> Von Neumann was a child prodigy. When he was six years old, he could divide two eight-digit numbers in his head and could converse in Ancient Greek.
> By the age of eight, von Neumann was familiar with differential and integral calculus
> At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő. On their first meeting, Szegő was so astounded with the boy's mathematical talent that he was brought to tears.
> By the age of 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor's definition.
Yeah right.
Sure his privilege helped. But a lot of people all through the world had that amount of privilege or more.
Really? A lot of people all throughout the world have had people outside the school system to teach them integer factorization, Ancient greek, and integral calculus as soon as they could?
In the real world 99% of parents don't have the time to teach their child anything beyond how to speak and walk and answer their questions. 90%+ of parent's don't even remember how to efficiently factor integers or any math beyond arithmetic.
Certainly very few people have this level of genius, but if Von Neumann were to be born to an average milieu it is impossible he would have been able to reach those milestones.
Ramanujan learnt calculus at the age of 8 and was able to rapidly factor large numbers by the age of 6?
Come on now. Ramanujan was still doing arithmetic by the age of 10.
Unarguably Ramanujan was held back as his mathematical progress very strongly, and was not too far above that of his peers until he attended High School.
And the worst is that Ramanujan himself was incredibly privileged compared to the Indian average, being able to live in an urban milieu. Were he in an average rural, peasant context he would have been held back even more. Not to mention, he was a Brahmin, the highest caste in India.
This was one of the world's foremost mathematicians, an unprecedented genius who was born into relatively poor circumstances (by Western standards and by modern standards) and who was completely self-made. There's footage of his very modest family home, so if you're going to try to claim he's somehow "privileged" above and beyond an extremely poor person in the US today, that would be laughable. It's true he wasn't a child prodigy, but so what? You're trying to crap on Von Neumann's
adult accomplishments, which is what's impressive here (there's loads of child prodigies that flop as adults), by claiming without any basis that they're a product of his parent's success when Ramanujan is conclusive proof that this isn't a necessary condition for a Von Neumann calibre genius to arise. Another thing your analysis ignores is that intelligence is partly genetic, so of course smart kids are going to often have richer parents. If their parents are extremely smart then most likely they've figured out a way to make some money. No surprise there.
It's not really arguable that without his early advantage Von Neumann would not have been able to achieve what he did. Something can be the product of many things, as I'm sure you've learnt in elementary school.
As far as Ramanujan, it's not arguable either that if he had been recognized early and given proper opportunities, he would have been even more prolific and have made even greater contributions. It took him 10 years for his genius to be recognized locally! And that was as a Brahmin to an urban family, imagine how hard it would have been if he was a Vaishiya born to farmers - he might have never been recognized, and we would have lost his contributions.
If you believe that without being 100% self-made you're crap, that's your point of view, not mine.
As for your edit, extreme intelligence is not really correlated to income. In fact, once you leave the median by a standard deviation, there is almost no impact anymore, and even less when you start controlling for social factors. What is moreso correlated is low intelligence and low income. Descendance is a much, much stronger impact.
If you think that a very poor person can rise to a Von Neumann calibre genius, then we have no disagreement. I agree with you that having successful parents can only help the situation.
"As for your edit, extreme intelligence is not really correlated to income."
Ok, the marginal correlation breaks down at the extremes. But it's still the case that intelligence and income are correlated, so smarter kids are more likely from higher income parents.
"they'd just need significantly more innate intelligence, which is a very tall order."
I dispute this. Ramanujan is by all accounts on Von Neumann's level and so his example seems to disprove this statement. Or maybe you think Ramanujan has "significantly more innate intelligence" than Von Neumann? It's possible, but without evidence, and a bit farfetched.
I think wealth helps but through a different mechanism to what you're thinking. Avoiding malnutrition is the big one. A secondary point is avoiding the need to work and being able to focus on intellectual passions, which many average-wealth people can do. Adding more money to the picture doesn't help beyond a baseline. Ramanujan was fairly poor but still had enough family wealth to be able to eat enough food and dedicate a lot of time to his passion.
I have seen parents buying their kids Playstations and taking them to expensive vacations in 5/7 star hotels and are content about "doing a lot" for their kids.
I have also seen parents really investing time in their kids' future. Teaching them programming, foreign languages, advanced (for their age as per some regulatory bodies) math, etc.
Any wonder why the kids from the next group will turn out to be more successful statistically?
There is also nuance in this. Almost nobody (statistically) grows up to be geniuses from these families. But they certainly tend to have more accomplished lives.
You clearly don't have much exposure to the outside world.
I know a lot of parents, basically almost all parents that I know of, enroll their kids in all sorts of things.
They are admitted into schools where you speak only English, they are admitted into swimming school, karate, painting, singing, dance class, you name it.
My cousin's kid is enrolled into five extra-curricular classes. She is 7.
I have been seeing this for decades now. Despite being born into upper middle class homes, and having their parents shower money on stuff, most kids grow up to be vastly uninteresting individuals.
- Most of them speak grammatically incorrect, Indian-style English.
- Many struggle to find jobs even in the low-paying strata of the private sector.
- Most of them don't go to top schools since almost any college that matters takes admission through meritocratic channels (academic test scores and/or admission tests)
I have seen a lot of these rich babies fail in life.
Privilege never equals achievement.
There is always some element of genetics involved.
Hard work matters more than genetics, I believe so. But the influence of genes is not trivial.
Genes + extreme hard work + good environment provide a baseline for true genius.
I think this is a question of what your definition of "a lot" is. If you use percentage - for example, 1% of parents, of maybe even less - 0.01%, 0.01%*7.7 billion = about a million people.
Does percentage make more sense here or absolute number? It depends on your context. I would say in this argument, it seems more certain that Von Neumann's success, which is always a function of both nature and nurture, can probably be attributed more to nature. Or, perhaps most likely, it's a rare event of talent meets incredible luck.
Just as thousands upon thousands other people, that fail to become geniuses. So that’s more like a small semi-necessary part, not at all close to sufficient, which welcomes some awe.
> By the age of eight, von Neumann was familiar with differential and integral calculus
> At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő. On their first meeting, Szegő was so astounded with the boy's mathematical talent that he was brought to tears.
> By the age of 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor's definition.
Yeah right.
Sure his privilege helped. But a lot of people all through the world had that amount of privilege or more.
How many von Neumans are there?