Imagine an uncharged solid spherical conductor. Inside this spherical conductor, there is a cavity of a weird shape carved out of it. And somewhere inside this cavity, there is a charge +q. The charge +q induces an opposite charge -q on the wall of the cavity of the conductor, which distributes itself in a such way that its electric field cancels out that of +q for all points exterior to the cavity. Since the conductor carries no charge, this leaves +q to distribute itself uniformly over the surface of the sphere. The information about the shape and the location of the cavity seems to be lost, so does the information about the location and distribution of the charge +q within the cavity. I find this rather unsatisfying, unacceptable to my intuition. Is there a way to figure out the shape and the location of the cavity and of the charge without "cutting open" the conductor? I would have intuited that the charge distribution on the outer surface of the conductor should not be uniform and that one should be able to deduce the information about the cavity and about the charge within it from any asymmetry in the charge distribution on the outer surface. But apparently this is not true, so what is wrong about this intuition? In clearer words, what must I believe to be true for me to have such an intuition? I am thinking, roughly speaking, that information cannot be destroyed and should, in principle, be retrievable, even though the process of retrieving it (such as the measurement or calculation) may be very difficult in practice. But physics is seemingly now saying that the information is not retrievable even in principle and is forever lost to no where and for no reason.