Module 1: Now You Try I

Consider a single string on a (right handed) guitar tuned to the appropriate level. We can consider the problem of playing this string to be two dimensional: there is he location where you might finger the string with your left hand $\text{($\ell$)}$ and the force you apply to pick the string with your right $(r)$. A standard guitar has six strings. Using this description, how many dimensions are necessary to describe playing a guitar?

Solution:

There are six strings with two measurements per string. This gives $6 \cdot 2 = 12$ dimensions.
(Note: not all of these are actually physically playable!)