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What is a word which means something difficult or close to impossible to achieve? For example,

A ten-percent growth rate is a __: it is certainly possible on paper, but very difficult to accomplish.

I can think of a castle in the air or an ideal prospect, but I would love to have a simple one-word substitute.

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Sorry for being off topic, but wicked problems are problems which are very tough to solve. –  aitchnyu Mar 26 '12 at 14:29
    
We're really trying to avoid using this site for "single word requests." If you have a particularly interesting problem to solve, all we ask is that you include a bit of background and context for asking the question, instead of just repeating the title in the question again. See: meta.english.stackexchange.com/questions/1654/… or meta.english.stackexchange.com/questions/2160/… –  Jeff Atwood Mar 26 '12 at 18:47
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How can we tell people this while maintaining a single-word-requests tag? I mean no dissent. –  cornbread ninja 麵包忍者 Mar 26 '12 at 20:33
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@JeffAtwood: I only have one question for you: how does a poster know beforehand if there is a single perfect answer for his question? I have participated in questions both as an asker and answerer where we ended up zeroing in on one answer. I assumed that this would also be one such question. –  Bravo Mar 27 '12 at 4:14
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@JefAtwood: As you may recall, the most-upvoted answers to those Meta questions you posted were for allowing SWRs, provided that they were somewhat interesting and provided some background. This question arguably does that, so perhaps it would have been better if people had been able to vote to close (or not). For the recond, I personally dislike SWRs, but some people do like the more complicated ones, like this one. –  Cerberus Mar 27 '12 at 8:41
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17 Answers

up vote 17 down vote accepted

A pipe dream may be what you're looking for; possible, but impossible for all practical purposes.

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The brass ring ... –  GEdgar Mar 26 '12 at 14:06
    
+1 Definition from Wikipedia –  user14070 Mar 26 '12 at 14:38
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A ten-percent growth rate is unrealistic: it is certainly possible on paper, but very difficult to accomplish.

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The OP seems to be looking for a noun. –  Robusto Mar 26 '12 at 14:39
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impracticality

A ten-percent growth rate is an impracticality: it is certainly possible on paper, but very difficult to accomplish.

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+1 This keeps consistent with the second part, where unrealistic implies directly that it is not even possible. –  user14070 Mar 26 '12 at 14:41
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I can't believe nobody mentioned it so far:

chimera

a thing which is hoped for but is illusory or impossible to achieve:

the economic sovereignty you claim to defend is a chimera

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I think that definition is to all intents and purposes "incorrect". I don't doubt chimera is occasionally used with the sense of illusory, but I think this is primarily by people who don't actually know what the word really means. –  FumbleFingers Mar 26 '12 at 14:53
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@FumbleFingers: that would include the OED, then. "An unreal creature of the imagination, a mere wild fancy; an unfounded conception. (The ordinary modern use.)" –  TimLymington Mar 26 '12 at 15:11
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@TimLymington: I don't think I'm exactly disagreeing with OED, but I just don't think, for example, unrealistic sales targets can be properly called a chimera. To me, the word primarily means an unreal creature of mixed parentage, which can metaphorically extend to an untenable conceptualisation deriving from mutually incompatible antecedents. I don't see it extending to overoptimistic ambitions in general. –  FumbleFingers Mar 26 '12 at 15:39
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I upvoted because I've never heard that definition before, but I would tend to disagree with OED on this one. Perhaps there are a bunch of literary references that I'm unfamiliar with, but I've never seen it used like in their example sentence. I've always seen it used to refer to something that is created through combination (and not always unreal, although always freakish.) –  jhocking Mar 26 '12 at 18:01
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I'm familiar with this metaphor in my own language and I believe I've heard it used in English as well on several occasions. I honestly didn't think it would be unknown to so many people. –  Martin Tapankov Mar 26 '12 at 18:34
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I know this isn't one word, but will suggest Herculean task

A ten-percent growth rate is a Herculean task: it is certainly possible on paper, but very difficult to accomplish.

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But I think "Herculean task" implies that it is, in fact, possible, just very difficult, which is rather different from "not really possible in practice". –  Jay Mar 29 '12 at 21:34
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I have heard business managers call such a situation a challenge. When everyone in the room knows that the financial goal the managers just set forth is going to take a Herculean effort to achieve, they often follow up by saying something like, "We know this will be a challenge, but...."

In this case, it would used in the sense of this definition:

  1. A test of one's abilities or resources in a demanding but stimulating undertaking.
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Impossible, unrealistic, unattainable, unachievable, quixotic, dreamy, empty, even as a non-native English speaker, I can think up many analogues. Just for your fun, we call unrealistic story / plan “a story like a dream,’ 'a cake drawn in the picture (that you can not eat) - 画餅', and ‘castle in the air –空中楼閣', or 'castle on the sand -砂上の楼閣' as well in Japanese.

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unattainable might be the word you're looking for.

unattainable (adjective) Pronunciation: /ʌnəˈteɪnəb(ə)l/ not able to be reached or achieved: an unattainable goal

You would end up with a phrase like this:

A ten-percent growth rate is unattainable: it is certainly possible on paper, but very difficult to accomplish.

I hope it helps.

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If it's possible on paper, it isn't unattainable, merely very difficult. –  TimLymington Mar 26 '12 at 13:19
    
You set the goal or growth rate on paper, but it is not possible to achieve such goal/target in the real world. Otherwise the action of writing something unattainable would convert such action into something feasible. –  emaringolo Mar 26 '12 at 13:41
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Something that can be attained (however difficult) is not unattainable. Using the word in OPs context is akin to the common misuse of literally. –  TimLymington Mar 26 '12 at 14:06
    
I think you're right. Thank you. –  emaringolo Mar 26 '12 at 15:07
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Though not a noun, sisyphean is one of my more favorite words.

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a Stretch Goal, or a Big Hairy Audacious Goal(BHAG) would be the terms I would use in formal and informal contexts, respectively.

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What about the word "Utopia"? In Y. C. Zarka's 28 Aug 2011 NYT blog one finds

Utopia is often spoken of in a general, imprecise way, to characterize any conception of the state that is considered an unrealizable ideal.

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Utopia as such does not fill in there. Perhaps an utopian prospect or something does. –  Bravo Mar 26 '12 at 14:24
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I'd go with unfeasible. For example:

A ten-percent growth rate is unfeasible: it is certainly possible on paper, but very difficult to accomplish.

Inverting the dictionary.com definition for feasible, you get:

un·fea·si·ble adjective

  1. not capable of being done, effected, or accomplished: an unfeasible plan.
  2. improbable; unlikely: an unfeasible theory.
  3. unsuitable: a road unfeasible for travel.

Of course, the noun version is not quite countable. You could talk about the "unfeasibility of" something and that's fine, but to describe something as "an unfeasibility" sounds particularly awkard to me.

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Improbability

A ten-percent growth rate is an improbability: it is certainly possible on paper, but very difficult to accomplish.

Hope this is right.

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To toss out a couple: daunting? formidable?

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For that scenario I think aspiration is a good choice.

A ten-percent growth rate is an aspiration

Aspirations are typically things that people or organisations want to achieve, think they can, but cannot guarantee that they will. In business it's typically the best case scenario or outcome of a particular course of action.

A similar word is ambition.

In a more fanciful context, I would use dream.

There's no way I'll make it to the top of Everest with my asthma, it's just a dream.

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The first thing that came to mind for me was "an insurmountable task."

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Elusive: Difficult to find, catch, or achieve; Difficult to remember or recall.

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