I wonder if anyone in psychiatry tried to define such a thing as a general ability vector.
Suppose you find a set of orthogonal (uncorrelated) basic abilities that can be quantified in all humans (general intelligence, executive function, ...), and you assign each as a scalar in a vector.
You then use statistical methods to weight each scalar in such a way that the mean norm is 1 for the entire population.
I suspect that if you do it right, the magnitude will have a Gaussian distribution.