The quantitative (mathematical) description of particle spin is not any more understandable than the non-quantitative description. Dr. Felix Smith, Head of Molecular Physics, Stanford Research Institute, once related to me the true story of a physicist friend who worked at Los Alamos after World War II. Seeking help on a difficult problem, he went to the great Hungarian mathematician, John von Neumann, who was at Los Alamos as a consultant.
"Simple," said von Neumann. "This can be solved by using the method of characteristics."
After the explanation the physicist said, "I'm afraid I don't understand the method of characteristics."
"Young man," said von Neumann, "in mathematics you don't understand things, you just get used to them."
-- footnote in Chapter "The Particle Zoo"