the soul or self is a non-material center of consciousness.?

The soul is non-material and distinct from the body. The soul is an entity that is distinct from the material world and it is housed in the physical body like a ghost in a machine. While the body experiences tangible things within Space, the mind experiences itself in a different kind of way. For example, we can talk about physically experiencing a triangle but it makes no sense to say that my thoughts are triangular. This called mind-body dualism.

The idea of some sort of non-material "soul" is very old and likely dates back to primitive animism.

Our Renaissance-era thinkers like Rene can be excused for taking this notion seriously... First it's part and parcel of religious thinking and Faith... And it would have been impossible for people of that time to look at the human brain, a few pounds of squishy tissue, and understand that it by itself is entirely capable of producing consciousness and "self".

Now, we know better. The brain is "the most complex stuff in the universe" and is quite capable of generating self-awareness and consciousness. No "soul" required.

There is no evidence whatever of any sort of soul, and no model even of how such a thing could work.

How something "non physical" (whatever that means...) could retain memory, apprehend the world without sensory input, or do the rather large amount of physical work a brain does to maintain consciousness.

G

It means that Descartes was a good mathematician, and lousy philosopher.

The soul is non-physical and may be fully experienced through non-physical means.