New imaging research shows that brain activity differs in sleep-deprived and well-rested people. The study, in the May 21 issue of The Journal of Neuroscience, shows that individuals who are sleep-deprived experience periods of near-normal brain function, but these periods are interspersed with severe drops in attention and visual processing.

This seems a more plausible explanation than the typical "reduced cognitive ability" statement applied. I had sleep apnea for several years, undiagnosed, and did reasonably impressive cognitive things at the time. I guess I also had distraction or ambition trouble. Hyperconcentration, and then not so much. After treatment (CPAP, then surgery), cognitive function did not improve (not anywhere like my physical energy level did).

Sleep-deprived brains alternate between normal activity and ‘power failure’ | Think Gene