Really Dan Brown? Your brilliant physicist in The Lost Symbol was studying the mind seemingly without ever contemplating the involvement of the brain in this issue? Really?
No no, I'm not bitter.
But let's ignore that for a second, and consider this: do you really know what "pia mater" and "dura mater" are? Or were you just looking for a convenient angle for the "veil-like" metaphor?
Either way, a scientist as well read as Dr. Solomon - particularly one who studied the mind, albeit via physics - would not have referred to the brain as "built in two parts - an outer part called the dura mater and an inner part called the pia mater...".
No Dan, these layers, with the arachnoid mater, are the membranes encapsulating the brain - like the pericardium surrounds the heart. Together they are called the meninges. Meningitis = inflammation of these membranes. They are not the two parts of the brain.
Do your research Dan! I mean Wikipedia can tell you this much! (I'm just saying)