linguistics, music, chess and mathematics

What do these fields exactly have in common? The story goes like this.

A heated debate on the Corpora list started when someone asked if it's better to have a degree in linguistics or in computer science to pursue a career in computational linguistics. The question invoked comparisons of skills and whether it is easier for a computer scientist to understand linguistics or vice versa. Logic and mathematics also got involved in the discussion as to how they bear on the study of both linguistics and computational linguistics. A few names were mentioned, such as Larry Wall, the linguist who invented Perl, Noam Chomsky who revolutionized formal language theory, and Barbara Partee who had a degree in math and is now a major figure in formal semantics (no one mentioned a computer scientist who contributed to linguistics, though).

So, the interdisciplinary relationships emphasized here finally got to include music and chess too. John Sowa argues that linguistics, music, chess, and mathematics share an ability to recognize very complex structures. But then he wonders about the cause and effect relations between these fields. In other words, he asks:

Does the intense discipline required to master one of those fields carry over to the others? Or do they all depend on a similar kind of native talent? Or does the study of more than one type of pattern help develop more general ways of looking at and analysing  patterns? Or is it some combination of all of the above?

And the final answer is "no one really knows". I think the last option is more like it. But do you think someone's ability in one discipline would give any kind of clue as to his/her ability in another? So, since we all study math at some point in our lives, how about testing linguistics students in both music and chess just to get an idea? :)

p.s.
As a side note, at the end of this discussion, Sowa mentions this poem as an indication of the 'advantages' of having a background in logic:

If your thesis is utterly vacuous,
Use first-order predicate calculus.
With sufficient formality,
The sheerest banality
Will be hailed by all as miraculous.

If your thesis is quite indefensible,
Reach for semantics intensional.
Over Montague grammar,
Your committee will stammer,
Not admitting it's incomprehensible!

Henry Kautz