Let me give you the dirty little secret about Petraeus. He runs five miles a day. He’s sixty years old. He’s run a lot of miles. What do you think his body fat is? Pretty low, I’d guess. What is your brain made of? Petraeus rose to the top of an organization (The Army) that glorifies and rewards long distance runners and people with low body fat. The Army wants loyal Officers, not smart Officers. What would the university professors look like if they all had to be able to run five miles in under 35 minutes and have 5% body fat? Those generals aren’t as smart as you’d hope they would be.
I would say this...having spent twenty-two years in the Air Force...in the era when fitness wasn’t important and in the era when your career depended on fitness. The low-body fat folks weren’t exactly looking at a problem in the same way that others would. These folks ran for hours, then would come back to the office in an exhausted state but act like they were fully functional in the mental sense.
If you wanted the very best mentally out of one of these people...you did it in the early morning hours before their workout.