title_body: Are there any "unspeakable" languages?
upvoted_answer: The answer is a definite Yes, there are.
  
  The example that comes immediately to my mind is Bliss symbolics (also known as Semantography) by Charles Bliss from 1942–1949. As an additional bonus, it is still used and developped further, and may even be included into Unicode at some date.
  
  EDIT: The term to look for is pasigraphy. There were lots of pasigraphies (Blanke, Internationale Plansprachen, gives the number 60) mainly in the 19th century, but the most successful ones were created in the 20th century. There were both philosophical pasigraphies (often using digits or abstract symbols) and naturalistic ones (starting from pictograms).