castle in the air vs the cake is a lie

castle in the air

noun
  • A desire, idea, or plan that is unlikely to ever be realized; a visionary project or scheme; a daydream, an idle fancy, a near impossibility. 

the cake is a lie

phrase
  • The end being pursued is unattainable or misguided; the reward promised is false. 

How often have the words castle in the air and the cake is a lie occurred in a corpus of books? (source: Google Ngram Viewer )