Final answer:
Transformation describes both mental and physical changes, from shifts in understanding to movements within coordinate planes or reference frames, as well as significant societal reforms.
Step-by-step explanation:
Transformation in mathematics often refers to the movement of geometric shapes in a coordinate plane. The verbal descriptions provided suggest different transformation types. When we discuss the mental transformation mentioned by Keller, it indicates a change in thought or understanding, rather than a physical shift.
In contrast, Galilean transformations deal with the change in an object's velocity relative to different reference frames in classical mechanics, indicating a physical transformation. These velocities are simply added as vectors, signifying a quantitative change rather than the qualitative change implied by the mental transformation.
Apart from these, transformations can describe various other processes, such as the change in forms of mechanical energy during a skydiver's fall, molecular changes in nuclear reactions, or even social changes within movements or ideologies.