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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)

#71

Post by saeranv »

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…

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: As one of the comments below points out, you can also model it as a binomial distribution.

Probability of getting all heads, given p=0.5 is (n!)/((n-k)!k!) / 2^n. Since n=k since we're looking to get all heads at all times, this also simplifies to 2^(-n).

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

#72

Post by azinman2 »

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…

This is only true if each dimension is independent and identically distributed random variables, which is doubtfully true for humans. That said, the overall intuition is probably more correct than incorrect...

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

#74

Post by kube-system »

azinman2 wrote: post #72
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…

This is only true if each dimension is independent and identically distributed random variables, which is doubtfully true for humans. That said, the overall intuition is probably more correct than incorrect...

They are neither fully independent nor fully dependent. It falls somewhere in the middle. The same will apply, just in a slightly less dramatic effect.

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

#75

Post by philwelch »

battery_cowboy wrote: post #68
tgflynn wrote: post #62

Earlier quoted context omitted.

That must mean that well over 10% of adult male (from the other statistic that 90% of veterans are male) Americans have served in the military. I never would have thought the number was that high, especially with the military being all volunteer for decades.

There are about 2mm active and reserve military members and about 400mm Americans on the whole, so there are, at any time, 0.5% Americans in the military. Assuming the average enlistment is 1 term or 4 years, and people have about 80 year lifespans, then you get ~20 (80/4) "generations" of enlistments over a person's lifespan. 20 * 0.5% is 10%, so about what you would expect for "living veterans" if you had a constan…

Plus the size of the military has been even higher within living memory.

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

#76

Post by philwelch »

noir_lord wrote: post #59
TomMckenny wrote: post #50

Earlier quoted context omitted.

>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…

Not to mention desperation moves like the british STEN sub-machine gun which was basically what you get if you say "I need 800,000 of these and they just have to meet these criteria, eject everything else ". https://www.youtube.com/watch?v=8-PmLxkOmaM

The Sten was a beautiful accomplishment. Being cheap, simple, optimized for quick mass production, and just good enough to get the job done is a perfectly legitimate set of requirements. It’s like the IKEA LACK.

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

#77

Post by philwelch »

willyt wrote: post #37
Aloha wrote: post #25

Earlier quoted context omitted.

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…

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,…

And the Eastern Front was largely won and lost on the Atlantic Ocean.

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

#78

Post by tgflynn »

battery_cowboy wrote: post #68
tgflynn wrote: post #62

Earlier quoted context omitted.

That must mean that well over 10% of adult male (from the other statistic that 90% of veterans are male) Americans have served in the military. I never would have thought the number was that high, especially with the military being all volunteer for decades.

There are about 2mm active and reserve military members and about 400mm Americans on the whole, so there are, at any time, 0.5% Americans in the military. Assuming the average enlistment is 1 term or 4 years, and people have about 80 year lifespans, then you get ~20 (80/4) "generations" of enlistments over a person's lifespan. 20 * 0.5% is 10%, so about what you would expect for "living veterans" if you had a constan…

Possibly, though I would think that many who serve do more than 1 enlistment. It's just that from my own personal experiences I've encountered few veterans in my life (except for older generation family members who served in WWII), that's why intuitively I find the number a bit surprising.

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

#79

Post by travisjungroth »

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?"

Sometimes people just do things wrong. I imagine there’s some name for the fallacy of assuming all humans are perfectly intelligent, rational actors.

Why wouldn’t they do it? Because the people in charge of the decision didn’t think it was that important. That’s all it takes. And to their credit, making airplanes adjustable is harder than it sounds. A fixed seat is much lighter and cheaper than an adjustable one.

But, it turns out the trade offs are worth it. This is sort of like “never attribute to malice what can be explained by incompetence”, but “incompetence” is too strong of a word. They just didn’t know.

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

#80

Post by Balgair »

stygiansonic wrote: post #9
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…

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 surfac…

Numberphile has a good one on how these things can get crazy quickly:

https://www.youtube.com/watch?v=mceaM2_zQd8

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