Asking the question

Sometimes simply asking the question in the first place is a key step, even when it takes a genius to actually solve the problem. So, even though he couldn’t calculate his way out of a paper bag, Antoine Gombaud, Chevalier de Méré , played an important role in birthing probability theory – by asking Pascal and Fermat to solve the the problem of points – how to divide the stakes of an unfinished series of games. Of course asking the right people is also part of the goodness.

Franciszek Pokorny, who headed the Polish General Staff’s Cipher bureau after World War I, was the first to realize that cryptography and cryptanalysis are essentially mathematical in nature – and that you therefore want to hire mathematicians, rather than classical scholars or members of the band of the battleship California. He recruited Marian Rejewski, Henryk Zygalski and Jerzy Różycki: they weren’t considered world-beaters by other Polish mathematicians – not like Arne Beurling – but they broke Enigma.

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58 Responses to Asking the question

  1. eurogenes says:

    Has this anything to do with Nick Patterson’s recent interview at Talking Machines?

    Yeah, he didn’t mention the Poles when talking about Enigma. Tsk, tsk…

    • Fd says:

      Has this anything to do with Nick Patterson’s recent interview at Talking Machines?

      It probably has something to do with this:

      Gregory M. Cochran (born 1953) is a physicist and adjunct professor of anthropology…

      He must be upset with constant “but you are a physicist” replies. And I agree that in questions of evolutionary medicine and HBD you are more likely to get a pertinent answer from a physicist than, say, from a psychiatrist or a post-structuralist cultural anthropologist. Actually you are pretty certain not to get the correct answer from the latter two.

    • gcochran9 says:

      Haven’t seen it yet, so no. Nick Patterson is usually interesting: how’s the talk?

      • eurogenes says:

        Well, he talked a little about ancient DNA, but didn’t reveal anything new, so that was a bit disappointing.

        But it was interesting to hear his accent. He sounds like Q from James Bond or something.

      • I didn’t find the talk by Nick Patterson the least bit disappointing, but Eurogenes is right, the talk about ancient DNA was quick and really didn’t go into much detail. Here is the link to the talk, but I suggest you go right to the 16:43 mark if you want to hear Nick Patterson talk.

        What I found fascinating is his perspective on how a brilliant guy like Nick Patterson approaches problem solving and he gives, to little old me anyway, a fascinating perspective on how science has moved forward not just in code breaking but in sorting real discoveries from background noise.

  2. st says:

    I always suspected the role of Wittgenstein in breaking the code had been exagerated. Did not know the role of Turing had been exagerated too. BTw you could call Wittgenstein pre-structuralist without being wrong. Too bad the works of structuralists never became scientific after all. Too bad, because they were trying to be – at the beginning, which is a century ago. First theories are mostly borrowings from biology and evolutionary theory, at large, and attempts to apply the discoveries of Darwin on a social scale. Successful or not, they were backed by biology, zoology and in the case of Durkheim – descriptive statistics and higher math. Boaz and the marxist wing killed them all at the moment they were born. Then all social sciences suddenly went mad and have been like it ever since. There are some treasures buried at the times of their beginning – which are the times of their deaths as well, which might one day reconnect them with the real sciences. Not going to happen, because it’s too late – rest of the sciences are already there and beyond. I guess a physicist knows more about the society than any social scientist – alive or dead – nowadays. ust by the virtue of having never studied social sciences. If I want to check the scientific news on the field, i usually go to this blog and the likes. Pointless going anywhere else.

  3. rzg says:

    You mean that Enigma wasn’t single-handedly broken by Benedict Cumberbatch, over the protests of his homophobic, beer-guzzling dumkopf handlers?

    “Rejewski had often wondered what use Alan Turing (who in early 1940 had visited the Polish cryptologists at PC Bruno outside Paris[69]) and the British at Bletchley Park had ultimately made of the Polish discoveries and inventions. For nearly three decades after the war, little was publicly known due to a ban imposed in 1945 by British Prime Minister Winston Churchill.[91] In a 1967 book[92] Władysław Kozaczuk, associated with the Military Historical Institute, disclosed Poland’s breaking of the German Enigma ciphers.

    Until 1974, the scant information published concerning Enigma decryption attracted little attention. Ladislas Farago’s 1971 best-seller The Game of the Foxes presented a garbled account of Ultra’s origins: “Commander Denniston went clandestinely to a secluded Polish castle [sic] on the eve of the war [to pick up an Enigma, ‘the Wehrmacht’s top system’ during World War II]. Dilly Knox later solved its keying [sic]…”[93] Still, this was marginally closer to the truth than many British and American best-seller accounts that would follow after 1974. Their authors were at a disadvantage: they did not know that the founder of Enigma decryption, Rejewski, was still alive and alert, and that it was reckless to fabricate stories out of whole cloth…”

  4. It wasn’t that Turing’s contribution was exaggerated, but that popular versions forget the Poles who did the original heavy lifting, and hero worship cuts out other very bright contributors. Tommy Flowers, for example, the engineer who built Colossus, the destruction of which was Churchill’s biggest mistake.

    • There is a rebuild of Colossus which is working now–I have pics if anyone wants (my father used to work there–in fact he worked with Flowers although this was after the war and not to do with Colossus). The rebuild even has some valves from the original era. The whole area was secret until surprisingly recently. We used to play there as kids. The council tried to bulldoze it down and were surprised to find that the building were highly resistant to their machines! The full story took a while to emerge. Well worth a visit–and they will certainly set any visitors straight about the roles of the 1000s of different people that worked there as well as Turing (important and badly treated though he was)

    • Peter Lund says:

      But /were/ all the colossi destroyed? I somehow doubt it. Do you think all the bombe machines were?

      • Sorry, should have added that two were sent to the new decoding and listening station in Cheltenham, but in such secrecy that the first step in the computer age was lost, and that was more valuable than two prototype machines. If Bletchley Park and the Post Office had been put together to work on a general purpose calculator we in the UK would be rich, and even better, would never have had to put up with Windows 10.

        • Peter Lund says:

          The Leo machines were plenty interesting and came out very early. So was the work on the Ferranti Atlas — virtual memory, protected memory, operating system, etc.
          It seems to me there were plenty of practical offshoots of the war work at Bletchley Park and elsewhere (radar/radio, various controller circuitry for cannons, etc). A lot of the circuitry of these machines was developed by young men who “couldn’t talk about what they did during the war”.

          Perhaps the problems had more to do with the post-war ideas of a controlled, nationalized economy? Or with the much smaller and poorer home market in UK (even if we include Ireland) compared to the US? Besides, the British machines seem to have been using drums, delay lines, and serial circuitry for longer than the competition in the US that quickly switched to solid state and parallel circuitry. Perhaps even something like the ability to raise capital for R&D was a problem for the UK companies, more so than the (apparent) late start.

    • Greying Wanderer says:

      Tommy Flowers ought to be better known partly because it’s such a good name.

  5. dearieme says:

    “popular versions forget the Poles”: when the story of Bletchley Park first emerged, lots of credit was given to the Poles (and to the French for passing on their work). I suppose that stories tend to get simplified and distorted to suit popular taste and intellectual limitations.

  6. Pyrrhus says:

    First I had heard of Colossus, fascinating!

  7. Pyrrhus says:

    I notice that the Wikipedia article doesn’t mention Churchill’s destruction order….wonder why?

  8. If we are talking about films as a way of explaining anything, I must protest.

  9. Pyrrhus says:

    “After the war, Flowers was granted £1,000 by the government, payment which did not cover Flowers’ personal investment in the equipment and most of which he shared amongst the staff who helped him build and test Colossus. Ironically, Flowers applied for a loan from the Bank of England to build another machine like Colossus but was denied the loan because the bank did not believe that such a machine could work. He could not argue that he had already designed and built many of these machines because his work on Colossus was covered by the Official Secrets Act. ”

    Wow, national suicide by bureaucracy…

    • Edward Teller argued that the effects on a free society of excessive secrecy were more damaging than espionage, because secrecy restricted the otherwise permanent advantage that free societies enjoy: they develop ideas much faster than closed societies, and therefore get interesting things done sooner, always keeping ahead in any arms race, and in the development of the economy.

    • Drawbacks says:

      There’s an anecdote about an elderly couple doing the Bletchley museum tour in the late 90s. At one point the wife corrects the tour guide on his explanation of how a certain machine worked. “I should know,” she says, “I used to work here.” “You did?! Good Lord, so did I!” says the husband. (At its height, “some 9,000 personnel were working at Bletchley” – Wikipedia.)
      It’s maybe not quite too good to be true.

  10. IC says:

    “Sometimes simply asking the question in the first place is a key step, even when it takes a genius to actually solve the problem.”

    Intellectual curiosity.

  11. ohwilleke says:

    Fermat was both an attorney and an amateur mathematician, and since the question of points involved both law and math, he was an excellent person to ask.

  12. candid_observer says:

    I’ve long been struck by a particular example of the odd failure to ask the right questions until very late in the game.

    Aristotle invented syllogistic logic back in the 5th century BC. In the same era, the sophisticated mathematics of geometry summarized in Euclid was developed, and a powerful proof method, which started from a very small number of axioms and proceeded to complex theorems was employed.

    But here’s the thing: those mathematical proofs were inherently incapable of being captured by Aristotle’s logic. Aristotle’s logic was devoted exclusively to so-called “monadic” predicates — applying to single objects — and the language of geometry was intrinsically relational — applying to more than one object at a time — in nature.

    And yet, from Aristotle’s time to the late 19th century, when Frege and Pierce independently took up the question, there was not even the sense that there was something missing in Aristotle’s logic. Kant famously proclaimed that Aristotle had discovered and explained everything there was to know about logic.

    But weren’t the proofs of Euclid paradigm cases of logical inference? How could thinkers square these attitudes about what proof and logic consisted in?

    To this day, I puzzle over why it took so very long to see what was missing in our understanding of logic.

  13. Jim says:

    Yes, the late development of logic is rather strange. Also the proofs in Euclid are heavily contaminated by spatial intuition, but this was rarely noted.

    It’s true that tthere is an enormous gulf between the logic of monadic predicates (of which the syllogism is a part) which admits a decison procedure and predicate logic in general which does not. The valid statements of monadic logic are recursive while the valid statements of predicate logic in general while recursively enumerable are not recursive.The true statements of arithmetic are not even recursively enumerable. This is one of the most amazing discoveries of all time. Arithmetic is unknowable.

  14. John Hostetler says:

    The work of Rejewski and his colleagues is rightly seen as practical evidence that pure mathematics has a major role in cryptography, especially since some of the advances in cracking Enigma right down to its wiring were made sight unseen. However, two aspects of the project were not of that sort. For one, the Poles possessed a pre-military, civilian version of the machine. For another, they possessed information about it obtained by a flesh-and-blood spy.

    Hans-Thilo Schmidt was an employee of the German cryptography service whose offer to sell aspects of the machine to the French in the early 1930’s was accepted. This information was passed on to the Poles, and Rejewski’s later statements about the project suggest that his mathematical and inferential work were not sufficient to solve the problem in a reasonable span of time, not without Schmidt’s material.

    Schmidt’s identity eventually became known to the Germans after the fall of France, when his French contact was identified. He was arrested in 1943 and died either by execution or suicide.

    Interestingly, Schmidt had an older brother named Rudolf who had risen through the officer ranks in World War One and the inter-war period and gone on to become General of the 1st Panzer division in the invasion of Poland, and eventually Guderian’s replacement as General of the 2nd Panzer Army on the eastern front in late 1941. In 1943, upon his brother’s arrest, Rudolf Schmidt lost his command but was acquitted in a court-martial. Somehow, he managed to survive more than two post-war years in East Germany without attracting major Soviet attention, but he was arrested in late 1947, taken to Moscow and sentenced to 25 years of forced labor. He was among the last Germans released from the Gulag in 1955 and died two years later at the age of 70.

    It is irresistible for me to conclude that here we have a classic case of a dutiful, honorable, responsible older brother and a jealous, unstable younger brother. Aspects of birth order effects continue to intrigue. I do not believe for an instant they are all nurture. Like Greg’s homosexuality hypothesis, it may not be all genetic either. Biological, but not genetic.

  15. Fourth doorman of the apocalypse says:

    Actually, I have it on good authority that it was Ada Lovelace who cracked Enigma!

    • dearieme says:

      In a very real sense it was.

      • syonredux says:

        “In a very real sense it was.”

        And in a very real sense it wasn’t. Feminist propaganda has vastly overrated Ada Lovelace’s contributions:

        “Although it is clear that Lady Lovelace was a woman of considerable interest and talent, and it is clear that she understood to a very considerable degree Babbage’s ideas about the general character and significance of the Analytical Engine, and expressed them well in her notes to Menabrea’s paper, it is equally clear that the ideas were indeed Babbage’s and not hers; indeed, she never made any claim to the contrary. She made a considerable contribution to publicizing the Analytical Engine, but there is no evidence that she advanced the design or theory of it in anyway.”

  16. JayMan says:

    Speaking of asking the question, I recently put this out on Twitter. The ensuing discussion revealed that there is a lot about basic evolutionary theory that people are foggy on:

    I still don’t know the answer.

  17. IC says:

    Asking question or intellectual curiosity is really a luxury when you have too much time on your hand. Either you are well-off in the first place like Darwin or have very boring job without much to do like Einstein.

    Einstein daydreaming is very important at end.

  18. IC says:

    Happy international women’s day!

    • IC says:

      If you are always right and never admit any mistake like Trump, you are really a woman.

      Don’t argue with women. You get nowhere.

  19. j mct says:

    I always thought that probability stuff was about playing dice. At the time there was a dice game at court that was that one rolled three dice and if there was at least one six one of the bettors would win, and if there was no sixes the other better would win. At the time the odds calculation was thought to be (1/6) + (1/6) + (1/6) = 1/2 for a fair 1/1 bet, while the correct calculation of the odds of one or more sixes is actually 1 – [(5/6)(5/6)(5/6)] or 1 – (125/216), or one should always be on the no sixes side of the bet. I’m not absolutely sure if that’s exactly right, but I’m pretty sure.I suppose they could have tested all this empirically, but France is the land of yes it works in practice but does it work in theory. and that didn’t start yesterday.

    A little math back in the day could make one serious money.

    • Jim says:

      The theory of probability demonstrates the limits of intuitive thinking. A good example is the hat-check girl problem. Suppose she hands back the patron’s hats at random. What is the probability that at least one person gets the right hat back? And how does it depend on the number of patrons?

  20. Actually, the person who made the mathematics-cryptology connection first was probably William Friedman. Friedman was a geneticist in the pre-WWI days, when genetics was very largely statistical analysis. He accidentally drifted into cryptography, and ended up applying statistics to cryptography at a much higher level than ever done before. The “Riverbank Publications” from 1917 through 1922 led to his work becoming internationally known. He went to work for the U.S. Army after the war.

    In 1929, he was put in charge of codebreaking for the Army. He promptly hired four people as assistants: three mathematicians, one linguist. They were the people who ended up solving the Japanese “Red” and “Purple” machine ciphers.

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