A mathematical equation that correctly describes a physical relationship between quantities is dimensionally homogeneous. However, the converse is not true. An equation that is dimensionally homogeneous does not imply the existence of a physical relationship between the quantities in that equation. The dimensions of the velocity of money are generally taken to be t^-1. In what follows we examine this assumption and show that it is physically impossible. We then show what the correct dimensions of velocity are and arrive at the surprising inference that at their core Keynesianism and monetarism amount to the same thing.

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