If the computational hypothesis for minds and brains is true, and it is only conjecture though a tempting one, I can only see one way out. Analogies are a wicked thing to indulge in here. But bear with me.

If an engineer designs a computer that computes on encrypted information, from an observer's naive perspective, the entire contents of memory is rewritten with a random value for each step. Yet there is a mathematical relationship between those seemingly random bits and whatever is encoded. Even just using some error correction and non-deterministic parallel processing and it might look pretty much like noise if you don't have the decoder ring.

Something like that is the only explanation I can come up with. Information is stored at a level of abstraction in a structure that is maintained by being continuously re-encoded in the ephemeral computations at a lower level.