one-dimensional vs skin-deep

one-dimensional

adj

  • Lacking personal depth and substance; conceited, vain, shallow, superficial. 

  • Having length, but no width, height or depth. 

  • Lacking depth or believability; flat. 

skin-deep

adj

  • Shallow, superficial. 

How often have the words one-dimensional and skin-deep occurred in a corpus of books? (source: Google Ngram Viewer )