Think of every workout as a vector, where every dimension represents how much a given muscle was trained. Then, workouts form a vector space: the zero vector is sitting on your ass and doing nothing, vector addition is just doing 2 workouts after each other, and scalar multiplication is adding weight and/or reps. We ignore the fact that there are no negative workouts.
We can then find a set of exercises (push ups, squats, pull ups, etc) that form a basis for the vector space. The vector representation of each exercise can be found by calculating the forces applied by each muscle and the movement of each joint during the exercise.
Then, we represent the ideal workout as a vector, and then represent this vector as a linear combination of the basis vectors, which then becomes our workout routine. For example, if the ideal workout is 30 * pushup + 40 * squat + 8 * pullup, then we have determined that the ideal workout is 30 pushups, 40 squats and 8 pullups.
Would this work?
We can then find a set of exercises (push ups, squats, pull ups, etc) that form a basis for the vector space. The vector representation of each exercise can be found by calculating the forces applied by each muscle and the movement of each joint during the exercise.
Then, we represent the ideal workout as a vector, and then represent this vector as a linear combination of the basis vectors, which then becomes our workout routine. For example, if the ideal workout is 30 * pushup + 40 * squat + 8 * pullup, then we have determined that the ideal workout is 30 pushups, 40 squats and 8 pullups.
Would this work?
