If you had to choose between the two alternatives as stated, would you rather be an expert in one specialized subject (e.g., astrophysics, commodities market for pork bellies, hydrodynamics) but ignorant in all other subjects, or well-versed in many subjects but an expert in none?

Why?

Being an expert in one subject makes you a rather dull dinner guest.

Well-versed in many would be my option: it allows for a view of the bigger picture in life, and satisfies my own sense of curiosity. I think it would be enough to know what the main debates and conclusions of previous debates are in astrophysics (to take one of your examples) and who the experts acutally are. I don't think that one is better than the other, because I think you'd need both types of people (people who have the detailed knowledge to do the work and find out more, and people who can reflect upon said knowledge with respect to other areas); but that would be my personal preference.

What if the one subject was widespread like Maths?

Would a command of calculus will help you analyse the use of iambic pentameter in Hamlet, or a command of trigonometry reveal crucial insights into 16th century Spanish foreign policy...?

Well versed in everything

I think it would have to be well versed in many for me, for pretty much the same reasons as oo. I could have a discussion about anything even if I couldn't go into the finer details of the subject, and have enough knowledge of everything to get by sufficiently.

Related to this, I've just read a book about the "social misconstruction of reality". The author looks at three key 'myths' in particular that no specialist in the field would accept, but are widely accepted as fact by other people. So, for example, Weber's idea that the Protestant work ethic which resulted from the Reformation gave rise to modern capitalism is still widely maintained by sociologists without much thought (as it happens, I came across a re-working of the thesis by a non-specialist in anything here).

In fact, no economic historian and no Reformation historian accepts that the Reformation had any such consequence at all, and he explains everything that is wrong with the evidence for the thesis that Weber puts forward, and what's wrong not just with the data, but how Weber used the data, to demolish the idea. Yet it still persists in being taught on sociology courses, pretty much uncritically.

One of this author's conclusions - among others - is that compartmentalisation within universities is to blame. Sociologists (in this case) generally do not consult with people outside of their area to see if their ideas make sense, and are very unlikely to have encountered Reformation or economic history in any detail in their previous studies. In this sense, becoming an expert in a single area can be detrimental.

oolongcha has been reading The Social Misconstruction of Reality, by Richard Hamilton.

What I am getting at in the opening post is that there is something positive to be said for being the best (or one of the best) or creating something new or being an innovator in one field, even at the cost of being (relatively) one-dimensional.

Take Einstein. He was socially inept. He supposedly owned seven identical suits, one for each day, because he couldn't be bothered with deciding what to wear (which is kinda cool). But he was brilliant beyond compare in his field. Einstein may not exemplify exactly what I'm getting at (because I don't know if he was well-versed in other subjects), but he is analogous.

There are (or were) people like Leonardo da Vinci and Benjamin Franklin who were experts in several fields and well-versed in many others, but note that they lived centuries apart. With very rare exceptions, people who reach the very pinnacle in a field or invent or create great things are single-minded in their efforts to the virtual exclusion of everything else.

In fields not directly related to business, the motivation is rarely financial (e.g., great scientists, violinists and other classical musicians, opera singers, athletes in sports that are not lucrative, among others). Such people literally love one pursuit and essentially do not care about anything (and often anyone) else.

I know many people who excel in their chosen field and are also well-versed in other fields, but I have known only two people who reached the very pinnacle of their field. Both are essentially one-dimensional. One of them is an innovator in corporate finance and the other is equally innovative in the field of robotics. Neither one cares about much else outside his field.

I would not - and I'm pretty sure I could not even if I wanted to - be so single-mindedly driven. But I admire such devotion. I think this may be what it takes to achieve historical greatness in any field (unless you are da Vinci or Franklin).

Now that I think about it, no such person would ever succumb to the distraction of posting in an internet forum. So I guess the opening post answers itself.

Incidentally, ever hear of Daniel Temmet, the young Englishman who is an "autistic savant" but is not autistic or a savant? He is probably the smartest person in the world, and he is mentally normal in every other way. The guy is truly amazing. Check him out: http://www.wibbler.com/2007/01/31/daniel-t...t-the-brainman/