The act of transforming (or manipulating) data is permissible because the same rule is applied to all data in a given set. in other words, you're not just transforming some of your data while leaving other data points alone. the same concept appears in algebra when isolating a variable to solve a given equation. as long as each step applies the same rule to both sides of the equation, it is permissible. even driving safely by car is possible because all drivers agree to drive on the same side of the road. can you think of two other examples where a similar logic might apply?