The Sapir-Whorf hypothesis: a language's nature influences the thought of its users.
Apparently Chomsky's Universal Grammar (underlying universality of language, due to brain structure) has reduced the "popularity" of the Whorf hypothesis. I believe some lefties (in the political sense) also do not like the idea, as it hurts their feelings of equality.
But is this not common sense that the hypothesis must hold? In terms of computer languages we can say that any Turing complete language is theoretically equivalent, but anyone who has done assembly versus any higher language coding knows that in practice there is huge differences - in theory you could write everything we currently have on a computer in binary, in practice you do not and could not. Language makes some things easier, and coders pick languages (in part) based on what they make easy to do. The fact we have pretty constrained resources (puny brains, limited time, etc.) suggests the language we use will have a profound effect on what we think and do. This should effect how a culture evolves, as language and culture play back and forth on each other.
An interesting question is - are all languages "Turing complete" (in the sense that all cultures can represent ideas from other languages) or not? Are languages even close to Turing complete in a functional manner? Persumably, languages can be close or far apart in ease of transfer of ideas - do "they" have a map illustrating the relative positions to each other?
Are some languages functionally more orthogonal relative to each other? (i.e. if I want to expand my capability to think, what language should I pick as my second language?) What is the most limited and easy to learn language? Pirahã? Rotokas? Klingon? Are there good books out there that teach minimal languages, that evolved in the "wild"? Is it worth someones time? English is the Borg of languages, so it is very rich and useful, but what should one pick to supplement it? Perhaps a "clean" language like latin or Haskell brings more to the table than any real language (i.e. more logical, structured, mathematical, closed (well defined, and essentially static, base), and "clean" then the messy, wonderful, evolved, and crazy language that is English - and therefore nicely orthogonal.). Is Englishes "borg like" tendancy one feature that has lead to Western societies strength? Can we measure this?
Are there people who try to predict political situations and reactions based on language (and other insitutional) constraints? Is there a team of neat people in some think tank or militiary group that analysis how the Chinese may react to things to gain predictive power? Are the Chinese doing this to us? (sorry for the bad pun) I suspect the Chinese are doing this, and Western nations are not, possibly in part due to the nature of our insitutions which makes for some easier predictibility (though, apparently not by most of us...) and the fact that our society tends to focus on short term (think tanks and universities being partial exceptions).
Notation, language, logic, mathematics - very interesting stuff, very deep stuff: if anyone can recomment a great book on linguistics that works through a lot of the ideas, with examples and practical applications in it, please post on this ("Contemporty linguistic analysis", by O'Grady & Dobrovolsky, is decent with a wide survey of stuff including "Bee language" and I have vague happy recollections using this book for an intro class, but I would like something similiar but with a few "case" studies threading through the book - for example, learning Rotokas or some small or subset language to really illustrate things).
A final idea - I liked Star Trek as a child, but do not know the backstories, how intelligent the writers were, etc (TV is very limited for addressing "big ideas"). But is "Worf", the Klingon, a hat tip to the Whorf hypothesis, with his language being warlike and having a feedback effect on his society? It seems quite plausible - does anyone know? Have the writers spoke on this? Have the rabid fans declared this? Have linguists chuckled and wrote about this as a nice tie in to connect with the "general public" and leverage the zeitgeist in promoting their ideas?
Update (8 April 2009): The cover of "Lognet" had a cartoon regarding this...