As negative space has its merits in photography, so do the words not written. Take the following image as an example:
I shot it in the Black Forest on a chilly autumn morning on the top of the Hornisgrinde. Though the fog became my accomplice in erasing the superfluous, creating negative space still required action. Namely, there was a wind turbine on the mountaintop—I could have claimed the presence of a medieval castle, or you might imagine a small cabin. My picture emphasizes how nonexistence stimulates our imagination. It also shows trust in the reader: by not stating the obvious, it relies on the mental delicacy of the audience.
This is an active step: akin to the photographer moving the camera; the writer needs to cut through the jungle of words. The difference is that the jungle is created by herself. The photographer will not feel remorse for not including the umpteenth building in his cityscape; the writer will when realizing that that paragraph written in the last three hours is rubbish. This is why Stephen King calls eliminating the overhead “killing our darlings” in his memoir On Writing.
But why is striving for brevity so hard? By fighting the written word, your written word, the mind starts to protect its own creation. Since we have already invested our time, it would be wasteful to omit those parts. Wrong. This is why it is known as the sunk cost fallacy. We have already spent time writing, but we should not convince ourselves that, hence, it is good writing. Time investment and quality do not correlate perfectly, though practice improves our chances.
Writing is not about hoarding words.
Let us see why not.
Practice
It sounds like a cry to the heavens to exclaim words written with tears and sweat as practice, but that is what they are. Expect the first (second, third, …) drafts to be of bad quality. They are the whetstones to sharpening your mind, pen, and keyboard.
Clarity
This should be the end goal. In a story, you do not tell about failed attempts; neither do you in scientific papers. (You can include negative findings in the appendix, but lo and behold, to put that into the main narrative; it will confuse the reader). Shoot for a clean story.
Humbleness
Readers are not interested in how much you thought about that aphorism, story, or joke. They only care about whether the story works. Being aware of this will keep our egos in check.
Empathy
Put yourself in the reader's shoes: would you read what you have written without any incentive? Well, then make it more compelling.
Actionable advice
Copying is an effective learning process: Benjamin Franklin honed his penmanship by reading, making notes, and then reproducing articles from his favorite periodical, The Spectator.
Look for scientific papers, which you find well-written; horribile dictu, do the same with fiction to hone your style. Try to ingrain their best practices by reproducing them.