Using "their" in the singular is perfectly fine. Quoting from the "Language Log" blog:

"singular they" is deprecated by a few authorities, but is supported by most informed grammarians, and has often been used by great writers over the centuries

or more harshly:

use of forms of they with singular antecedents is attested in English over hundreds of years, in writers as significant as Chaucer, Shakespeare, Milton, Austen, and Wilde. The people (like the perennially clueless Strunk and White) who assert that such usage is "wrong" simply haven't done their literary homework and don't deserve our attention.

The sin/cos arm motions were 180 degrees out of phase when they should be 90 degrees.

If my math is right, I came up with a 2% chance that that would happen in the US and 31% it would happen in the world.

My numbers are a bit iffy since I assumed everyone was alive and that births are equally likely across all the days, but the change is minor.

BTW, with only 4 birthdays on the same day there's a 99.8% chance of happening at least once in the US, and likely 10 such families.

Again, assuming my math is right.

Quite a few caves are also underwater, and there are caves in glaciers.

Liquid nitrogen isn't expensive. It's roughly $1-2/gallon.

My favorite is the Swedish word gökotta: "to go out early in the morning, traditionally on Ascension day, to listen to the birds of spring, especially the cuckoo."

Regarding this topic, see http://en.wikipedia.org/wiki/Ilunga which says "When asked for confirmation by one reporter, representatives of the Congo government recognized the word only as a personal name." and see the commentary at Language Log at http://itre.cis.upenn.edu/~myl/languagelog/archives/001104.html .