In Spain used to be as low as 13 a few decades ago; but that law was obviously written before
the rural exodus of inner Spain into the cities (from the 60's to almost the 80's), as children since early puberty got to work/help in the farm/fields or at home and by age 14 they had far more duties and accountabilities than today. And yes, that yielded more maturity.
Thus, the law had to be fixed for more urban/civilized times up to 16. Altough depending on the age/mentality closeness (such as 15-19 as it happened with a recent case), the young adult had its charges totally dropped.
He was really brilliant, made contributions all over the place in the math/physics/tech field, and had a sort of wild and quirky personality that people love telling stories about.
A funny quote about him from a Edward “a guy with multiple equations named after him” Teller:
> Edward Teller observed "von Neumann would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us."
Are there many von-Neumann-like multidisciplinaries nowadays? It feels like unless one is razor sharp fully into one field one is not to be treated seriously by those who made careers in it (and who have the last word on it).
IMO they do exist, but the popular attitude that it's not possible anymore is the issue, not a lack of genius. If everyone has a built in assumption that it can't happen anymore, then we will naturally prune away social pathways that enable it.
I think there are none. The world has gotten too complicated for that. It was early days in quantum physics, information theory, and computer science. I don’t think it is early days in anything that consequential anymore.
Centuries ago, the limitation of most knowledge was the difficulty in discovery; once known, it was accessible to most scholars. Take Calculus, which is taught in every high school in America. The problem is, we're getting to a point where new fields are built on such extreme requirements, that even the known knowledge is extremely hard for talented university students to learn, let alone what is required to discover and advance that field. Until we are able to augment human intelligence, the days of the polymath advancing multiple fields are mostly over. I would also argue that the standards for peer reviewed whitepapers and obtaining PhDs has significantly dropped (due to the incentive structure to spam as many papers as possible), which is only hurting the advancement of knowledge.
Sounds like the increased difficulty could be addressed with new models and right abstraction layers. E.g., there’s incredible complexity in modern computing, but you don’t need to know assembly in order build a Web app, to reason about architecture, to operate functional paradigms, etc. However, this doesn’t seem to happen in natural sciences. I wonder if adopting better models runs into the gatekeepers protecting their status, tenures, and status quo.
Neither does a Web app developer need to know how to use CNC or make a transistor. Your example is about different levels of abstraction than what I meant.
I was replying to “even the known knowledge is extremely hard for talented university students to learn”. If complexity of the known knowledge one must learn to substantially contribute is the reason becoming an accomplished multidisciplinary is impossible nowadays, then it sounds like we could use some better models and levels of abstraction.
More than that, as professionals' career paths in fields develop, the organisations they work for specialize, becoming less amenable to the generalist. ('Why should we hire this mathematician who is also an expert in legal research? Their attention is probably divided, and meanwhile we have a 100% mathematician in the candidate pool fresh from an expensive dedicated PhD program with a growing family to feed.')
I'm obviously using the archetype of Leibniz here as an example but pick your favorite polymath.
Is it fair to say that the number of publicly accomplished multidisciplinaries alive at a particular moment is not rising as it may be expected, proportionally to the total number of suitably educated people?
My favorite Von Neumann anecdote/quote is this one:
John Von Neumann once said to Felix Smith:
"Young man, in mathematics you don't understand things. You just get used to them."
This was a response to Smith's fear about the method of characteristics.
It took me a while to fully grasp what he meant, but after diving into Mathematics and Physics for a while, I now hold it as one of the capital T truths of learning.
