My father was an architect and he once challenged me to find an area of study that he didn't need to know anything about, and as of yet I haven't. Designing a church? You better know something of the religion. An arena? You should understand the sport, otherwise how do you optimize the sight lines? A pharmaceutical factory? You need a good grasp of chemistry to design a safe environment. And then there are the studies of human psychology and interaction that should help inform the design of any structure as well as your requisite art, history, design, math and engineering knowledge.
Hasn't the amount of knowledge in math, science, and engineering been growing exponentially whereas our capability to learn and teach is still mostly linear?
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.
I think our capacity has expanded also. Not nearly quickly enough, but we can learn more now than we ever did before (or at the very least, we can cut out a lot of the noise in our learning experience).
Also, at least in math, while there is certainly more content than one can learn in a lifetime, with more content being created every day at an increasing rate, many different abstractions have been developed and clever analogies applied in order to simplify new learning.
True - I was only half joking, though. With the internet we really can browse through new topics outside of our field very quickly. Not to become experts, but to find specific aspects of other areas of research that might apply to our problem.
Who knows what Leonardo would have done with the internet...
It depends on what you mean by "polymath" specifically, but I always think of the multi-talent programmers and artists. PG designed Viaweb and also is an essayist and breakthrough investor, for instance. One of my favorite authors, Daniel Handler, played accordion with the Magnetic Fields and he's a pretty excellent singer as well.
When I think polymath, Ludwig Wittgenstein comes to mind. He was a successful mechanical engineer, received his PhD in philosophy based on the notebook he kept during World War I, taught philosophy, taught grammar school (though, admittedly, that didn't work out so well), and designed a house for his sister.
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.
PG was the first example I could think of that seemed to fit. I agree: there are people who are certainly more renaissance than him. That was just the first name that came to mind.
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.
