When the U.S. air force discovered the flaw of averages

What are you talking about?

I was thinking it was a Venn diagram, where none of the bubbles had complete intersection with the others.

"This bubble represents all pilots between 5'6" and 5'11" in height. And here's the bubble that represents those with 40" chests. Note how they barely intersect."

I can't speak for the entire military[1], but I've known a few "brilliant military minds" and they rarely, if ever, talk in terms of killing. The military's goals are usually things like area denial, disrupting lines of communication, limiting access to materiel and supplies, degradation of morale, etc.

These aren't just euphemisms. If you're trying to win a war solely by killing the enemy, you're going to be in for a looooong and bloody war. In fact, there's long been a thinking in the military that "a dead soldier removes one soldier from the field, but a wounded soldier removes two".

What makes the military, and war, seem "outdated" or downright "despicable" comes down to, I think, two things:

1. War is often what happens when two sides have let long lingering issues fester to the point that dialogue is not possible. In other words, the only thing anyone wants less than to throw the first punch is to be unable to throw the second.

2. Yes, military industrial complex. Specifically, the MIC has muddled the "goals" and abstracted them away behind many layers of "weapons systems" and "advanced tactics". That is, if you're a general attempting to disrupt lines of communication, and you have to decide on committing the lives of your soldiers and potentially taking the lives of your enemy, you might consider a battle plan that minimizes loss of life. If you're that same general and Raytheon (or Lockheed or Honeywell or...) offers to sell you the CommsRuptor 7000 that will take out enemy communications at the press of a button (and a signature on a check for $300M), you might not adequately question the impact on lives. War used to be about loss of blood and treasure. Lately it seems to be more about treasure and blood...

[1] Especially not the "grunts" that see front-line action. I've heard, anecdotally, that enlisted soldiers are often trained in such a way that they enter war zones with raw blood-lust. Whatever your opinion on this practice, I took from your question that you were more interested in the thinking of the decision-makers, i.e. commissioned officers.

Wow! This has implications for human genetics (a study that originated partly in considering human body size measurements like those described in the article) that I think most popular writers on human genetics have not taken into account. There was an article posted to Hacker News earlier this week that suggested, surely falsely in my opinion, that human genomes can be optimized for intelligence to such a degree that we won't even be able to estimate IQ scores for future individuals with the same kind of tests that we use now. I rather doubt it. Because of pleiotropic effects of genes, almost surely there isn't a gene shuffle that will massively increase human intelligence, but rather just strategies (as likely to be environmental as genetic) to improve average intelligence within the range already found in the worldwide human population.

Similarly, imputation of "race" by genome testing depends crucially on assuming that the average genome is informative, but for any trait of interest, a person who by both genome testing and known historical ancestry is categorized in some "race" category might have any degree of variance from "average" in the trait found in the whole human genome. It will be exciting to follow up on larger and larger data sets on these issues as human genomics projects continue.

Or as one of my professor would say (after showing the calculation for n-dimensional spheres): "and that's why infinite dimensional oranges are all skin!"