[HN Gopher] When U.S. air force discovered the flaw of averages
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When U.S. air force discovered the flaw of averages
Author : elorant
Score : 150 points
Date : 2020-04-23 15:07 UTC (7 hours ago)
(HTM) web link (www.thestar.com)
(TXT) w3m dump (www.thestar.com)
| ethbro wrote:
| The USAF employs averages in all kinds of interesting ways!
|
| "How US nuclear force modernization is undermining strategic
| stability: The burst-height compensating super-fuze" (or: How I
| Learned to Stop Worrying About Undershoot and Love Terminal
| Detonation Timing)
|
| https://news.ycombinator.com/item?id=16642280 (2018)
| MyHypatia wrote:
| Consider this set of statistics: 90% of elementary school
| teachers are female [1]. 90% of veterans are male [2].
|
| Unsurprising.
|
| But, there are 2 million female veterans in the US, and only 1.7
| million female elementary school teachers. That means if you talk
| to a random American female, it is more likely that she is a
| veteran than an elementary school teacher. I think a lot of
| disagreements on Hacker News and elsewhere stem from people
| saying "Well 90% of the time, X is true" without realizing that
| the 10% they are choosing to ignore is comprised of millions of
| people.
|
| [1] https://nces.ed.gov/programs/coe/indicator_clr.asp [2]
| https://www.google.com/url?sa=t&source=web&rct=j&url=https:/...
| pmiller2 wrote:
| > ...the 10% they are choosing to ignore is comprised of
| millions of people.
|
| I don't understand your point here. Is it that somehow, some
| people are more than 10% likely to run into the 10%? Well,
| that's obvious. Roughly speaking, you'd expect 10% of
| commenters to be _in_ that 10%, unless we 're talking about
| something that disproportionately does or does not affect
| people interested in technologies, startups, _etc._.
| MyHypatia wrote:
| The point is that people often have an opinion, cite one
| statistic to validate their opinion, miss the bigger picture
| (because summarizing anything complex with a single number,
| rarely tells the whole story), and in the face of additional
| evidence stick to that one statistic that validates their
| original opinion. I see it happen a lot. Both on HN and
| elsewhere too. Presenting multiple statistics that shine a
| different light on the same population, enriches the
| conversation, and gives a more complete characterization of
| the population/situation/phenomena etc.
|
| I also personally found that combined set of statistics
| enlightening because I previously did not realize how large
| the population of female veterans is, since I had only read
| about the percentages not the absolute numbers.
| TeMPOraL wrote:
| It's a problem of lack of STEM education, unfortunately.
| More specifically, of metrology.
|
| "90% of elementary school teachers" is not directly
| comparable to "90% of veterans". You have to multiply them
| by their respective populations to get numbers that can be
| compared. In general, a thing of the form "$amount of
| $something" is not comparable to "$amount of
| $somethingelse". That amount being a fraction with a '%'
| sign in front of it doesn't change anything.
|
| Unfortunately, schools aren't beating people with sticks
| until they internalize that point, while at the same time a
| good part of sales and marketing _relies_ on people not
| being formal enough in their thinking.
| MyHypatia wrote:
| Yes, I certainly wish schools would teach this better. I
| think showing different examples with surprising
| conclusions/outcomes helps people internalize that point.
| Natsu wrote:
| That's because you need to know that there are ~20 million
| veterans and ~1.87 million elementary school teachers, i.e. you
| need to know the base rate if I'm reversing the calculations
| properly.
|
| Another flaw of averages is apparent when you realize that the
| average person has less than two eyes.
| noizejoy wrote:
| And half of the population is dumber than the average. :-)
| abrahamneben wrote:
| Enter bayes theorem
| sudosysgen wrote:
| Bayes' Theorem should be getting taught with quite some
| emphasis in high school, imo.
| larrydag wrote:
| I would argue that Bayes Theorem is taught in high school
| basically conditional probabilities and inferences. The
| issue is that applied Bayes Theorem is not taught. What do
| you do with information given with the data at hand?
| TeMPOraL wrote:
| Bayesian updates should be taught in schools, at least at
| the most coarse-grained level. Not to let people
| calculate anything; almost nobody is going to need that
| in life anyway. But so that some authority (which a
| school is) tells people _they 're allowed and supposed
| to_ update their beliefs on evidence. That evidence drags
| belief more in one direction than the other. That 0 and 1
| are not probabilities in real life. That being certain of
| something is a rare thing, that they should embrace being
| more or less sure. That this is not someone's random
| worldview, but there is a proper (and rather fundamental)
| mathematical formalism behind it, it's just impossible to
| apply it fully in real life, so we have to approximate
| it.
| noname120 wrote:
| This is called Simpson's paradox[1].
|
| [1] https://en.wikipedia.org/wiki/Simpson%27s_paradox
| def8cefe wrote:
| >The Aero Medical Laboratory hired Daniels because he had majored
| in physical anthropology, a field that specialized in the anatomy
| of humans, as an undergraduate at Harvard. During the first half
| of the 20th century, this field focused heavily on trying to
| classify the personalities of groups of people according to their
| average body shapes -- a practice known as "typing." For example,
| many physical anthropologists believed a short and heavy body was
| indicative of a merry and fun-loving personality, while receding
| hairlines and fleshy lips reflected a "criminal type."
|
| Can anyone point me in the direction of more information on this?
| Curious to learn more but my searches didn't turn up anything
| related.
| krenzo wrote:
| I think they're referring to this:
| https://en.wikipedia.org/wiki/Somatotype_and_constitutional_...
| AdrianB1 wrote:
| This is a duplicate, see
| https://news.ycombinator.com/item?id=11230287,
| https://news.ycombinator.com/item?id=16220499 and more.
| pintxo wrote:
| > any system designed around the average person is doomed to
| fail.
|
| Daniels published his findings in a 1952 Air Force Technical Note
| entitled The "Average Man"?
| barbegal wrote:
| Which you can read here
| https://apps.dtic.mil/dtic/tr/fulltext/u2/010203.pdf
| stcredzero wrote:
| I remember when this idea came around Hacker News the last time.
| I mentioned this over lunch, and one of my (highly respected and
| deservedly considered intelligent) younger coworkers called BS on
| it. His object was: "Why would a government build an expensive,
| high tech piece of equipment, then not ensure it could fit the
| operator?" He just couldn't imagine it.
|
| Between 2020 and WWII, there is a huge difference in available
| technology and scale. There were a lot more planes and a lot more
| pilots back then. It's practically a WWII trope: Arguably
| "inferior" weapons systems win out because they can be produced
| in larger numbers with better maintainability and support
| logistics. (1)
|
| Depending on how you evaluate it, the amount of firepower and
| capability embodied in one WWII fighter is greatly dwarfed by
| that in one gen 4 or gen 5 fighter jet.
|
| (1) (Though, in WWII, Allied planes often had a tremendous
| advantage in performance, largely because they had access to far
| better fuel. This allowed for much higher compression ratios and
| higher pressure superchargers, so they could produce more power,
| more efficiently, for less weight. "Greg's Airplanes and
| Automobiles" on YouTube covers this.)
| TomMckenny wrote:
| >Why would a government build an expensive, high tech piece of
| equipment, then not ensure it could X
|
| Maybe short design periods in some cases too. Either way it was
| not too uncommon. There were bombers with escape hatches big
| enough for the crew, provided they didn't wear parachutes[1].
| Fighter bomb releases that required ducking down to reach
| them[2] and fighter planes who's fuel feed stopped when pulling
| negative Gs [3]
|
| [1] Lancaster bombers
|
| [2] P-26 or F2A I think
|
| [3] https://en.wikipedia.org/wiki/Miss_Shilling%27s_orifice
| Aloha wrote:
| Our technology also continued to evolve throughout the war,
| updated fighters, better engines, even whole new designs. The
| Germans as far as mass produced designs went were effectively
| frozen in 1939. A lot of this was the complete inefficiency of
| the Reich Air Ministry at project management, as well as the
| political supremacy of the Heer over the Luftwaffe. In addition
| to the political whims of a dictatorship (Technological choices
| were often driven by ideology, and perception, much more than
| in the other dictatorship at the time (the Soviet Union, where
| for the most part, the technocrat reigned supreme))
|
| All this said, from purely a material point of view the war in
| europe was won by the allies in 1941 when the US joined the
| conflict, but the Axis could have dragged the conflict out much
| longer had they had an effective strategic bombing program, and
| more modern fighters.
| willyt wrote:
| Regardless of Spitfires, Alan Turing, anti-sub technology,
| RADAR etc, WW2 was won and lost on the Eastern front. The
| Normandy invasion would have been impossible without the
| Russians sacrificing between 8-11 million soldiers. This
| compares to about 400k each for the UK and US.
|
| I'm just saying, don't get carried away with the
| technological superiority argument, there was plenty of
| innovation on both sides. After all, the engineer that
| designed the Apollo rocket was a Nazi weapons scientist.
| Aloha wrote:
| No real disagreement there - the war was won on the back of
| Russian Bodies, American Trucks, and British Grit.
|
| The germans did indeed have wonderful technology in labs,
| and had it made it into mass production, it would have made
| the war stretch out much much longer.
| stcredzero wrote:
| _Our technology also continued to evolve throughout the war,
| updated fighters, better engines, even whole new designs. The
| Germans as far as mass produced designs went were effectively
| frozen in 1939._
|
| Well, not completely. "Greg's Airplanes and Automobiles" has
| a nice video on, "Why was the BF109K faster than the P51D? MW
| 50!" So to try and compensate for only having lower octane
| fuel, German engineers in WWII went to water/methanol
| injection for emergency power. Things did go back and forth
| quite a bit. Granted, the BF109 was one of the most advanced
| late 1930's designs going up against 1940's allied wartime
| designs. But there were times when updates on older designs
| would outclass the other sides slightly older versions, and
| this happened repeatedly on both sides.
|
| _Technological choices were often driven by ideology, and
| perception, much more than in the other dictatorship at the
| time_
|
| "Yes, but can it dive bomb?" probably did about as much to
| compromise designs of Nazi fighter/interceptors and slow the
| release of new airplanes as espionage and sabotage by the
| allies!
| artsyca wrote:
| How many software engineers fit the mold of the bearded male
| craft beer connoisseur vs how many are trying to shoehorn
| themselves into it?
| artsyca wrote:
| Not to pick on a single stereotype but it seems we've become
| memes and it's led to an attack of the clones on the ideas of
| diversity and inclusion flipping everything on its head
|
| Think about how 'fitting in' is also a term for 'averaging out'
| and ask yourself how much we value mediocrity?
|
| You can only join our group if you fit within one of these
| narrow guidelines and wear one size fits all clothing
|
| For crying out loud I'm sick of all the fakeness in the name of
| technology
| lalaithion wrote:
| Note that this is not some sort of unexpected effect due to
| humans not behaving mathematically ideally; this is what happens
| when your intuitions about 1, 2 and 3 dimensions are applied to
| higher dimensional spaces. Consider the goal of being in the
| middle 50% of a random value on one dimension; you have a 50%
| chance. But if you have two dimensions, and you want to be in the
| middle 50% for both of them, it's a 25% chance. And if you have
| 3, it's a ~12% chance. This already is counterintuitive, but when
| you ramp it up to 10 dimensions, it's a ~0.01% chance. That means
| that if you have a thousand people, only one of them (on average)
| will be in the middle 50% of all of them. Even the praised end
| state of the air force, with 9 dimensions and a required support
| of 90% of individuals of each dimension, implies that only 38% of
| individuals will be supported overall. (Granted, human dimensions
| aren't wholly uncorrelated.)
| whiddershins wrote:
| 1 of 10,000 is .01% right?
| 6gvONxR4sf7o wrote:
| I find it more intuitive to to discard the spatial intuition
| and think in terms of events. You want something in the X%
| norm? Think about it like a X%-heads biased coin flip. If you
| flip it enough times, it'd be shocking to get all heads. Even
| if the coin flips (dimensions) are correlated, many coin flips
| (dimensions) means at least some tails (dimension outside the
| norm).
| clintonc wrote:
| That last bit seems to be the Crux of why this is so surprising
| -- being in the middle 50% on some dimension correlates
| positively with being in the middle 50% on the other
| dimensions, rather than each dimension being independent as in
| your calculation. It's difficult for me to reconcile that, for
| the 400 in the study within 5% of average height, each was a
| standard deviation away from the mean in some other
| measurement.
| Retric wrote:
| It's two different effects. First being within a range is not
| the same as being at the center of the range. Someone 4%
| above average height should have ~50% of their dimensions
| larger than that. Similarly someone at 4% below average
| should have around 50% of their dimensions below that. At
| best someone in the exact middle of the range only has so
| much buffer to work with.
|
| Second the correlation is less significant than your
| assuming. My legs are the same length as some people a full
| foot shorter than I am.
| MauranKilom wrote:
| Or to work the example in the article: Being in the middle 30%
| of any three traits has a 2.7% chance (matching the quoted 3%).
| For ten traits it's a 1e-6 chance.
| user5994461 wrote:
| Should note that the study seems to be working on an extremely
| narrow range, the 30% in middle to quote the article. So
| measurements in the 35-65% percentile from what I understand.
|
| In layman's term. It's so narrow that there are more people 1
| inch off than there are people within the expected height. It's
| crazy.
|
| Probability is talking in terms of standard deviations
| nowadays. They are selecting less than half a standard
| deviation, it's hyper selective. I'm curious how many people
| would fit the norm if the study was looking at 1 standard
| deviation. Surely a lot more.
|
| For reference. Selecting the 30% on six metrics is keeping less
| than 0.01% of participants. Selecting the 68% (one deviation)
| on six metrics is keeping 10% of participants. It's night and
| day. Should be even more in practice because measurements are
| correlated.
| stygiansonic wrote:
| Great explanation. This is an example of the curse of
| dimensionality. An intuitive way to think about this is that
| each dimension you add is another "chance" for one of them to
| fall outside of the range.
|
| Another way to think about it is the often-cited unit
| n-dimensional sphere. If you were to uniformly sample points
| from within this n-dimensional sphere, as n increased, the
| proportion of points lying near the surface of the sphere would
| increase.
| war1025 wrote:
| Thought this sounded familiar then realized it's a book review
| for a book I read a few years back.
|
| It was an interesting book. Recommend it to anyone who finds the
| article interesting.
| cpascal wrote:
| This reminds me of a Planet Money podcast where they try to
| figure out the characteristics of the most typical American, or
| as they put it "who is the person I'm most likely to run into?"
|
| To construct this archetype, they used the mode of various
| dimensions rather than the median or average.
|
| https://www.npr.org/2019/08/28/755191639/episode-936-the-mod...
| leephillips wrote:
| This is a really interesting article. The most fascinating part
| is to learn that the AF actually listened to the man and changed
| their policies.
|
| This kind of thing can happen even when only measuring a single
| dimension, if the distribution is multimodal. If everyone is
| either really short or really tall, then nobody will be near the
| average height.
| macintux wrote:
| I realize that the audience is quite different, but it's
| interesting to compare the response to "no woman matches our
| expectations" (means they're fundamentally broken) vs "no man
| matches our expectations" (means the model is fundamentally
| broken).
| MaxBarraclough wrote:
| Anyone else seeing _Firefox blocked a fingerprinter_?
|
| Outline link: https://outline.com/uqNUEe
| lucas_membrane wrote:
| The referenced study of human dimensions was not the only thing
| done by the military to improve aviation safety. The discovery of
| human factors in user interfaces was also recognized. There had
| been some standardization of the cockpit controls of different
| aircraft during WWII and before, but not so much for the
| instruments and displays. That was no easy task, but the problem
| was recognized and addressed.
| duxup wrote:
| I wonder if this applies to something like performance reviews
| where measuring overall performance as something relative to
| 'average' inevitably doesn't make sense to anyone as perhaps
| there is no average there for a job with any level of complexity.
| Symmetry wrote:
| Huh, the conventional story is that the UN forces won the air war
| in Korea because of better plane ergonomics despite Migs having
| better theoretical performance. But this report didn't come out
| until the war was mostly over. The conventional story emphasizes
| things like bubble canopies but still.
| RcouF1uZ4gsC wrote:
| > Out of 4,063 pilots, not a single airman fit within the average
| range on all 10 dimensions.
|
| > Less than 40 of the 3,864 contestants were average size on just
| five of the nine dimensions and none of the contestants -- not
| even Martha Skidmore -- came close on all nine dimensions.
|
| This seems more an issue of the "curse of dimensionality"[0] more
| than the "flaw of averages". Be very wary when you are trying to
| draw conclusions from a dataset with many dimensions.
|
| 0. https://en.wikipedia.org/wiki/Curse_of_dimensionality
| ken wrote:
| I don't think so. They also said:
|
| > Even more astonishing, Daniels discovered that if you picked
| out just three of the ten dimensions of size ... less than 3.5
| per cent of pilots would be average sized on all three
| dimensions.
| Someone wrote:
| FTA: _"These formed the dimensions of the "average pilot,"
| which Daniels generously defined as someone whose
| measurements were within the middle 30 per cent of the range
| of values for each dimension."_
|
| 0.33 = 0.0027 = 2.7%, so if those measurements are
| independent of each other, it isn't surprising that he found
| "less than 3.5 percent".
| Worker32850 wrote:
| Human dimensions are closer to a normal distribution. (Not
| quite normal, but let's pretend.) In that distribution then
| 46% of subjects should be in the middle 30% of 3
| dimensions. [0]
|
| [0] With 4000 subjects they presumably have all sizes
| within ~3.5 stddevs represented. The middle ~1.2 stddevs
| should hold ~77% of the population. 0.77^3 = ~46%
| Retric wrote:
| I think the general assumption is arm length and height for
| example are strongly correlated.
| JoeAltmaier wrote:
| Been noted here on HN: the average web form excludes lots of
| people. Lots of folks cant fill in: First/middle/last name;
| unique username/password; social security number; street address;
| bank account.
|
| And not just folks in Micronesia or whatever. Heck my business
| partner hasn't got a deliverable street address - no mailbox at
| his house. He has a PO box. Is a nightmare getting Amazon
| deliveries that aren't lost, or left in the bushes, or returned
| undeliverable.
|
| Anyway, yes, there is no average person.
| astrea wrote:
| The name field situation has never bothered me as a typical
| American with the standard name format, but as I've grown and
| met people from different cultures I've learned just how
| frustrating that part of forms can be. Even (or rather,
| especially?) government forms are terrible about this.
| NickM wrote:
| Even typical Americans struggle with this sometimes if they
| have, say, hyphenated last names. I've encountered plenty of
| software out there that will reject or fail on even such a
| common case as this.
| CalChris wrote:
| This reminds me of an old math joke. A statistician and a
| mathematician went duck hunting. From a blind, the mathematician
| shot and hit a duck. Their retriever went and got the duck. Then
| the statistician spotted and shot at another duck but shot too
| high. Quickly the statistician shot again but too low. The
| statistician then beamed with pride, _on average, that 's a dead
| duck_.
| clircle wrote:
| Even with just one dimension, the average may not be
| characteristic of the population.
| tinalumfoil wrote:
| This interesting but all a bit wordy and meandering.
|
| Tldr: The air force was using the average dimensions of their
| pilots to design aircraft. Coincident to this, there was a large
| number of downed planes questionably attributed to "pilot error"
| but that many believed to be from an unknown cause. A recruit
| from Harvard charged with collecting data on pilots realized few
| people were close to the average, and recommending cockpits be
| fit to each individual. The AF took the recommendation and
| eventually companies produced aircraft with adjustable seating
| and cockpits.
|
| Tldr tldr: dont just reach for the average
| jimhefferon wrote:
| > meandering
|
| I know. Isn't that wonderful?
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