She took a deep breath, calmed herself, and continued speaking.
"You mentioned before that we can use the 'path optimization equation' to verify Mr. James's conjecture. That is, when an object moves from one point to another, it chooses a path that minimizes a certain 'action quantity'."
"Initially, I couldn't understand what this 'action quantity' is, nor how to describe it in mathematical terms. But in your class, I was inspired by the energy conservation law you discussed."
She picked up a feather pen and quickly wrote a line of scribbled formulas on the draft paper, her bright eyes flashing with confidence.
"To quantify and calculate this idea of 'least effort', we need a mathematical tool to define the 'total cost' of a path. I define it as S, which is the kinetic energy T of the system at any given moment, minus its potential energy V."
"Then, the 'total cost' S of a system from time t1 to t2 is the accumulation of the 'cost' at each moment during this period—integral!"
