This exchange got me thinking about how mass is represented mathematically. Newton wrote his Principia and formulated his three laws of motion before the invention of vector algebra. Bearing this in mind, I would argue the only quantity in Newton's principia which posseses vector-like attributes is mass. The assumption that velocity and acceleration in Newton's principia can be treated as vectors is an interpretation of the three laws. However, vectors cannot be systematically applied to mass without contradiction because according to the first law mass of the same quantity can be both moving in a specified direction and at rest without a specified direction. Mathematicians who were keen to apply the techniques of vector algebra avoided this problem by designating mass as a scalar quantity, but this too is an interpretation. The question arises is there a mathematically sensitive way to capture mass's dual quality instead of reducing it to a scalar quantity?
Harry
