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Math Idle

How That 'Extra .9%' Could Ward Off a Zombie Apocalypse 204

Posted by samzenpus
from the protect-ya-neck dept.
netbuzz writes "The questioner on Quora asks: 'When is the difference between 99% accuracy and 99.9% accuracy very important?' And the most popular answer provided cites an example familiar to all of you: service level agreements. However, the most entertaining reply comes from a computer science and mathematics student at the University of Texas, Alex Suchman. Here's his answer: 'When it can stop a Zombie Apocalypse.'"
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How That 'Extra .9%' Could Ward Off a Zombie Apocalypse

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  • The question isn't how to ward off the zombie apocalypse. The question is how could a zombie apocalypse realistically happen at all. Any explanation is a huge stretch.
    • Re: (Score:3, Interesting)

      by Sussurros (2457406)
      A zombie apocalypse happened in Britain and was shown in a BBC documentary by Derren Brown.
      • por supuesto
      • A zombie apocalypse happened in Britain and was shown in a BBC documentary by Derren Brown.

        I don't even know where to start pointing out what's wrong with that sentence.

      • You may have confused Derren Brown with Danny Boyle... ;-P
        But if not, I wanna see that Derren Brown special, he does some seriously cool stuff. You know you're a good magician/mentalist when some people think you're the "real deal", (even when you admit you're not). I guess that makes him the Kreskin of the times.
    • by 91degrees (207121)
      Zombie apocalypse is just the writer being cute. This applies to any potential pandemic.
      • by ceoyoyo (59147)

        Or any disease at all. What he's really pointed out is that you need to have an extremely specific test before you can even consider using it for screening. The textbook example is mammography.

    • by ceoyoyo (59147)

      If you want to be boring replace "test for zombification" with "mammogram for breast cancer."

      Both are examples of why we have so few screening tests. That's why full body CT is detrimental when used as a screening test.

  • Statistics 101 (Score:5, Interesting)

    by blackicye (760472) on Thursday April 04, 2013 @12:56AM (#43355193)

    An example we were given in my Intro to Stats module once upon a time used the Space Shuttle Program.

    The numbers following the decimal point are very important when it might mean the difference between a Space Shuttle failing catastrophically instead of leaving / returning through the atmosphere intact.

    And the vast differences in manufacturing costs between a 99.9%, 99.99% and 99.999% fault tolerant component and why
    it would be necessary in the bigger picture of the complete system.

    • Re:Statistics 101 (Score:4, Interesting)

      by cusco (717999) <brian@bixby.gmail@com> on Thursday April 04, 2013 @01:07AM (#43355217)
      I read once that one of the most important things to come out of the entire Apollo program was the concept of 'zero defect manufacturing', which until then had only been possible in small custom workshops.
      • by Cryacin (657549)
        Unfortunately 'zero defect manufacturing' was quickly negated by 'rubber stamp testing' and 'austeric quality manufacture'
        • by sjames (1099)

          Which meshed perfectly with the epidemic of management 9 envy. Er, Um, SURE, the stapler is five nines, six sigma, ISO 9000, and CORBA compliant.

    • Re:Statistics 101 (Score:4, Insightful)

      by girlinatrainingbra (2738457) on Thursday April 04, 2013 @01:16AM (#43355241)
      Yes, but the other key item is the incidence of "false positives" and "false negatives". Both of these incidences are very dependent upon the penetration of the disease in the general population in the first place. See the concept of sensitivity and specificity [wikipedia.org] for more details.
      .
      But the summary is a test that is 99% accurate (for both true positives and true negatives) with the zombie incidence rate shown would have :
      the possibility that a positive test result being a true positive of only 1/6 = 16.66%

      whereas a test that is 99.9% accurate would have

      the possibility that a positive test result being a true positive of only 2/3 = 66.66%

      for the incidence of Zombies (Mad Human disease) given in that student's example.

      • by AK Marc (707885)
        Yeah, but if you say "zombie" then it's suddenly fun and interesting.
      • Be the kind soul to explain me why a test that works in 99 out of 100 times in the lab only actually works 1/6th of the time when applied in the real world?

        • Re:Statistics 101 (Score:5, Informative)

          by suutar (1860506) on Thursday April 04, 2013 @11:45AM (#43358753)

          The key factor is that the trait being tested is rare; only one in 500 people has it. In this case, the false positives can still be (substantially) more frequent than true positives.

          Say you test 50,000 people. 100 have it, 49,900 don't. Of the 100 who have it, there will be 99 correct 'yes' results and one incorrect 'no' result. And of the 49900 who don't have it, there will be 49401 correct 'no' results and 499 incorrect 'yes' results.

          So total, we have 598 'yes' results. But 499 of those are false positives, which is 83.4444%; only 16.5555% of the folks who test positive are really positive.

      • Or, y'know, instead of hogging all of the test kits, you could just use the bad test twice on one person. If the chance of failure is fully independent, then you suddenly have a 99.99% accurate test. Even a test that's only partially independent is likely to yield better results than a single use of the 99.9 test when repeated—and in the real world, medical tests rarely give false positives consistently, especially for something as dramatic as the presence of an incubating pathogen.
    • Re:Statistics 101 (Score:5, Insightful)

      by Solandri (704621) on Thursday April 04, 2013 @03:39AM (#43355697)
      Actually, the Challenger disaster hinged on a different failure in statistics. Originally the SRB segments were mated with 2 O-rings. Inspection of the SRBs after launch revealed the O-rings were failing at a higher than expected rate. So to mitigate the risk they redesigned the system and... added a 3rd O-ring. The reasoning was that if a single O-ring had a (say) 1% chance of failure, then two would have a .01^2 = .01% chance of failure, and three would have a .01^3 = .0001% chance of failure.

      Unfortunately, that reasoning only works when the failures are independent events. If a single event (like cold weather) can cause the failure of one O-ring, it can also cause the failure of the other O-rings, so that failure mode is not independent. And your chance of all three O-rings failing is closer to 1% instead of 0.0001%.

      Same thing happened at the Fukushima nuclear plant. They had something like a dozen diesel generators under the theory that even if a few failed to start, it was highly unlikely that all would fail to start. They completely missed the possibility that a single common event could cause all the generators to fail the same way.
      • by stiggle (649614)

        Which is why you'd make the O-rings out of different compounds, and install no set with all the same type.
        Locate the diesel generators in 2 or 3 power houses around the site.
        2+ server rooms on site with replication between them (with additional replication off-site).

        But how much resource do you throw at the problem? Its easy for us after the events to decide if NASA should have used O-rings of differing compounds or Fukashima have multiple power houses on different levels.

        • Re:Statistics 101 (Score:5, Interesting)

          by digitig (1056110) on Thursday April 04, 2013 @07:59AM (#43356487)

          Which is why you'd make the O-rings out of different compounds, and install no set with all the same type.

          Which still doesn't eliminate dependent failures, because the failure of one O-ring increases the stress on the next O-ring (particularly the burst of pressure as the first O-ring fails).

          Locate the diesel generators in 2 or 3 power houses around the site.

          Which doesn't eliminate dependent failures when the failures are due to a contaminated fuel delivery.

          2+ server rooms on site with replication between them (with additional replication off-site).

          Which doesn't eliminate dependent failures when the failures are due to common software running on all sites.

          But how much resource do you throw at the problem? Its easy for us after the events to decide if NASA should have used O-rings of differing compounds or Fukashima have multiple power houses on different levels.

          For that you could call me in. Working that out what I do for a living.

      • by drinkypoo (153816)

        Actually, the Challenger disaster hinged on a different failure in statistics.

        Yes, the specification sheet for the O-Rings stated that they would fail in those conditions 100% of the time...

      • by Electrawn (321224)

        You do realize that the SRB bands were completely redesigned following Challenger? Not just add a third O ring and be done?

        http://science.ksc.nasa.gov/shuttle/technology/images/srb_mod_compare_3.jpg [nasa.gov]

        A retainer band around the pins, longer pins, changing the mating feature (Clevis and Tang) from a U to more an S to further prevent gases from escaping. And joint heaters for cold weather.

      • by roc97007 (608802)

        (Insightful content snipped.)

        > Same thing happened at the Fukushima nuclear plant. They had something like a dozen diesel generators under the theory that even if a few failed to start, it was highly unlikely that all would fail to start. They completely missed the possibility that a single common event could cause all the generators to fail the same way.

        It may not have been that simple. In that area tsunamis are fairly common. There are (according to articles, I've never been there) stones hundreds of

      • And why just settle on one letter? Also have P-rings and Q-rings and R-rings etc. to cover more of the alphabet to distribute risk.

    • Just think, if you are right 99.9% of the time, then you spend 8,640 seconds per day being wrong - or 2.4 hours.
      If, however, you are right 99.9% of the time, then that reduces to 864 seconds, or 0.24 hours.

      So based on that, I can only conclude that my wife is the 99.99% one and I am the 0.1% one.

      • Your math is terrible. ;-p There are 86,400 seconds in a day. 1% of that 864 seconds, not 8,640. You calculated for 10%. 864/60 = 14.4. You'd only spend 14.4 minutes a day being wrong.
  • by complete loony (663508) <Jeremy...Lakeman@@@gmail...com> on Thursday April 04, 2013 @01:13AM (#43355235)
    A better answer; False positive medical tests.
    • Actually, that's pretty much the context that the zombie plague answer is given in.

      • by Darinbob (1142669)

        Except that if it really was known that a zombie apocalypse could result, they'd take the chance on the 99% test, thus curing one proto-zombie while harming five uninfected people (who won't all die). If it's the fate of all mankind, then should you quibble over that?

    • Spot on. I once spent some time (fruitlessly) trying to explain to a guy that a cheap test for HIV that has a false positive rate of 5% will be useful in sub-Saharan Africa (where the occurrence of HIV is around 10-20% of the population), but that very same test is useless in Scandinavia (where it will almost always report a false positive).

    • by steelfood (895457)

      We all have cancer, just like we're all eventually going to die. It's a matter of whether it's under control or not.

  • Is this supposed to get us interested in Quora? If so, it failed. If this is an example of the level of intellectual masturbation on Quora now I will continue to stay away from that boring site.

    • by naroom (1560139)

      If this is an example of the level of intellectual masturbation on Quora now I will continue to stay away from that boring site.

      As opposed to Slashdot, where we discuss posts about blogs about Quora answers. Much more interesting..

  • by GauteL (29207) on Thursday April 04, 2013 @03:13AM (#43355629)

    "You can't justify subjecting 5 people to the negative effects of the cure in order to save one zombie, so your discovery is completely useless."

    No. You would administer it and risk killing many healthy humans, because the alternative is certain annihilation of the human race.

    The premise of the story is fine though. Although my zombie analogy would be the difference between a 99% chance of no zombie outbreak in a year vs. a 99.9% chance. The former would mean a 37% chance of a zombie free century. The latter would mean a 37% chance of a zombie free millennium.

    • by Kvasio (127200)

      is anyone outside USA (and not exposed to horror movies) really worried about zombie apocalypse? Really?!

    • Even poorer judgment, in fact, as his probability calculation relies on an actual rate of infection of 1 in 500. For such a highly contagious disease the rate of infection will grow (well, duh!) So if 1 in 500 gives about 83% false positives, when the infection rate reaches 1 in 50 the false positive chance drops to 33% and for 1 in 5 to 4%.

      So indeed 99% is quite good for a high contagion rate, not so good for low contagion and useless for something that's exceedingly rare (for a disease that affects only o

      • ... and of course this uses his assumption for the chance of false positives, which is basically ... wrong. Quite embarrassing for a math student, since instead of stating it as an independent variable (as he should have) he assumes that

        P(test positive | not infected) = 1 - P(test positive | infected)

        where in fact the right hand side is P(test negative | infected), quite a different thing from the left hand side.

        If otoh your zombie test has 0 false positives, that .9% will be irrelevant as anyone flagged po

        • by ceoyoyo (59147)

          I didn't read his math because I'm not registering for a Quora account, but from what his text describes he's come up with the right answers. I think you've got your conditional probabilities the wrong way around.

          He states early on that the test is 99% accurate, with equal sensitivity and specificity. 99% specificity implies a 1% false positive rate.

      • by Kelerei (2619511)

        Even poorer judgment, in fact, as his probability calculation relies on an actual rate of infection of 1 in 500. For such a highly contagious disease the rate of infection will grow (well, duh!) So if 1 in 500 gives about 83% false positives, when the infection rate reaches 1 in 50 the false positive chance drops to 33% and for 1 in 5 to 4%.

        That said, one could argue that then the infection rate reaches those levels, it would be too late for the cure.

        In fact, it may be able to prove (or disprove) this with the equations of motion that we learned back in elementary physics (here's a refresher [wikipedia.org] if you've forgotten them). Substitute velocity with rate of infection, acceleration with how the rate of infection grows, and displacement with number of people infected (obviously, time stays as is), and you'd have a pretty decent starting point. No

  • putting it on completely different subject: if a filter stops 99% of pollutant, you get 10x pollutant unfiltered when compared to the filter with 99.9% efficiency and 100x than with filter of 99.99% efficiency.

  • Brains (Score:4, Funny)

    by meta-monkey (321000) on Thursday April 04, 2013 @06:37AM (#43356149) Journal

    I was with him until he said one of the perks of being the plague-stopping hero was having your biopic narrarated by Morgan Freeman, when I'd obviously much rather have Zombie Morgan Freeman doing the VoiceOver.

    "Brains. My, my, my, some sweet delicious brains would be mighty fine indeed. Brains."

    You know you just read that with Morgan Freeman's voice in your head.

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