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Can a noun be used before "without" as in example (1)? Does (1) read well? Or should a verb ending in -ing be used instead as in example (2)?

(1) Analysis without a deep understanding of science is pointless.

(2) Analysing without a deep understanding of science is pointless.

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Nouns, whether concrete or abstract, are very often used with "without".

Supper without you tonight, a melancholy prospect.
— Marilynne Robinson, Gilead (sentence fragment)

Your first example reads better because the parallelism is clear. For the second one, I would prefer:

Analysing without deeply understanding the science is pointless.

However, even this is not as good. The abstract noun "analysis" works well on its own, but the transitive verb/gerund "analyzing" feels incomplete for lack of an object.

I also added "the" before "science", which yields the meaning "whatever science is relevant to the analysis" rather than suggesting you somehow have to understand all of science. An alternative solution would be "how science is carried out" or "the scientific method", according to what you mean.

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Generally speaking, preposition phrases often come after nouns:

a bike with a basket on the handlebar
the container in the back of the fridge
a book on the top shelf

Your example of "analysis without a deep understanding of science is the same.

These preposition phrases are adjuncts to the noun.

The difference between your two example sentences is that "analysis" is a noun that refers to the process or result, while "analyzing" is a gerund, which refers to the action of following the process. This means the second sentence could be rephrased, "Doing analysis without a deep understanding of science...", so they're very similar in meaning, but not exactly the same.

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