For example, consider the notion that IQ is a measure of capacity. To wit, let's use an extended and natural analogy -- a container.
Consider a notional container measured only by its depth.
A yard of beer is 36 inches (~91.5cm) tall and most people would consider this a lot of beer. This plays out in people who are extreme specialists -- extremely knowledgeable in only one or two areas. But are they geniuses?
So we have to consider breadth. I have a large mixing bowl I use when marinating meat that's about 26 inches (66.04cm) across, and most people would consider it to hold a lot of meat. This plays out in people who are extreme generalists, not particularly good in any one area, but can cut across disciplines easily.
Yet both containers pale when compared to a 55 gallon (~208.2L) drum in terms of volume. Yet the drum is not as tall as the yard of beer and not as wide as my marinating bowl!
But volume is not the only thing that matters!
I wouldn't pour molten steel into any of the containers above. And I've used stoneware that cracks when used with extremely cold liquids.
What about containers with different compartments that can hold both?
We also know about people who have perfect recall but almost no creativity, and creative geniuses that can barely remember their own name.
Can somebody who is a generalist only know about several topics or can they synthesize it into something new and novel?
How about the person that, regardless of depth or breadth, can see far reaching implications -- second, third, forth degree effects -- when new information is presented? Or the extreme tactical thinker that can react to new things with extreme speed?
Napoleon and Einstein are both commonly regarded as geniuses, but the nature of their intelligence couldn't be more different.
This statement is false. They could be more different in ways you can't even imagine, for no one currently completely understands the nature of intelligence.