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I am trying to understand the difference, if any, between feasible, possible and potential. Most online dictionaries report them as synonyms. Is this right?

More specifically, I want to use these terms in the context of a maximization problem (that is a mathematical problem where a user-defined function should be maximized with respect to some input variables). Referring to all the input combinations of the function, which term should I use? Or is it simply a matter of style?

The phrase reads:

The variables define the search space which includes all the ... voltage patterns.

*I control the voltage patterns. The goal is to find the voltage pattern that maximizes my function.

P.S. I have also encountered the term candidate solutions to describe the possible solutions.

  • If words are synonyms, they are interchangeable in some sentences (with no significant change in the meaning of the sentence). Very, very rarely all. – Edwin Ashworth Feb 10 '15 at 15:30
  • Potential and feasible don't sound right in this context. Possible and applicable work for me. Disclaimer: non-native speaker. – Armen Ծիրունյան Feb 10 '15 at 15:31
  • Yes, I'd use possible here. Feasible has the main sense 'that we can sensibly achieve' ('possible and practical to do easily or conveniently' according to Google D) and potential 'that may [well] arise' (whereas you will probably be selecting voltage patterns). And 'potential voltage' is best avoided for obvious reasons. – Edwin Ashworth Feb 10 '15 at 15:38
  • 'Feasible' is a terminus technicus for optimization problems en.wikipedia.org/wiki/Feasible_region – anemone Feb 10 '15 at 15:51
  • @anemone This also shows the controversy. In the first paragraph of the wikipedia link you posted there are the terms feasible region, possible points and candidate solutions. Therefore, I think that a linguistic approach might give a better insight in the meaning of the different adjectives. – orestis21 Feb 10 '15 at 15:58
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In some contexts feasible and possible have very similar meanings.

It is feasible to get the train to Paris.
It is possible to get the train to Paris.

I would see both of these as conveying the same idea.

I would use feasible when I have a more specific goal:

It is feasible for me to get the train to Paris in time for the 10:30 meeting.

the defining characteristic being implications of the duration of journey and scheduling of a suitable service, and availability of seats. The conditionality being intrinsic to the course of action.

I would use possible when the constraints are not just the travel but also my own availability (and perhaps being somewhat evasive) my own preference.

It is not possible for me to get the train to paris in time for the 8:30 meeting.
(not specifying that I simply am not getting up at 04:30 to do that)

Possible also has connotations of situations that arise outside my control.

It is possible that the train may be delayed.
It is possible that it will rain tomorrow.

I don't think we would say

It is feasible that it will rain tomorrow.

Potential doesn't seem quite to fit any of those scenarios, butI think in general it has a feeling of the unrealised, of a specific thing that has yet to happen and may not, it may for ever be unrealised.

He had the potential to be a great Rugby player until he suffered concussion.

I mention the above to give a flavour the nuances that separate these synonyms.

In your context we are talking about voltage patterns, and I can see merit in all three

In your sentence my instinct is:

Potential is less good because I don't believe it works well when dealing with a wide range of outcomes, and trivially, because Potential Difference is a synonym for Voltage.

Feasible seems technically correct, in that the real determinant of the candidate set of patterns is your ability to create them, its under your control, it's what you are capable of "making" as in the etymology of Feasible from the French "faire".

However I would use Possible, as I think this is a theoretic problem where you will calculate answers to specified inputs and may never actually "make" anything at all.

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The phrase :

The variables define the search space which includes all the possible voltage patterns.

Why not feasible-

Its proper sense is "capable of being done, accomplished, or carried out". That is, it means the same as possible in one of the latter's senses, and its true function is to be used instead of possible where that might be ambiguous.

  • A thunderstorm is possible (but not feasible).

  • Witness said it was quite feasible (better possible) that if he had had night binoculars he would have seen the iceberg earlier; We ourselves believe that this is the most feasible [better probable] explanation of the tradition.

  • (Fowler) Modern English Usage:

    Feasibility: (a) (of a design,project, etc.) capable of being done, practicable, (b) (of things in general, also of persons) capable of being dealt with successfully.

Each case must be treated on its merits, but when the context requires the sense of likelihood or probability it is prudent to test first whether possible or probable might not be the more satisfactory word, and to use feasible only if both the other words seem unnatural or unidiomatic.

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The difference between possible and feasible is that feasible means "possible given the means available". So it's perfectly reasonable to say that a solution "is possible, but not exactly feasible", where "exactly" is an ironic accentuation of "not".

"Getting rid of an anthill in your front yard by blowing it up with 20 pounds of TNT is certainly possible, but not exactly feasible."

A potential solution is one which seems possible at first glance, but which has not been analyzed in detail sufficiently to tell whether or not it would actually work.

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Use a dictionary to look up the differences in meaning of these three words. Briefly summarized: feasible - capable of being done; potential - capable of becoming real; possible - within the limits of ability, capacity, or realization.

I'd say that 'possible' is a generic version of the more specific words 'feasible' and 'potential'. It's possible they could all be used in some contexts interchangeably, but it's probably not recommended in all cases.

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