formal science vs natural science

formal science

noun
  • A study that is concerned with theoretical formal systems, such as logic, mathematics, systems theory and the theoretical branches of computer science, information theory, microeconomics, statistics, and linguistics. 

natural science

noun
  • Any science involved in studying phenomena or laws of the physical world: physics, chemistry, biology, astronomy, and so on. 

How often have the words formal science and natural science occurred in a corpus of books? (source: Google Ngram Viewer )