all the three sentences below are grammatically right?

[Unregistered]

Could any teacher let me know if all the three sentences below are grammatically right?
1. Statistical operation can not bridge the gap “that lie between” description and explanation.
2. Statistical operation can not bridge the gap “lying between” description and explanation.
3.Statistical operation can not bridge the gap “between” description and explanation.

Could any teacher let me know if all the three sentence above are grammatically right?
There is three questions pertaining to these sentences I would like to raise.
1. in what occasion can we replace the relative Clause by a participle construction while keeping the rest of the sentence unchanged?
2. What is different in meaning between the phrase “ the gap between” and ”the gap lying between”
Thank you

 

[David L.]

.Statistical methods cannot bridge the gap between description and explanation.

... is the correct wording.

'gap lying between' : the use of 'lying' would emphasize the magnitude of the gap, as if one was saying, ...the gap, lying like a gaping chasm between us.

The use of 'lying between' is not appropriate in scientific writing.

 

[notatall]

.Statistical methods cannot bridge the gap between description and explanation.

... is the correct wording.

'gap lying between' : the use of 'lying' would emphasize the magnitude of the gap, as if one was saying, ...the gap, lying like a gaping chasm between us.

The use of 'lying between' is not appropriate in scientific writing.

David
Do you mean you would not suggest replace the relative clause by a participle construction in scientific writing?

if so, why not do you think? and in general. in what situation we use participle construction instead of relative clause with same meaning to modify the antecedent?
Thank you