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When U.S. air force discovered the flaw of averages (2016)

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Re: When U.S. air force discovered the flaw of averages (2016)

#111

Post by [deleted] »

clintonc wrote: post #16
lalaithion wrote: post #7

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% ch…

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 measurem…

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Re: When U.S. air force discovered the flaw of averages (2016)

#112

Post by saeranv »

spappal wrote: post #103
saeranv wrote: post #71

Earlier quoted context omitted.

This comment was what made this article make sense to me. Just to add to add to the mathematical intuition here (please correct me if I'm wrong): if you're thinking of it as a unit line/square/cube then total n-dim area is 1^n, and the portion in the 50% range is (1/2)^n, where n = number of dimensions. So that should simplify to 2^(-n). Note this works out to 10th dimension as 0.09765% or 0.1 person per 1000. ETA: A…

P(simultaneously within middle 50 % of n independent distributions) = 0.5^n = 2^(-n), like my parent comment says. But interestingly, every relevant comment here either got something wrong about the final frequency or percentage, or corrected the wrong thing. (Parent comment, grandparent, 2 aunts and 1 cousin.) 0.5^10 = 2^-10 = 1/(2^10) = 1/1024 [i.e. exactly 1 person per 1024] ~= 0.00097656 ~= 0.09766 %.

Hah, you are correct. I even had access to numpy and still managed to get this wrong.

Re: When U.S. air force discovered the flaw of averages (2016)

#113

Post by mbrodersen »

BeetleB wrote: post #96
stcredzero wrote: post #21

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 avai…

> Why would a government build an expensive, high tech piece of equipment, then not ensure it could fit the operator? Why would they send a $250M probe to Mars, and not ensure a consistent set of units is used? I mean, putting the above two examples aside, one could list plenty of much bigger screwups by the government. Why is this person assuming a competent government? I wish I knew the name for this fallacy, but i…

I am sure you can also produce a long list of screwups by private companies. Assuming you made an honest effort of course. Private companies fail and go bankrupt every single day. 90% of private companies fail within a year. The real problem is not government/private. The real problem is making a large number of people work well together while making sure millions of decisions are all 100% correct. That is a very hard problem. What is surprising to me is that large organizations (governmental/private) sometimes succeed. That is the real miracle.

Re: When U.S. air force discovered the flaw of averages (2016)

#114

Post by mbrodersen »

TomMckenny wrote: post #50
stcredzero wrote: post #21

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 avai…

>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 G…

Those bombers were designed and built by private companies. Paid for by the government.

Re: When U.S. air force discovered the flaw of averages (2016)

#115

Post by mbrodersen »

Aloha wrote: post #25
stcredzero wrote: post #21

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 avai…

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 (Techno…

The end of the war began when Germany invaded Russia. Europe/Russia had already killed 30+ million German soldiers and destroyed most of the German war machine when the US joined the conflict. The real contribution of the US was stopping Russia from invading Europe after the war (see Berlin Airlift) by threatening to drop nuclear bombs on Russia (Russia at that point wasn't a nuclear power).
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