Dear Sir Roger Penrose,
please allow me to provide the minimal ontology that fixes the problem of the separation of the platonic, physical, and mental realm.
In the beginning there was nothing. Then nothing related to itself. That relation started being (of anything). Then relations of already existing relations subsequently yielded all of reality (meaning that all existence is merely collections of dots within the (infinite) relational "tower"). Being of anything is the "matter"/isness-substance of those relations. Mathematics traces their structure patterns. The mind does not connect to anything fundamentally separate. Because all that exists is originating from fundamentally shared patterns. Even most remote things share the pattern of the relation of nothing to nothing being the component of their chain of existential derivation.
As you can see, that is one possible elegant solution of the problem of platonism. In fact, the most powerful solution from those accessible to the human mind.
Kind regards,
a human being.
