Humans are examples of general intelligence
I think of humans as a conglomeration of various narrow modules. Quite often, our skills in one domain to not transfer to other domains, even when those domains are isomorphic - see wason selection task. Many clever algorithms, both for doing tasks and for deciding which algorithm to use. Autism and many other illnesses are the result of some modules being damaged while others are left intact.
If humans are part of what we define as general intelligence, then that's at least one path to it;
That's a good point, actually... are we (the humans) examples of general intelligence ? I personally know that there are many problem domains which I am unable to even pronounce, let alone comprehend; and yet there are many other humans who are happily solving problems in these domains even as we speak. What does "general intelligence" mean, anyway ?
Thinking aloud:
Humans are examples of general intelligence - the only example we're sure of. Some humans have various degrees of autism (low level versions are quite common in the circles I've moved in), impairing their social skills. Mild autists nevertheless remain general intelligences, capable of demonstrating strong cross domain optimisation. Psychology is full of other examples of mental pathologies that impair certain skills, but nevertheless leave their sufferers as full fledged general intelligences. This general intelligence is not enough, however, to solve their impairments.
Watson triumphed on Jeopardy. AI scientists in previous decades would have concluded that to do so, a general intelligence would have been needed. But that was not the case at all - Watson is blatantly not a general intelligence. Big data and clever algorithms were all that were needed. Computers are demonstrating more and more skills, besting humans in more and more domains - but still no sign of general intelligence. I've recently developed the suspicion that the Turing test (comparing AI with a standard human) could get passed by a narrow AI finely tuned to that task.
The general thread is that the link between narrow skills and general intelligence may not be as clear as we sometimes think. It may be that narrow skills are sufficiently diverse and unique that a mid-level general intelligence may not be able to develop them to a large extent. Or, put another way, an above-human social intelligence may not be able to control a robot body or do decent image recognition. A super-intelligence likely could: ultimately, general intelligence includes the specific skills. But his "ultimately" may take a long time to come.
So the questions I'm wondering about are: