i was using this (latin available here) translation of caesar's commentary on the gallic war, and i noticed that they translated frumenti as corn, which made no sense to me since corn (maize for the rest of this post) as i knew of it wasn't brought over to europe until the late 15th century, but it turns out that the word corn in english has been around longer since before maize was brought to europe. behold the following definition:

1. a. gen. A small hard particle, a grain, as of sand or salt.

as well as a usage (and apparent definition) contemporary to the translation i'm using:

1876 Mid-Yorksh. Gloss., Corn, a grain, or particle, a ‘corn of tobacco’, a ‘corn of powder’, a ‘corn of rice’.

both of which were retrieved from the OED. so, it appears that, no, my translation isn't wrong (as was my first suspicion) but rather that my understanding of the word corn was faulty.

there's an article over at /. about the hubble space telescope capturing galaxies colliding.

normally i wouldn't have mentioned it, but these really (15mb in jpeg, 31 in tiff) high resolution pictures of it are absolutely stunning. go check it out for yourself (the pictures, not the article. it doesn't really matter so much).

i was looking at euler's formula recently, and i decided i simply HAD to understand it. i also decided i had to blog about it.

preliminaries:

euler's formula (also referred to as euler's identity, but i found this most often referred to a special case, (e^πx) -1 = 0):
e^ix = sin(x) + i cos(x)

useful constants/functions:
i = sqrt(-1)
e = 1/0! + 1/1! + 1/2!...
e^x = 1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4!...
cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6!...
sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7!...

and also, keep in mind, multiplication distributes over addition, and this applies even to the elements of a function which can be represented by an infinite sum.

first, the taylor series expansion of e^ix...

e^ix = 1 + (ix^1)/1! + (ix^2)/2! + (ix^3)/3! + (ix^4)/4! + (ix^5)/5! + (ix^6)/6!...

as a result of raising i^n, we end up with some pairs of negative terms and positive terms (the second of each pair being complex, the first being real.)

= 1 + ix - (x^2)/2! - (i(x)^3)/3! + (x^4)/4!) + (i(x^5))/5! - (x^6)/6!...

then, if we separate out each term raised to an even number and put them on the left hand, and the remaining odds on the right hand, we end up with an equivalent of sin(x) + i cos(x):

= (1 - (x^2)/2! + (x^4)/4! - (x^6)/6!)... ) + i(x - (x^3)/3! + (x^5)/5! - (x^7)/7! ...)

(note that the series on the right is multiplied by i, which raises i to the respective powers of each term in the series, hence yielding some positive and some negative terms, and some real and some complex terms.)

interspersing the terms after distributing i over the right hand series, we end up with this

= 1 + ix - (x^2)/2! - (i(x^3))/3! + (x^4)/4! +(i(x^5)/5! - (x^6)/6!...

which you can see is also the expansion e^ix that we started with, hence proving (altho perhaps not with usual mathematical rigour...) euler's formula.

there's an interesting post over at knowledgeproblem about various uses of cellphones in india: from a fishermen haggling with various retailers before choosing which port to come into with his catch to farmers sending photos of their diseased crop to specialists for diagnosis.

i was recently made aware of an alternate meaning of camp. apparently, in british and australian usage, it can also mean gay. this shocked me, as i couldn't see a possible connection between camp as in tents. so i went to the OED to check it out:

Ostentatious, exaggerated, affected, theatrical; effeminate or homosexual; pertaining to or characteristic of homosexuals. So as n., ‘camp’ behaviour, mannerisms, etc. (see quot. 1909); a man exhibiting such behaviour.

hmm. so i checked out the 1909 usage:

1909 WARE Passing Eng. 61/2 Camp (Street), actions and gestures of exaggerated emphasis. Probably from the French. Used chiefly by persons of exceptional want of character. ‘How very camp he is.’

so, seeing it's probably from the french, i googled around for a bit, not finding much except a wiktionary entry (along with a page on wikipedia describing a descendent usage of this 1909 sense.) which all seem to corroborate that it's from the french. hence, i went to my le petit robert and under camper found the following:

SE CAMPER v. non. Se tenir en un lieu dans une attitude fière, hardie ou provocante.

To compose one's self in an arrogant, bold, or provocative manner. (my translation, feel free to correct me in the comments...)

but that's not quite gay, which is what we're looking for. well, hold up, altho we've not found strong evidence of camper meaning gay, given the last two senses of these two definitions and the history here (with a reference to Gay talk: Formerly entitled The queens' vernacular : a gay lexicon, and which also seems to imply a descent from campagne, in reference to transvestite actors strolling thru the country side.), we have enough information to infer that camp, whether from camper or campagne, is likely descended from french, and that in any case, the french camper has a sense which can be seen as similiar to the gay-friendly version of this alternative usage, camp as a style.

i'd love to hear other people's input on my analysis, and if they know anything else about the origins of this usage. i LOVE a good etymology when i can get my hands on it...

EDIT:
an e-mail from languagehat (solicited, i should add.) brought me back to earth on this one: the evidence is definitely inconclusive, and altho i may like the idea of this history, we really can't be sure. so don't go telling your friends about how i proved camp comes from french.

language mixxer is one of the single best resources for language learning around (assuming you've got a start in the language, already, of course). it's a directory of people who want to practice a language, like your average penpal site, except it's base around skype. i've been able to find language partners for every language i'm learning (chinese, japanese, french, german, spanish and hindi) with it.


you could also check out my delicious which has plenty more resources.

nothing special here.

just an introductory post to what will be my blog about life, the unvierse, and everything. or more specifically, anything i find cool and worth talking about.

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