One form of intelligence testing gives people a lot of different tests
that involve mental abilities. These will include memorization, math
problems, spatial puzzles, synonyms, producing words with certain
properties, etc. This gives you a bunch of numbers, the scores on
each test.
Then a procedure called factor analysis is applied to the statistics.
This looks for underlying factors which can explain all or most of the
variation in scores. For example, we might have two tests which have
almost perfect correlation among the test subjects. Everyone who does
well on test A also does just as well on test B, and vice versa. This
suggests that both tests are measuring the same underlying factor.
This statistical procedure is relatively automatic. It can be thought
of as finding the base vectors in a multidimensional space. As a result
it tells you the dimensionality of the space, which is the number of
different independent kinds of intelligence you have measured. Once
you have your factors, you can try to use your judgement to give names
to them; one might be reading speed, for example, if it turns out that
tests which involve a lot of reading are heavily influenced by that
factor.
One controversial question is whether there is a single base factor which
influences all the scores, the so-called "g" factor. Some people have
argued that there is no "g", that people's scores on all the different
skills are randomly distributed, and that there is no correlation between
abilities in the different skills. Others have claimed to find in the
statistics evidence that there is such a correlation, that people who tend
to be good at math equations also tend to be good at finding the real point
of a story. Presumably the existence of the controversy suggests that the
"g" factor, if it exists, is relatively weak. So this would suggest that
David has the right idea in thinking of intelligence as being a bundle of
skills.
What this implies is that people we think of as conventionally intelligent
may actually be much more diverse than we imagine. They may all have
different skills, and they have learned to compensate for weaknesses
in some areas by using their strengths in others. Maybe one person is
very creative but weaker in logical reasoning; another has an excellent
memory so they have all relevant info always at hand, even if they don't
do that much with it. Still another person can easily see the effects
of an action, and although he's not that good at coming up with new
ideas he tends to be very successful.
Probably most so-called smart people do not have too many significant
mental weaknesses, so they are not too hampered by their relative
handicaps. Other people may have a wider range of abilities, as when we
run into a seemingly mundane person who startles us with a mental skill.
Some people will be high in all areas, and they probably fall into the
genius category. Others will be extremely high in some specific area,
pretty high in others, and these also would be geniuses of a different
kind.
Overlayed on all this variation is the pervasive socialization effect
which drives us all to be similar. Probably we are a lot more different
under the surface than most people think.
Hal