General Impossibility:
* Trying to catch the wind: This highlights the futility of chasing something intangible.
* Trying to fit a square peg in a round hole: This emphasizes the mismatch between resources and the task.
* Trying to climb an invisible ladder: This emphasizes the lack of a clear path or means to achieve the goal.
* Trying to build a castle in the air: This emphasizes the impracticality and lack of foundation for the task.
Physical Impossibility:
* Trying to hold back the tide: This highlights the overwhelming force of nature against which the task is futile.
* Trying to outrun a speeding bullet: This emphasizes the sheer impossibility of achieving something due to physical limitations.
* Trying to stop time: This highlights the impossibility of altering natural laws.
Logical Impossibility:
* Trying to prove a paradox: This emphasizes the inherent contradiction and self-contradictory nature of the task.
* Trying to square the circle: This highlights the impossibility of achieving something that is mathematically impossible.
Figurative Impossibility:
* Trying to find a needle in a haystack: This emphasizes the difficulty and near-impossibility of finding something very small and lost amidst a large and chaotic environment.
* Trying to teach a pig to sing: This emphasizes the impossibility of achieving something that is inherently unnatural.
Specific to Your Context:
To choose the best analogy, consider the specific context of the impossible task you're describing. What is the nature of the impossibility? Is it a physical limitation, a logical contradiction, or simply a task beyond someone's abilities?
For example, if you are talking about a task that requires resources beyond what is available, the "square peg in a round hole" analogy would be suitable.