Is it possible to be a polymath these days?
ask.metafilter.com
ask.metafilter.com
Edit: Should also mention Malcolm Gladwell's recent book which posits that it takes on the order of 10000 hours to become an "expert" at something.
http://www.guardian.co.uk/books/2008/nov/15/malcolm-gladwell...
Who knows what Leonardo would have done with the internet...
http://www.amazon.com/Cambridge-Handbook-Expertise-Expert-Pe...
suggests that it takes longer than a week to become an expert (by a reasonable definition of "expert") in any domain of significance.
I'm not trying to belittle others, like PG, who clearly are knowledgeable (and skilled) at many things, but given the genesis of the term, I think the entry bar is pretty high.
In da Vinci's time, how many people could imagine a flying machine in a time when machines of any type were extraordinarily rare and expensive?
In 2008, most people in the developed world have the opportunities to excel that were almost unattainable 500 years ago, so the standards of nominal accomplishment are higher. Developing blueprints for a new style of flying machine is now an amateur's task; to be a world-changer, you have to build and market one. Or for another example, to work at the cutting edge of physics, you'll probably need access to expensive resources so you can test and refine your theories. This means that a lot more time and energy are sucked up by unglamorous tasks (e.g. raising money, or proving yourself in order to secure access to the choice labs).
In the Renaissance, few had any opportunities to excel, but those who did could get started right away. In modern times, there are a lot more brilliant contenders, but it takes longer to acquire the material and social resources necessary in order to get to work on the front lines.
However, the standards of creativity and aesthetic genius have not gone up nearly as fast. Shakespeare would still be considered a great writer today; and da Vinci, a great painter.