Those two are probably not uncorrelated either. For homeschooling to be good, you'd need parents who are sufficiently knowledgeable and well-rounded and have enough time to invest.
(Though I get the impression that there are plenty of kids who are also homeschooled because their parents are determined to "save" them from things like learning about evolution.)
Yes, with wealth you can work much less (if at all) and spend time with your child. Furthermore, wealthier parents have jobs which exercise their minds, so they're not deadened and just want to plop in front of the TV. Their managers are much more polite to them, so they're not so angry. Less financial woes means less family fights and likelihood of abuse.
For a zillion reasons, I agree, and would never want to put a child through a family institution without sufficient wealth. Because in the world I live in, kinship and economic institutions are horrifically dysfunctional. Lucky people get to reach their potentials; most certainly don't. They go to schools whose interests are something other than supporting the child's personal interests.
Having academically experienced parents is different enough from the status quo to merit mention. People who could hold a discussion on "Archimedes, Galileo, da Vinci, Faraday, Newton, Maxwell, Tesla, Pasteur, and Darwin" are rare. It's cliche to say that a child's success starts with the parents, but that's quite a positive influence there.
I agree that having parents with a broad base of knowledge is a hugely positive influence--but I think you're misattributing the genesis of that base of knowledge when you refer to "academic experience". The rarity of those people, I think, is tied more towards (smart) people's willingness to over-focus. If, like a lot of computery folks I know, you choose to devote your time almost exclusively to computery stuff, you're going to be limited outside of that area--but you can choose not to do that.
I found it fairly easy to avoid over-focus by seeking out new stuff to learn about. I'm 24, with a bachelor's in CS from a state school, and I went to a pretty normal high school; the works (and in most cases) lives of each of those people listed in your quote are pretty familiar to me, though some more than others, and I could recall offhand enough of substance to at least be able to hold my own in conversation.
I think three things in particular helped me. I credit a lot of it to my dad taking away my computers when I screwed up as a kid. It forced me to entertain myself, and a lot of that was going to the library and reading everything I could get my hands on. Another factor was that (against my parents' advice) I explicitly refused to get a B.S. in CS in college. Instead, I took a B.A. so I could get out of the CS building more often. I hung out in the honors college of my school, which was heavily humanities-focused and where the students skewed towards the humanities and towards real engineering degrees (zero other CS students). I had to broaden my horizons just to keep up. The third helpful factor was that I started programming computers when I was about eight years old (I started in on C around 11 or 12), which provided much more to get good at what I do while still leaving a lot of time to follow up on other interests.
(I am skeptical of unschooling largely due to what I see as the predilection of very smart people to hyper-focus--unless a child's parents are sharp and have a broad set of interests, the child seems incredibly likely to become one of these hyperfocused people. I can see it being really valuable and effective if parents have that baseline broad-scope curiosity.)
You sound like a neat person, and congrats on having become such. :)
I am curious about one thing you shared - the choice to get the B.A. rather than the B.S. in CS. Did the B.A. require less coursework in CS, since the choice allowed you more time out of the CS building? Our son's state U didn't even have a B.A. in C.S., only a B.S. option. It was in math that he had a B.A./B.S. option and there, the B.S. required more math courses (and maybe more science courses, too), and his CS advisor urged him to relax and not bother with the B.S. in math since he'd already had a B.S. in C.S. and it would seem more well-rounded to have both a B.A. and a B.S., but our son felt that was B.S. since in fact, he needed no more coursework to get the B.A. and needed two extra math classes for the B.S., so really the B.S. was a "higher level" of education and he didn't care what things looked like to others. He also had finished his first B.S. with a 4.0 GPA in CS and we questioned whether he should really sign up for yet more CS credits when he didn't need them, but he again didn't care about risking the GPA; he only cared about learning, and back then, I don't think auditing much crossed his mind (where in graduate school, he has just sat in some courses because the program wouldn't allow him to load up formally on more credits, where his undergraduate school dean had no issue signing off on a 25-credit semester rather than the typical 12-15 credits).
I feel pretty confident that it's not like all people with a B.S. in C.S. lack a well-rounded education in college. Our son took above and beyond the college's requirements in arts and humanities, social sciences, language/culture (he took German and French courses plus a bunch of culture credits, and had taken some Spanish and Italian before going to college), science (the university only required students take two courses in bio, chem, or physics, and our son took one in bio at 9, two in chem at 9, and also three physics courses), and English (he got freshman English credit from his CLEP score, but since he also was in the Honors College, if he used test credit for freshman English, he had to take an upper level English). In addition to that, he was on a college sports team for a year (won a gold medal in it), was in SGA from sophomore to senior years, and was active in a bunch of other things on campus while also staying active which younger students off campus (was in a handchime choir for those 10 and up, did tap performances with other children, gave magic performances with children ages 5 to 18, etc.) as well as socializing with senior citizens (he volunteered once a week at a local retirement home from ages 7 to 14, when he moved out of state for graduate school, though he did come back at 15 to give a eulogy for one of the residents, as she had requested he do a eulogy for her even since she heard him do one for another resident when he was I think 10). He also spent summers doing 40 hour/week internships at a tech company in another state from ages 9 to 12. Oh, and he did study abroad programs in eleven countries while in college and had been to over 30 countries before he moved away from home at 14, I believe (is up over 40 countries now, I think).
An early start programming no doubt does give one a leg up. Our son began programming at age 5, and by the time he finished college, I think he had dozens of computer languages on his resume, most of which were learned outside of college and not in classes.
As with others in this thread, I'd urge you to research homeschooling more before you make any decisions for your own offspring's education, if you ever go the route of having children (as I realize many smart people opt out of the parenting path, just as I had planned to do before meeting my husband).
They are related, but even being smart and having smart, dedicated parents isn't enough. You also need to be motivated and have staying power.
I know so many smart, but unmotivated people who drift through life, rarely achieving anywhere near their potential. The same goes for people, like me, who get bored too quickly, and can't manage to stay dedicated to any one subject for long.
I can theorize one "sign" of innate smartness. When I was pregnant, my hands at one point in the pregnancy came to rest on my belly, and at some point, I happened to tap on my belly, and back came the same number of kicks or punches. I thought this had to have been coincidence, so tried a different number of taps, only to have that number tapped back, and so I tried a third number, which again came mirrored right back to me. It was at this point that I became freaked out and did my best to keep my hands off my belly for the remainder of the pregnancy. I have only heard of one other woman having this experience, and she told me her child is also one with a rather high IQ.
Rolling over soon after birth might be another such indicator. Our son did this as a newborn and I've heard other mothers of high IQ children (not just one other, but several others) say their children did the same. One would think such a move would have more to do with muscle strength (and our son was born a typical 7 pounds and 6 ounces, so no football player baby) but perhaps it's more how quickly the mind can figure out how to pull off the turn, I don't know.
And yes I am envious.