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The phrase "take on dimensions" is correct and usable in written English.
It can be used when discussing how a concept, issue, or situation becomes more complex or multifaceted.
Example: "As the project progressed, the challenges began to take on dimensions we hadn't anticipated."
Alternatives: "assume complexity" or "gain depth."
Exact(2)
So I've learned that no matter how excited I am by a particular setting or idea or image, unless it functions as a means to get at truth, to be honest about something that feels emotionally true to me, some genuinely mysterious and interesting aspect of our natures, then the story ultimately will never take off, or take on dimensions.
In this case the Xi coordinate matrices take on dimensions m×3, for m equivalent residues in the pair-wise consensus set.
Similar(55)
"Every high-profile case, civilian or military," he said, "takes on dimensions and dynamics that are less familiar and less predictable because there are often interests, both expressed and implied, that transcend resolving this individual case justly.
Nevertheless "militancy" in Kashmir has taken on dimensions significantly altered from the violent insurgency of the 1990s.
I pictured an ancient young woman rearing off the table, taking on dimension, shredding our assumptions, challenging our ventriloquy of her mute body.
And inevitably struggles in the relationship take on the dimensions of a political power struggle.
When we read lyrics on a page they can be profound, but it's only when you put them with music that they take on another dimension.
Chilis take on a metaphysical dimension in Taylor's telling.
In the meantime, the words of Don Mattingly take on a new dimension.
Orwell's labors take on a potent moral dimension.
This whole big pile of nonsense that one might call an "issue" has since taken on unimaginable dimensions.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com