The power of abstractions
If we want to build a car, we can just use a pile of steel and
the appropriate tools, and maybe we can build a box with four wheels. But if we
want to build an efficient and reliable car, we have to use diagrams and
mathematics. The more we are using abstract models (for example by using
computer aided design), the better we can model matter and build our
car.
There are other examples in the field of software development: if you work
very close to the physical layer, this means that you are going to program the
microprocessor by using machine langage, this means controlling directly the
"matter" of the processor. You are closer to the physical universe, but that
method is quite limited. In order to overcome these limitations, software
engineers have invented more and more powerful langages: assembly langage, C
langage, object oriented langages, modeling langages, etc. The more you are
using abstractions, the more you can build powerful programs.
So we have here a first indicator: raw matter alone cannot control very
efficiently raw matter. It is better controlled by something which is not
physical: models, abstractions, mathematics.
As models, abstractions and mathematics are not physical, we have definitely
to class these in a "not-physical" category. This indicates that
non-physical entities do exist.