The sayings of Vedanta can appear to be mystical to be illogical and opposed to common sense.
They appear as such is because there is a fundamental difference in the core between what Vedanta teaches and what science and common sense says is true.
The common sense and scientific view is that reality is the sum total of things in space (i.e. physical objects).
What does Vedanta have to say about this? It says that reality is the sum total of experiences and nothing more.
In the scientific view perception emotions etc do not appear at all.
In the vedantic view they are first class citizens of reality.
In the scientific view dreams are just illusory and unreal.
In vedantic view they are as real as anything else since they are valid experiences.
Now we come to the very core of Vedanta i.e.: I am Brahm.
If you take experience to be the fundamental nature of reality, then what lies at the root of each experience.
At the root of each experience is the experiencer of the experience.
The experiencer having no attributes is indistinguishable from one experience to another.
It is the enveloper of all experiences, just as space is the enveloper of all physical objects.
