Our experiences have two components, object of experience and consciousness. Objects keep changing but that does not mean consciousness is changing. What we see here, smell, taste, touch, what we think, what we feel, what we remember, what we desire, keep changing throughout the day. The things that you see are continuously changing. Other things come and go. This is a subtle point, but it's important to notebut our experiences keep changing? Yes.
Inspired by the 15th chapter of the Ashtavakra Gita, Swami Sarvapriyananda gives a discourse on the nature of the Self.