Jack of all trades

How "potent" is a scientific field? The sexual connotation is not accidental: I'm trying to find out, how successful one school of thought is in cross-pollinating others..

Most educated people think of their education as part of their identity. Being a mathematician, a physicist, a biologist obviously influences our way of thinking just as native language and upbringing does. While there are many generalists, there are also many who seem to be typical representatives of their field or subfield (in their way of thinking).

For example, a computer scientist's or programmer's way could be easily summarized as the tendency of splitting tasks into infinitely small subtasks that can then be almost mindlessly executed. Making a sandwich? First I slice up bread, then I spread butter on it... No, wait, first I put the bread on the table, take up the knife... No, first...

Different schools of thought have evolved to deal with different aspects of the world. They are all relatively successful in their respective fields (or they would have been abandoned by now, one imagines), but I am more curious about how successful they are when applied out of context? How does a physicist build a house? How does a programmer go about losing weight. How does a linguist design a rocket? How does a painter handle investments? How does a mathematician change a light-bulb?

It is safe to assume that just as native language would give people different competitive advantages (if the (partially) discredited Sapir-Whorf hypothesis were true with the Eskimos having 200 words for snow, etc. etc.), their professional "native language" should also have an impact on how successful they are in dealing with the world at large. If all theories are metaphors for the world, some must be more suitable, more accurate, more general. Also, let's try to find an objective measure instead of asking the suspects themselves. Most people grossly overestimate how potent their way of thinking is... "If only I had time to split this up into sufficiently small sub-tasks..."

An obvious first guess would be mathematics. Hardly anything can be more general than mathematics, the fabric out of which (almost) all other theories are woven. The first objection is that no-one today holds the whole of mathematics in their head, so we should instead talk of such as a group theorist's way of thinking or a geometer's view of the world (which incidentally might have been the most potent worldview 2500 years ago). A more serious problem is that even if there is such thing as "the mathematician's approach", in many cases it is not successful at all and is often ridiculed as a pedantic care for irrelevant notational issues, a.k.a. nitpicking as opposed to Getting Things Done^TM.

So is physics then the most potent? I don't know much about a physicist's worldview except that it must involve idealized weightless balls and probably some jokes about Schrödinger's cat. However, I do notice that people with background in physics are often successful in engineering, machine learning, macroeconomics, computer programming or other fields. Is it so that physics just happens to be a potent metaphor for a wide variety of different phenomena, or does this have to do more with the economic opportunities in each field. Computer science seems to have been on the receiving side for mass immigration in the past decades but then physics is the equivalent of Ireland during the great potato famine. On the other end of the spectrum are the fields in which everyone seems to be an expert (besides the obvious football and cricket, international politics comes to mind) or the fields which don't have anything to say to other fields (insert example here).

So what is at play here? Is any school of thought more potent than the others? If so, which one and why?

EDIT: with a bit of embarrassment I realized how much I was influenced in this post by a Paul Graham essay I read years ago:
http://www.paulgraham.com/college.html