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Math The Military Science

How Allies Used Math Against German Tanks 330

Posted by CmdrTaco
from the tanks-for-the-memories dept.
Pepebuho writes "This an article about how the allies were able to estimate the number of German tanks produced in World War 2 based on the serial numbers of the tanks. Neat! Godwin does not apply."
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How Allies Used Math Against German Tanks

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  • by spun (1352) <`moc.oohay' `ta' `yranoituloverevol'> on Tuesday October 26, 2010 @01:59PM (#34028220) Journal

    If I want to quote Mike Godwin, you quote-Nazis aren't going to stop me. All he said was, the longer an Internet discussion goes on, the more likely it is that someone will mention Hitler. Well, duh.

  • by fantomas (94850) on Tuesday October 26, 2010 @02:02PM (#34028238)

    Note to self for world domination plans: don't stamp my robots/tanks/drones with plain text serial numbers, always encrypt! :-)

    • by Capt.DrumkenBum (1173011) on Tuesday October 26, 2010 @02:04PM (#34028266)
      Also the first tank serial # should not be 1.
      Try something like 24370239.
      • by tool462 (677306) on Tuesday October 26, 2010 @02:19PM (#34028476)

        Reminds me of the prank where you release 3 goats with the numbers 1, 2 and 4 on them and watch while everybody searches for the one with the number 3 on it.

        • no, no, no

          the prank is you release 3 sharks with the numbers 1, 2 and 4 on them and watch while everybody searches for the one with the number 3 on it...

          in all seriousness WHO THE BLEEP EVER HEARD OF THAT PRANK BEFORE

          • by sumdumass (711423) on Tuesday October 26, 2010 @05:57PM (#34031990) Journal

            in all seriousness WHO THE BLEEP EVER HEARD OF THAT PRANK BEFORE

            It's a simply ploy on misdirection. It's been around in one form or another for years. Back in grade school, we had word problems that played on this where we had to select the proper information to solve a math problem.

            It can be done/demonstrated easier with coins and not harming any animals. Assemble 3 coins (US currency) a penny, a nickle, and a quarter.

            Now tell them that Johny's mom had three kids. Point to the penny and say the name Penny, point to the nickle and say the name Nicolas, then point to the Quarter and ask what the third one's name is. Most people will spend a considerable time attempting to work quarter or some variation of it into a name even after repeating that Johny's mom had three kids. Eventually they give up.

            (in case anyone is wondering, the third one's name if Johny- as in Johny's mom). It's a little easier then how far can a dog run into the woods.

        • by Chris Burke (6130) on Tuesday October 26, 2010 @02:50PM (#34028910) Homepage

          You mean the prank where you release 3 goats, and everyone just looks at you and says "Wow, sucks that your goats got loose. Good luck catching them," and then goes back to playing beach volleyball?

        • by Anonymous Coward on Tuesday October 26, 2010 @03:13PM (#34029328)

          Reminds me of the prank where you release 3 goats with the numbers 1, 2 and 4 on them and watch while everybody searches for the one with the number 3 on it.

          I'm a programmer, I'd be looking for the one with number 8.

      • by Artifakt (700173)

        Supposedly, there was an underground fibre optic install running between several of the Las Vegas casinos back in the 1980's, where every box junction and repeater had a serial number that fit some zany formula, i.e. for anything that really belonged in the system, the sum of the first and fourth digits was always twice the absolute value of the difference of the third and eighth digits. The system was used for something like sending pictures of suspected card counters and other cheats back and forth, and p

      • Then you just do the analysis twice, once calculating the upper estimate and once calculating a lower estimate. You increase the variance but don't really prevent the attack from working. To prevent the mathletes from doing the analysis at all you need to either encrypt it (in which case the crypto-letes move in) or use randomly generated serial numbers, which might get interesting using WWII technology with production spread out over a war torn continent.

      • Also the first tank serial # should not be 1. Try something like 24370239.

        Hitler knew this trick: he was member number 555 of the DAP [wikipedia.org], the first member had number 501. When the DAP changed into the NSDAP, he became member number 1.

      • by houghi (78078)

        # date +%s|md5sum

    • Probably best to hash them.

      That way, you don't need any particularly privileged crypto keys floating around(only the plaintext serials, and each one of them only reveals one hashed serial) and a logistics officer in possession of a plaintext serial can trivially generate the hashed serial and verify it against a piece of hardware. People below a certain security level can just be handed the hashed serials for the stuff they are supposed to keep track of, thus preventing large lists of plaintext serials f
    • by bragr (1612015) * on Tuesday October 26, 2010 @02:17PM (#34028442)
      I am implementing this at my factory. In fact, tanks c4ca4238a0b923820dcc509a6f75849b, c81e728d9d4c2f636f067f89cc14862c, eccbc87e4b5ce2fe28308fd9f2a7baf3, a87ff679a2f3e71d9181a67b7542122c, and e4da3b7fbbce2345d7772b0674a318d5 just rolled off of the the assembly line.
      • Re: (Score:2, Interesting)

        by fregaham (702982)

        I am implementing this at my factory. In fact, tanks c4ca4238a0b923820dcc509a6f75849b, c81e728d9d4c2f636f067f89cc14862c, eccbc87e4b5ce2fe28308fd9f2a7baf3, a87ff679a2f3e71d9181a67b7542122c, and e4da3b7fbbce2345d7772b0674a318d5 just rolled off of the the assembly line.

        You should at least use some salt if you just use md5 on those serial numbers... I could decode your serial numbers just by using publicly available reverse md5 lookup table...

    • by by (1706743) (1706744) on Tuesday October 26, 2010 @02:17PM (#34028448)
      Actually, I think the best course of action would be to stamp false serial numbers / easy-to-decrypt serial numbers. Giving the enemy false information is likely better than none at all.

      Of course, I guess that means the "real" serial numbers will have to be encrypted...
    • Or do what the leader of Seal Team Six did.

      Supposedly he named the team 6 to create the false impression there were 6 seal teams when the number was less.

      So couldn't you just inflate the numbers of your World Dominating machines... heck the first 6 digits could be a model number or something.

    • That's exactly why the Soviet Navy gave their ships non-sequential pennant (hull) numbers, and frequently re-assigned them. They would also sometimes paint one number on one side of the bow, and different on the other.
       
      Security is a difficult business.
       
      Intelligence can also be a weird business... I once read an account of how the CIA broke into a warehouse rented by the Soviet Embassy in Mexico City in order to examine (very closeup and very clandestinely) a high fidelity mock-up/prototype of a satellite the Soviets had on tour. The idea was to gather information on any real cable, connectors, or other hardware on the bird - as well as to collect any serial numbers, drawing numbers, etc.. that they could find. (It's not uncommon for such to contain 'real' items that have been discarded from production or operational use.)
       
      You'd be surprised what a trained and knowledgeable analyst can derive from just a few seemingly unconnected bits of information.

  • original source (Score:5, Informative)

    by slshwtw (1903272) on Tuesday October 26, 2010 @02:05PM (#34028278)
    Here's the original source [guardian.co.uk]... from July 2006.
  • minimum-variance unbiased estimator (MVUE, or UMVU estimator)

    I think this only works if most of the tanks that are no longer in service, are in your collection of serial numbers. If you send your first 1K produced to the western front and the next 1K produced to the eastern front, the US/English/etc are going to calculate a number about 1/2 as high as the Russians.

    So, in theory either the Germans sent certain model of tank only to certain fronts, or the western and eastern guys were sharing data, or maybe the Germans sent all the odds west and all the evens east or

    • It is quite possible(at least until things started going really badly for them) that the germans were producing tanks in multiple locations, with each factory/complex serializing independently, and then sending to the front with the most optimal combination of high need and low shipping distance.
      • by idontgno (624372)

        with each factory/complex serializing independently

        with pre-assigned blocks of serial numbers, if I recall correctly, so if you saw the output of only one factory you might get a slightly low number (unless you saw the product of the factory with the highest serial number block).

        It's all probabilistic, and the variance calculation is documented in the article for a very good reason.

    • by Yold (473518)

      huh? Minimum Variance Unbiased Estimator is a mathematical/statistical property that guarantees that your estimate will have small variance(basically small standard deviation), and is also unbiased (the estimate isn't systematically high or low). What you are trying to say is there was a possibility for sampling error/bias.

      I see your point with respect to the sample though, but it obviously wasn't an issue since the article states that the true maximum was very near the estimate. 1000 tanks is a lot; the

  • by zach_the_lizard (1317619) on Tuesday October 26, 2010 @02:08PM (#34028308)
    You know who else was able to estimate the number of German tanks?
  • by ZipK (1051658) on Tuesday October 26, 2010 @02:09PM (#34028328)
    I have an uncle with a small lighting business. He has one truck, proudly labeled #6. I guess the German's didn't think about their tanks as an advertising canvas.
  • by Attila Dimedici (1036002) on Tuesday October 26, 2010 @02:09PM (#34028332)
    This is very similar to the method that the CIA used to get a seat at the Big Boys table in U.S. Intelligence operations in the 1950s. When OSS became the CIA after WWII, they became a junior member of the U.S. Intelligence operations. In the 1950s, the Defense Intelligence Agency (I may have the wrong department, but it was the organization that got the lion's share of the U.S. Intelligence budget) estimated how many intercontinental bombers the Soviets had by looking at the size of the factories where they produced them and estimating how many the U.S. could produce in a factory of that many square feet. The CIA wanted to get a bigger chunk of the Intelligence budget, so they started looking at satellite photos of the Russian bombers. They noticed that the numbers on the tails of Soviet bombers went 1, 2, 3, 4, 5....11,12, 13, 14, 15,...21, 22, 23, 24, 25, etc. Based on this they determined that the Soviets had many fewer bombers than earlier estimates. When other sources provided corroborating evidence, the CIA was able to get a bigger chunk of the Intelligence budget. Of course, they then made the same sort of mistake in estimating ICBMs that they had corrected with this methodology.
    • by vlm (69642) on Tuesday October 26, 2010 @02:14PM (#34028408)

      in the 1950s

      so they started looking at satellite photos of the Russian bombers

      Hmm. Correct theory, but wrong implementation.

    • Re: (Score:3, Insightful)

      by LWATCDR (28044)

      Do you have a source because what you are saying is physically impossible?
      Tail numbers are on the vertical stabilizer. You can only read them from the side not from the top. Think about the slant range involved and do the math. We are talking about 1950s/ tech so think solid lenses and film with not digital image processing.

      Now if the pictures where from a U2 or if they put the numbers on the wing, that is a bit more reasonable but not from an early spy satellite.

      • by jandrese (485)
        This may come as a shock, but when someone is taking pictures from a plane they don't always do it from directly overhead. Sometimes the pictures come in at an angle.

        I do agree that satellite photo evidence would have been rather hard to come by in 1950 though.
    • by sznupi (719324)

      At least at some point it weren't mistake, but deliberate falsifications:

      http://en.wikipedia.org/wiki/Team_B [wikipedia.org]

      (just look at the names involved...)

  • by Kupfernigk (1190345) on Tuesday October 26, 2010 @02:13PM (#34028392)
    It can work backwards. At the Battle of Verdun in WW1, Petain (who only became an anti-hero in WW2) rotated French regiments through the Verdun front (a system called noria) so that whole regiments would not be destroyed. The Germans left their troops in battle till all were killed. From captured French uniforms and the number of regiments recorded, they greatly over-estimated the size of the French defense.
  • They used it to estimate that the Germans produced 255 tanks per month between the summer of 1940 and the fall of 1942. Turns out the serial-number methodology was spot on. After the war, internal German data put der Führer's production at 256 tanks per month -- one more than the estimate.

    It's comforting to realize I'm not the only one plagued by off-by-one errors!

    And what's with the power-of-two number--Numerology or what?

    • by h4rr4r (612664)

      I am just amazed one single methhead was able to make over 200 tanks a month. I would have thought they had some lackeys to do that sort of work.

    • by guruevi (827432)

      Nah, they recorded these data on punch cards. However they quickly noticed the buffer overflow created by using only 8 bits.

    • Re: (Score:3, Interesting)

      by geekoid (135745)

      What was the number of the first tank? zero, or one?

  • by xxxJonBoyxxx (565205) on Tuesday October 26, 2010 @02:20PM (#34028482)

    256 tanks per turn? Impossible! That would take a regular supply of 1280 IPCs...

  • They have "Panzers". Know the difference between your Civilizations. Yeesh!

  • On the arms production side, USA was able to convert so many auto factories into tank factories and airplane factories. Allies had breakthroughs in cryptography. The Generals were at least listening to the statisticians. Or at least the quants were able to get their idea up the chain of command. And people bought war bonds and planted victory gardens.

    Now we are fighting two wars (Afghanistan and Pakistan). Even that is proving to be a handful. Can USA stand up to a mighty enemy likes of WW II Germany or J

    • by alen (225700)

      it takes so long to produce a tank that you have to have everything ready and made before you go to war

    • Afghanistan doesn't threaten the existence of US, therefore you can't beat them. Just like Vietnam.

    • by h4rr4r (612664)

      Totally different kind of War. No amount of production can win when you are wasting a million dollar missile on a guy, his camel and their tent.

      Bombing also fails in those regions, you cannot bomb people who have no infrastructure to lose in any effective manner. We are repeating the mistakes of Vietnam.

    • by ErikZ (55491) *

      With a few hundred long range Nukes at the US's disposal, signs point to "Yes, easily.".

    • by jandrese (485)
      One of the big reasons Iraq and Afghanistan are such a mess is because the US Army was still set up to fight Germany and Japan. They're two very different battles, and because the military is so large and lumbering, it takes a long time to retool to fight the war you're in. You would think they had learned after Vietnam, but it's a tough lesson and nobody likes to hear it.

      Maybe someone in the government will finally learn the lesson that fighting insurgencies is just not worth the effort and avoid any
    • Re: (Score:3, Informative)

      by Wyatt Earp (1029)

      The wars in Iraq (which is all but over for the US, good luck with that INA) and Afghanistan are very different from World War Two. If the US had fought Vietnam, Iraq or Afghanistan with the same disregard for civilian casualties and overwhelming firepower there wouldn't be a problem.

      Modern Mindset - Isolate Fallujah, tell the civilians to get out, then go house to house to secure the city with Marines and Army.

      World War Two Mindset - Mass on one side of Fallujah, carpet bomb the far side of the city for a

  • Houses too (Score:4, Interesting)

    by mccalli (323026) on Tuesday October 26, 2010 @02:25PM (#34028564) Homepage
    My dad drove a tank in WWII. I believe one of the Churchills but I'm no war historian and I'm happy to be shown otherwise. He was in the Normandy landings and eventually in the invasion of Berlin too.

    Thing is, the German tanks had bigger guns and longer ranges - significantly longer. There was apparently a speed advantage to the British tank (I'm going by what I was told, again I'm not a WWII-buff by any means) though, so what they used to do was lure the German tank into a village, then drive round back of them. The German guns were so big they couldn't turn them in in a normal street with buildings on either side whereas the smaller British tank certainly could. Not sure this was by design, but they took any advantage they could of course and I'm told that this trick was used by my dad a number of times.

    Cheers,
    Ian
    • by psergiu (67614) on Tuesday October 26, 2010 @02:55PM (#34028992)

      http://www.imdb.com/title/tt0065938/ [imdb.com]

      Is your dad's name Sgt. Oddball ? :)

    • Re:Houses too (Score:4, Interesting)

      by david_thornley (598059) on Tuesday October 26, 2010 @03:26PM (#34029558)

      I am a WWII buff.

      If your dad drove a tank that was faster than German tanks, it probably wasn't a Churchill. Could it have been a Cromwell? Those also showed up in Normandy, were still in service at the end of the war, and were pretty fast.

      The tactic you describe was used against the bigger German tanks, as the ones the size of most Allied tanks didn't have especially long guns. He probably used it the most in the Normandy fighting, as that's when the Germans concentrated heavily against the British and Canadian armies.

  • Much is said about the 5:1 tank ratio (Sherman:Panzer), which did have an impact for rapidly owning ground. Air superiority was the winner, as the Germans couldn't reliably resupply their own troops. Rocket attacks from the Typhoons (and other similarly-equipped planes) on German armoured columns laid waste to reinforcement efforts.
  • Meth (Score:5, Interesting)

    by Robotron23 (832528) on Tuesday October 26, 2010 @02:49PM (#34028892) Homepage

    I read the title as 'Meth':

    For once a misreading made perfect sense in the summary title's context: use of amphetamines throughout World War II on land and air personnel is well-documented. There's a phrase one hears infrequently that amphetamines 'won the Battle of Britain' - fending off constant attack from the Luftwaffe made necessary the use of stimulants as hiring and training a new pilot took too long. Whether it really did tip the scales in that battle we'll never know. As one would expect abuse orose within both Allied and Axis forces, and the spike in use persisted after the war. The Vietnam conflict saw American troops use methamphetamine very widely, and today the drug is popular amongst the poor as a relatively inexpensive stimulant.

    If there's anything that isn't widely known by the public and merits publicizing it's history of drugs such as this in the context of 20th century events like warfare. What laid ground for a forerunner to the modern drugs situation to me represents a phenomena of greater gravity than the serial numbers of tanks which one would expect would be used simply through using good old oxymoronic common sense.

    Presently there's a drug by the name of 'Modafinil' which mimics amphetamine but removes almost entirely the euphoric element and much of the crash that accompanies sudden cessation. It has been around for a number of years, and sees much use in modern conflicts. It also has much off-label use, and has even been used by astronauts to cope with heavy exercise regimens.

  • This an article about how the allies where able to estimate the number of German Tanks produced based on the Serial Numbers of the Tanks. Neat!. Godwin does not apply.

    Seriously?!?! Is there an editor in the house? Try:

    This [is] an article about how the [Allies were] able to estimate the number of German Tanks produced based on the Serial Numbers of the Tanks. Neat!. Godwin does not apply.

    Geesh!

  • by mbone (558574) on Tuesday October 26, 2010 @07:35PM (#34033064)

    I read somewhere (maybe Max Hasting's book on Winston's War) about a problem the British had with some infantry equipment getting wet and non-functional. They supposedly solved it by going to condom makers, who made a several foot long condom to fit over the gear and keep it dry.

    When Churchill saw this, he said that it wouldn't do at all - he wanted each pack labeled "British Condom. Size - Medium."

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