve around decryption. It’s also still very topical and relevant today. Google “seatec astronomy” for some fun related to the film.

    Also, there was a film made about Feynman’s work on the atom bomb – Infinity. It’s quite charming and quite good. I think it evades the “lonely, tortured genius” trope quite well.

  23. Patrick Says:

    With respect to powerful mathematicians, wouldn’t people like Vikram Pandit or James Harris Simons be the obvious counter examples?

    Math and mathy people control the distribution of resources today on a scale that war has never approached.

  24. KWillets Says:

    The film No Way Out revolves partially around an attempt to computationally enhance a photograph to identify a killer.

    Come to think of it they probably didn’t need to enhance the upper left-hand corner first (in the movie it takes days to get to the face, working one raster at a time).

  25. Joshua Zelinsky Says:

    By the way, the Complexity Zoo seems to be down.

  26. Scott Says:

    Joshua #25: Yeah, yeah, I know. They told me it would be down, since they’re fixing the server or something.

  27. Raoul Ohio Says:

    Patrick: Thanks for pointing out James Harris Simons, whom I was not aware of. Looks to be an excellent person.

  28. Alan Migdall Says:

    There was a movie, whose name escapes me, where the plot the involved a researcher who found a fast factoring algorithm. The bad guys kidnap his child to force him to use the technique to crack the security around foreign currency trading markets, so they could trade on inside information. One memorable twist was that it was the evil/bitter journal editor who received the manuscript submitted by the protagonist, realized its value, and sold it to the bad guys.

  29. Jeremy Says:

    I’ve never understood why the theoretical computer science community holds Turing to be such a foundational figure. Alonzo Church had already equivalently defined computability through the lambda calculus before Turing machines. Isn’t mathematical credit supposed to go to the discoverer and not the expositor? For instance, Turing also apparently rediscovered a proof of the Central Limit Theorem, which is nearly as foundational to statistics/probability as TMs are to TCS, but no one puts him with Fisher and Neyman on the statistical Mt. Rushmore because it was a re-discovery. Turing machines were an exposition, and let’s face it: without his fame and status as a father of TCS it’s far less likely that there would be movies about his head cog exploits at Bletchley park.

  30. Rahul Says:

    Are there any movies on Quantum Computers yet?

  31. Scott Says:

    Jeremy #29: Firstly, Turing’s discovery of computability should really be considered independent of Church’s. It certainly wasn’t just an “exposition”; Turing had already finished the work before he knew Church had published similar results the same year, and before he started as Church’s PhD student. (Making him the best-prepared first-year grad student in the history of the world? 🙂 ) And news traveled a lot more slowly before the Internet.

    Secondly, Turing’s treatment was better: practically better, in that he made the connection to actual machines that one could actually imagine building, but also philosophically better, in that his was the first to satisfactorily explain why this definition of computability should be the right one. Or at least, that’s what Gödel thought. Gödel was skeptical that lambda-calculus picked out anything special: why shouldn’t there be an infinite hierarchy of more and more powerful natural computability notions, just like there’s an infinite hierarchy of more and more powerful formal systems? But as soon as he saw the definition of computability in terms of what a finite-state machine could actually do by reading and writing symbols on a tape, he was satisfied that the problem had been solved.

    (Analogously to your question, there are people who ask why Einstein’s special-relativity paper is so celebrated, given that Lorentz had already published the Lorentz transforms a year before. Once again, the simplest answer is: because while Lorentz gave the right formulas, Einstein explained why they were inevitable.)

    Thirdly, if this is all Turing did, I agree that his foundational status would be less. But then there’s also the ACE, the morphogenesis work, Computing Machinery and Intelligence (which anticipated almost everything said in the strong-AI debate over the next 65 years), and the small matter of helping to win World War II—so many different themes of historic importance happening to coalesce in a single person. Indeed, we have some empirical evidence for Bletchley’s importance: even though the Turing Award was named for him in the 1960s, Turing was not seen as nearly the foundational figure he is today until after Bletchley was declassified in the 1970s, and then Hodges wrote his biography.

    Fourthly, of course, there’s the non-scientific part, what I called the “triumph and tragedy” of Turing’s life (similar to how being an excellent physicist was necessary for Stephen Hawking to become the global icon he is today, but obviously not sufficient). I trust you agree that a movie about the life of Alonzo Church would have trouble filling seats in the theaters.

  32. Bill Kaminsky Says:

    I’d just add the following bit to Scott’s list of Turing’s accomplishments beyond his eponymous finite-state machines and his resulting theory of computability: Turing is a seminal figure in the history of numerical methods for linear algebra (which pretty much makes him a seminal figure in all modern numerical analysis as the numerical solution of linear equations underlies pretty much all of numerical analysis you do on electronic computers).

    Most notably, Turing in a 1948 paper “Rounding-off Errors in Matrix Processes” introduced the idea of the condition number of a matrix \(A\) as the key figure-of-merit to characterize how much perturbations to the matrix \(A\) or the vector \(\mathbf{b}\) from rounding errors or data uncertainties would perturb the solution \(\mathbf{x}\) of $$A\mathbf{x} = \mathbf{b},$$
    as well as the idea of LU decomposition of a matrix.

    Granted, it may be argued that Turing’s LU decomposition reframing of Gaussian elimination and his resulting error analysis really was more a brilliant feat of “exposition” than one of origination. Quite a few other leading lights of WWII-era computation (von Neumann, Goldstine, Hotelling, Wilkinson, etc.) were certainly turning their attention to error bounds in numerical analysis generally and numerical linear algebra particularly. Nevertheless, it’s still pretty frakkin’ awesome to see one guy have such major pure and applied math skills.


    (1) Turing’s seminal 1948 paper:

    (2) An expository history paper about Turing’s seminal paper:

    (3) The current bible of error analysis in numerical analysis (Nicholas Higham’s Accuracy and Stability of Numerical Algorithms), which also has many historical notes about Turing’s contributions to the field:

  33. Fred Says:

    Turing also worked on the mathematics of explaining patterns in animal fur, I’m not sure if he was a pioneer in that domain though

  34. gasarch Says:

    Alan M- The movie you describe sounds like it could be an episode of NUMB3RS, though I’m not sure. In the episode the bad guys do kidnap the child of a mathematician working on RH— the show claims that RH –> Factoring easy, which while not currently know is not so implausible for a TV show, and that once you have the proof you could, within hours, have a fast algorithm, which is implausible.

    bill g.

  35. Hamish Says:

    Regarding Yooler for Euler, upper-class Brits have a penchant for the crude anglicization of foreign names. Perhaps the best example is “Quicks-oat” for Quixote.

    That said, British physicists are known to giggle when their American colleagues say “Plonk” for Planck (according to my German-speaking colleague it should actually be “Plank”). In the UK, plonk is a derogatory term for cheap wine and a plonker is a not-too-clever person.

  36. Travis Says:

    I think in general, it’s pretty realistic for the movie to call him Yooler, since, well, that’s what *most* people (wrongly) call him…

  37. Raoul Ohio Says:

    Scott: Another contender for best prepared grad student of all time might be Lars Onsager. As I recall from the obituary in Physics Today, he was in the US on the eve of WW2. He was hired to be a physics prof at Yale, but did not have a PhD dissertation. Upon learning that he had solved all the problems but four in Whittaker and Watson’s “Modern Analysis”, which was known to have dozens of unsolved problems, the Math department gave him a PhD on the spot.

  38. Murray Meehan Says:

    My russian professors pronounced Euler Yooler too, and consequently I pronounce the name of my rabbit Yooler, so don’t think the movies invented that one out of whole cloth.

  39. Dez Akin Says:

    While I think Turing did great work, the lambda calculus and its application to type theory and higher order logic was huge, and the application to solve the Entscheidungsproblem was also huge. Turing’s work, while important, is most appropriately labeled as computer science. Church’s is broader, in the field of mathematics and proof theory. I don’t think either figure should be minimized. If you’re a mathematician, you’re going to use Church’s work more, and if you’re a computer scientist, you’re going to hold more reverence for Turing.

  40. asdf Says:

    I’ve heard of this guy:

  41. James Gallagher Says:

    Fred #33

    Turing was most certainly original (brilliantly so) in that paper – but it wasn’t pioneering in dynamical systems theory for the same reason Poincare’s late 19th century paper on the stability of the Solar System wasn’t pioneering – not enough people understood its importance

    But back to the more controversial point – how pioneering/inflential was Turing in the history of (practical) computing?

    hmm, Scott will not like this comment, but I think that the (many) engineers of computers in the mid 20th century were far more important than the “theoretical computer science” ideas of Turing and others. Even Von Neumann is incorrectly credited with a (original, but not spectacularly so) contribution to the design of computing architecture – which was essentially due to engineers.

    In WW2 the british computers owed the biggest debt to Tommy Flowers, not Turing.

    And really, once the transistor had been discovered, how hard is it to work out that is it good to put the program in fast transitor memory (instead of on cards) along with the data.

    Furthermore, really, how hard would it be for an intelligent undergraduate to design a computer from scratch given modern circuit components, and a basic course in boolean algebra?

    Many engineers solved that problem with rudimentary devices available to them, all oblivious to the theoretical ideas of Turing, Von neumann etc

  42. fred Says:

    James #41
    indeed in electronics class we had to design an entire ALU by hand on paper using basic gates. We certainly didn’t need any high level CS knowledge to do this (just understanding transistors, boolean logic, and binary arithmetics).
    To me Turing’s contribution was to take such a basic hardware and do a crazy jump into the magical realm of software, with fascinating practical concepts like emulation, virtual machines, etc.

  43. BPL23 Says:

    The current Prime Minister of Singapore is, if not a professional mathematician, at least a talented amateur who was Senior Wrangler in 1973.

  44. Chris D Says:

    James #41

    The argument about whether the architect or the stone-cutter deserves credit for a building has been going on since Plato’s time and is unlikely to be resolved in a comments section (though if there were ever a blog that it would be, this is probably it).

    However I think you are underestimating how hard it is to come up with ideas that seem obvious in hindsight.

  45. Vijay Says:

    Scott #31: The idea of a movie involving Alonzo Church reminded me of this quote from Barkley Rosser about him.

    “In his lectures he was painstakingly careful. There was a story that went the rounds. If Church said it’s obvious, then everybody saw it a half hour ago. If Weyl says it’s obvious, von Neumann can prove it. If Lefschetz says it’s obvious, it’s false.”

  46. James Gallagher Says:

    Chris D #44

    “Stone-cutter” is a very unfair way to describe the various brilliant engineers involved in the early development of practical computing architecture. Engineers Eckert and Mauchly, who were the real “architects” of the “Von Neumann” architecture, weren’t aware of Turing’s ideas at the time (Also Zuse)

    The history seems convoluted, but I think it’s hard to argue that no one else could see that a stored program architecture was inevitable.

  47. Greg Kuperberg Says:

    I think it’s hard to argue that no one else could see that a stored program architecture was inevitable.

    I don’t know what it is about the invention of the computer, or maybe generally the contributions of mathematicians to society, that lead people to take it for granted on the argument that it’s “inevitable”. Sure, the ideas that Turing and Von Neumann gave to computer science and to humanity were inevitable. What invention in history wasn’t? The airplane was inevitable. The phonograph was inevitable. Do the Wrights or Edison deserve scare quotes just for that? Heck, what Eckert and Mauchly did was just as inevitable as what Turing and Von Neumann did.

  48. Joshua Zelinsky Says:

    Off topic: Scott, just saw your paper with Bouland, Fitzsimmons and Lee. Do you have any idea of ring isomorphism is in PDQP? I ask because both graph isomorphism and factorization are reducible to ring isomorphism and both problems are in PDQP.

  49. Scott Says:

    Joshua #48: Good question! Yes, I believe any natural isomorphism problem (including ring isomorphism) will be in SZK, and therefore in PDQP as well.

  50. Sniffnoy Says:

    Oh, hey! Neat to see this model being explicitly studied now (I certainly wasn’t going to do it 🙂 ).

    Personally I’m still wondering about the probabilistic equivalent of this (PDPP?) — I seem to remember that the use of PDQP for solving the collision problem in constant time doesn’t use anything quantum, just the “non-collapsing measurements” part, which still makes sense probabilistically. (I have “figure out how long it takes to search an array / invert a function in that model” somewhere low down on my to-do list, but that’s probably not a problem I’m actually equipped to solve…)

    (arXiv link for those confused: )

  51. James Gallagher Says:

    Greg Kuperberg #47

    Maybe it’s just me, but I think that the stored-program solution for practical computing is easier to see than a proof of Bertrand’s conjecture, for example, or even a proof of Fermat’s little theorem, from scratch. So I don’t consider it such a huge intellectual breakthrough (but of course it had enormous practical impact) – it was even kinda obvious?

    The big breaktrough, like in the Wright brothers case, was the practical realisation by engineers, the pure mathematicians were by then redundant.

    (Bertrand’s Conjecture: there is a prime between n and 2n, Fermat’s little theorem a^(n-1) = 1 mod n when n is prime, a,n coprime)

  52. aviti Says:

    Gallagher#46 et al., I want to know, between ZUSE, BOMBES, whatever the americans made (at time of WWII), which one first used softwares to run?

  53. James Gallagher Says:

    aviti #46

    Ada Lovelace circa mid 19th century

  54. James Gallagher Says:


    Perhaps I didn’t really get your question – Babbage was able to create algorithms for his analytical machine in the 19th century (and, famously/infamously Ada Lovelace may have contributed).

    But do you mean – when was the first stored-program executed? That’s very convoluted – obscured by WW2 history, and pretty poor communications just after that war. The Americans and British had stored-program architectures running in the years after WW2 – and many other nations would have had the capability if not for economic conditions.

    It’s a bit of a boring question really – like how far did people travel with poor aerodynamic designs before the Wright brothers?

    The big breakthrough occurred when the transistor was invented – that made a lot of previously impractical ideas, by probably hundreds of people, viable.

  55. Chris D Says:

    James #46

    It’s a historical term, and in a historical context it referred to some of the most highly-skilled craftsmen around.

  56. joe Says:

    Scott: I seem to remember hearing, perhaps 10 years ago, how people were trying to find a quantum algorithm for graph isomorphism in the hope that it would yield an exponential speedup, spurred by the intuition that graph isomorphism may not be in NP, but also not in P. What has happened since then that graph isomorphism is now considered to be intractable even for quantum computers?

  57. Scott Says:

    joe #56: There’s no consensus on whether graph isomorphism is easy or hard for quantum computers. Indeed, many of us suspect that it might even be easy for classical computers (i.e., in P). What we can say is that, after 20 years of effort on the problem, a quantum algorithm for graph isomorphism beating the best-known classical algorithms has still not been found; and that certain avenues, like reducing to the hidden subgroup problem over the symmetric group and then doing coset sampling, that initially looked promising to people ended up being probable dead-ends (sometimes for deep and nontrivial reasons).

    In any case, it’s important to realize that the classes PDQP, DQP, and SZK contain not merely graph isomorphism, but a much wider class of problems, including not just any other isomorphism problem of your choice, but also (e.g.) finding collisions in arbitrary cryptographic hash functions. So the case for BQP≠PDQP is much, much stronger than merely PDQP containing graph isomorphism.

  58. Cem Say Says:

    Just watched BBC’s “Breaking the Code”. (“The Imitation Game” doesn’t open in this part of the world until February.) Derek Jacobi is a great actor, but he was ridiculously old to portray Turing. That ruined it all for me.

  59. William Hird Says:

    I read somewhere ( cant recall the reference though) where Turing claimed to have developed his own encryption algorithm that he said was unbreakable. Does anyone know about this, any details? Thank you!

  60. Sniffnoy Says:

    You know, “PDQP” contains the acronym “PDQ”. This might suggest to the uninformed that it’s supposed to be a smaller complexity class than P! 🙂

  61. Joshua Zelinsky Says:

    Sniffnoy @60, How would PDQ suggest that?

  62. Joshua Zelinsky Says:

    Also, I just added PDQP into the Zoo. If people who know more about this could look the entry over and verify that I haven’t said anything terribly wrong or did something horrible with the formatting or presentation that would probably be a good thing.

  63. Sniffnoy Says:

    That was a joke; “PDQ” stands for “pretty damn quick”. I don’t believe anybody will actually make that mistake. That would require some serious confusion.

  64. Carlos Says:

    William Hird 59

    I believe Turning’s scheme was called Delilah. It’s described in some detail in Hodges bookm and see also here:

  65. Anonymous Says:

    If anyone is interested, the mentioned adaptation of the play seems to be available on YouTube: .
    (I haven’t watched it yet.)

  66. Gaillard T. Hunt Says:

    Between “Monuments Men” and “The Imitation Game” I see a new genre emerging: the trashing of the best stories from WWII to replace them with cliche plots, with only the names or identities of real people preserved to confuse the innocent. Next can we have the Manhattan Project with General Groves as a woman? He and Oppenheimer could have a torrid affair. The possibilities are endless.

    There’s no problem with dramatic license. (The movie “Walker” conflated William Walker’s two invasions of Nicaragua into one, and used a lot of deliberate anachronisms to good effect.) But you lose me when you throw out a really good story like the cracking of Enigma.

  67. Jim Holt Says:

    Vijay #45

    I once quoted Rosser’s jibe about Church, von Neumann, Weyl, and Lefschetz to Peter Lax (who knew them all). Lax looked reflective for a moment; then his eyes twinkled and he said, “Lefschetz never put forward a false conjecture and he never produced a valid proof.”

  68. Vijay Says:

    Jim Holt #67: Ha! By the way, I got that quote from The Princeton Mathematics Community in the 1930s

  69. Colin Says:

    Hamish #35: The difference in how Brits and Americans pronounce German names seems to be down to the difference in their inventory of sounds used to pronounce English. For someone from the south of England, ‘Planck’ is between ‘plank’ and ‘plunk’. (Accurate German pronunciations of names like ‘Kant’ or ‘Kuntz’ are likely to lead to raised eyebrows depending on where you are in England.) For a General American speaker, it’s between ‘plank’ and ‘plonk’, except shorter, so maybe ‘plonk’ is the closest approximation. (I have seen an actual pronunciation guide to German, presumably aimed at Americans, suggest ‘hot, but shorter’ as the way to pronounce German ‘hat’.)

  70. Jim Holt Says:

    But wasn’t Leonhard Euler one of the Houston Eulers?

  71. Nick Read Says:

    @Hamish, Jim, Colin: you may enjoy my comment #16 also.
    I’m from southern England myself, as it happens.

    1) Quixote is the origin of “quixotic”, of course, which everyone pronounces as it looks.

    2) I like to say that “in my philosophy, there’s no such word as Kant”. (Think about it.)

  72. joe Says:

    Scott 57: Thanks!

  73. Riot Nrrrd™ Says:

    Jim #70: LOL 🙂

    2 years ago I spent a rainy day in Manchester, England seeing a terrific Turing exhibit at the Manchester Museum called “Alan Turing and Life’s Enigma”. I was entranced by the displays of his work on Morphogenesis (i.e. “The Chemical Basis of Morphogenesis”) which I had previously been completely unaware of.

    I’ve not yet seen “The Imitation Game” – is this topic covered at all in it?


  74. Steve Says:

    As a result, The Imitation Game might be the first Hollywood movie ever made whose plot revolves around computational efficiency. (Counterexamples, anyone?)

    In the 1987 move No Way Out, the head computer analyst instructors a programmer to “program a Fourier transform”. The analyst tells the programmer that “the eigenvalue is off.” He’s actually trying to slow down an image enhancement process to give the Kevin Costner character more time — it’s his face that’s about to be revealed. So the algorithm is in fact working too well, and needs to be slowed down for the main character to work his way out of a jam.

    Yeah, it’s complete gibberish, but I think it meets your challenge.

  75. Steven Strogatz Says:

    on the pronunciation of Euler, there’s a moment in one of the “Story of Maths” episodes that appeared on the BBC, in which a descendent of Leonhard Euler pronounces his family name as “yooler”. You can find it on YouTube. My jaw dropped when I heard this!

  76. Léo Says:

    Also read this review from NYR that contrasts the movie plot with existing books, its conclusion seems quite on point:

    “To be honest, I’m a bit surprised that there hasn’t been more pushback against The Imitation Game by intelligence professionals, historians, and survivors of Turing’s circle. But I think I understand why. After so many years in which Turing failed to get his due, no one wants to be seen as spoiling the party. I strongly doubt, though, that many of those in the know are recommending this film to their friends.”

  77. Raoul Ohio Says:

    Here is an interesting update about Turing’s “lost notebook”:

  78. Raoul Ohio Says:

    Jim Holt and Vijay,

    I recall reading somewhere that Riemann never had a correct proof.

  79. Anon Says:

    I think it is the actor that made the movie’s Turing such an annoying person. If you have seen Sherlock you will notice it is just his style. He was a very bad choice in my opinion.

    I enjoyed Theory of Everything way more (possibly because I don’t know as much about Hawking, maybe it is a bless to be ignorant when watching these popularizations of the life of scientists).

  80. Michele Says:

    Finally, last saturday I had the opportunity to watch The Imitation Game. What a ugly movie!

    Some years ago I read Turing’s biography written by Andrew Hodges (very very detailed, maybe too much). This movie is both superficial and misleading, I think.

  81. Leiru Says:

    #21 I did see it! When allan and Joan are lying on the grass and the notebook is shown.

  82. Braithwaite Prendergast Says:

    You wrote that Christopher Morcom died of TB. I understood that he died from drinking unpasteurised milk.

  83. Douglas Knight Says:

    Braithwaite, both are true.

    Thanks! I have never before heard of anyone who died from unpasteurised milk.

  84. Braithwaite Prendergast Says:

    In the first lines of Chapter 2, “Alan Turing: The Enigma,” by Andrew Hodges, it is claimed that Morcom died as a result of drinking infected cow’s milk. In this way, he contracted “bovine tuberculosis.”

  85. Douglas Knight Says:

    Scott, you kind of answer the question: “should you see this movie?” but the question that interests me is how these three movies compare. It sounds like you prefer Breaking the Code (or maybe you like the play but haven’t seen the 1996 film?). And what about Enigma? The only thing you say about it negative, but without further input, I will assume that with Top Stoppard and Mick Jagger, it must be the best of the bunch.

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