It does not necessarily follow from the observation neural activity is equivalent to computation (or in simple cases, calculation) that a neural system is a computer. How natural neural systems carry out computation is as yet not known. The only thing that we can say with certainty is that the activity of natural neural systems is equivalent to computation.
The simplest of natural neural systems simply modify the sensor-motor flow of information.
The same inductitive methods used to sketch out the details about neural function can be used to determine how the neural system as a whole must function.
The study of dreams indicates that while visual perception is relatively invariant and fixed function (as indicated by REM sleep) most functions must be separate from the underlying hardware. The episodic memory of dreams is actively erased once a period of REM sleep has completed and this indicates the speed by which memory can be formed and then subsequently erased. The study of subjects suffering from multiple personality (or the more common phenomenon of alcohol-linked "black-outs") indicates that memory, skills and individual preferences are not fixed but can be arbitrarily installed in the same way that an individual program can be read from the storage system into active memory and then run.