While it is true that generally only pithy Latin sayings have stuck around, it is also true that Latin is an extremely concise and economical language. Ancient Greek is as well, though perhaps to a lesser degree due to handy little particles strewn about sentences to aid the reader in understanding the logical flow. Latin contains few such niceties.
MR
Contrary to the OP’s experience, I think it takes more words and syllables to convey the same idea in French than in English. When I go to Canada, I often see notices in both languages side-by-side, and almost invariably the Fench version is longer.
Certainly Latin can convey an idea in fewer words than English, but Latin words tend to have more letters and more syllables than English ones.
I should add that redundancy in language isn’t always a bad thing. Imagine if you’re talking to someone in a noisy room, or that you’re on a phone with a bad connection, and you can only hear half the words. In a language with high redundancy, you will be able to understand the idea anyway.
I’d wager that Manage-speak says the least while using the most words. 
You may be thinking of Cantonese. Mandarin only has 4 intonations for vowel sounds: level, rising, falling-then-rising, and falling. Further, words are either one syllable long, or made of compounds of single-syllable words (each ideogram represents one syllable). There are no inflections (endings), no articles, not even real tenses (you convey past or future by specifying the time of the action). I don’t think there are even any irregular constructions. There is a limited menu of initial and final sounds for each syllable-word, and not all possible combinations are even used.
The downside is that it is far more difficult to convey shades of meaning with such a limited vocabulary and highly-restricted grammar rules. Much meaning has to be inferred rather than stated. English, despite its often-nonsensical spellings and frequent irregularities, is far more useful even if nobody would call it compact.
I can back up FloChi on the German language’s ability to create highly descriptive technical terms. I remember once learning the original German word for what we call “tanks.” It was about forty letters long, and translated to something like:
“barbed-wire crushing, trench-crossing, heavy machine gun carrying, armored, tracked, self-propelled fighting vehicle.”
It was a cumbersome word, but it conveyed a lot more information than “tank,” which conveys no information about the vehicle at all. In fact “tank” is a ruse, designed to make one think that it is not a vehicle at all.
Then again, the Germans decided to can the original term and went instead for “panther.”
wolfman:
Is that pseudocode, or a specific language? It looks like a Basic dialect.
The link to Allnoun is: http://world.std.com/~tob/allnoun.htm
The maintainer no longer maintains the site, but the language still exists on the pages.
I remember reading in a cryptography text somewhere that each letter of English text only contains about 1.3 bits of information (on average). Since English text is usually rendered in 7-bit characters, it should in principle be possible to devise a written form of english that is ~5 times more compact than what we have now. I’d be interested to see what this figure is for other languages.
Sign language. Duh. One sign is worth a thousand words as you can give the emotional content, direction & a bunch of other cool things of a word as you say it.
Perhaps we can usefully distinguish between related questions: e.g. which is the most efficient spoken language, the most efficient written language, and the most efficient notation?
In a sense, there is no way to compare like with like, since all languages involve a trade-off between rapidity and detail. It’s easier to convey a given sentiment more quickly IF you omit some details which you trust the native speaker will simply infer from the context.
I used to make commercial video films with English commentary that subsequently needed to be translated into several different languages. French came out sorta okay, but German and Mandarin caused hours of extra editing to expand the duration of some scenes to accommodate the commentary.
What’s also interesting is that of course some languages are simply spoken at a faster average speed than others. WIth the video scripts mentioned above, the Mandarin translation often LOOKED as short as the English script on the printed page, but it simply is not spoken as quickly. Native Italians are not trying to show off their incredible vocal dexterity - it’s just a language which has evolved with rapid speech patterns. However, for natural conversational pace it is left standing in its tracks by something like Serbian. A perfectly natural chat between two native Serbian speakers can sound like two Uzis going off. They also seem to breathe through their ears, since a Serbian ‘sentence’ seems to go on more or less indefinitely.
I once worked with a Swiss colleague who had grown up speaking about 4 or 5 languages fluently, and could get by in a few others. She told me that for easy, efficient commmunication she always preferred Spanish, both for its relative grammatical simplicity and its vocal flow. She found English okay, but a little ‘clunky’ and lacking in flow, and of course riled at its weird, incomprehensible spelling (she was referring to UK English).
I do remember seeing an analysis something like this in a book I read. I can’t really remember, but it may have have been in a book called Grammatical Man.
Well, there’s always Entish, wherein it might take a good 4 hours for a group of Ents to say “Good morning.” But since ficitious languages are beyond the boundaries of the OP, my money is on any of the Aleutian languages. Not only are many words multisyllabic, but there are many, many words to describe any one concept, and the language is [insert some word that describes a tendency to make it up as you go along]. Cecil did a column on it a while back. I’ll see if I can find it…
I could be wrong, but I’d vote for (are you ready for this?) the Arabic language. I’ve heard somewhere that it’s referred to as a “high context language” due to this property.
Example 1: “If you ask for explanation, will they understand it?” can be said in 3 words.
Example 2: “Did you guys do it?” can be said in 1 word!
Example 3: The opening verse of the Qur’an is 4 words in Arabic. Saying the same in English would take 11 words.
Note: I’m referring to classical or “formal” Arabic, not the spoken/conversational dialects.
Of course, there must be some other high-context languages with similar properties.
Post hoc ergo propter hoc?
<<Then again, the Germans decided to can the original term and went instead for “panther.” >>
Panzer = armour: Panzerwagen = armoured vehicle
But “panther” is more interesting
Yeah, I think that is it. After [the fact], therefore because of it.
Your example 3 is: Bism Allâh al-Rahmân al-Rahîm ‘In the name of God the most gracious, the most merciful’.
A ratio of 4:11 = .36 –
I can top that: a ratio of .125 – one word in the Qur’ân that takes eight words to translate in English:
fasayakfîkahumullâh ‘But God will suffice thee as against them’. (verse 2:137)
So classical Arabic can verge on the polysynthetic structure of Eskimo or some American Indian languages: a whole sentence in one word.
Arabic sounds good to me, I guess. If I may, then, does anybody have any idea of how “high context” loglan or lojban is?
(background - loglan is an artificial language originally created to test the “Sapir Whorf” hypothesis, and as such, is an attempt to create an extremely logical language with no grammatical ambiguity and no difference between written and spoken forms. Its grammar is like nothing even remotely resembling any naturally evolving language (predicate logic based). What I find interesting is that it is a “speakable” thing which can be machine parsed, and could lead to practical natural language dialog.)
In The Art of Plain Talk (1944), Dr. Rudolph Fleisch, who also wrote Why Johnny Can’t Read, noted how efficent Chinese is with this comparison to English:
"…sign, meaning ‘a mark.’
'(…)
"insignificance, meaning ‘the making of no mark.’
"You have added no meaning but four empty syllables. Now you can be serious and philosophical and speak of the insignificance of man. A Chinese would say something about Man no mark.
Is that efficient or what?
This seems very interesting. Do you have reference or a link to a page?
One thing I might add about Arabic, words are written the same way they are pronounced. If some word is written correctly/completely, and you can read properly, there’s no way you can mispronounce it.