It feels like this article sets up something of a straw man. The analogy that a mind is like a computer is just that, an analogy . It's used to present the high-level structure of the brain in a accessible, understandable way, not as a logical argument. This analogy is not the justification for why people believe that "the mind can be replicated on a computer". And yet the article tries to disprove the latter, deep a…
So far, everything in reality seems to be "made of" either determinism or randomness. There might be a third option (and options beyond that), but we haven't seen one or thought of one yet.
So far, computation can model determinism perfectly well (after all, computation is just very orderly, bottled-up determinism harnessed to a predictable human purpose!), and model randomness as well by drawing random bits from an entropy source. When you get deep enough, mathematics is in fact reducible to computation (paging Robert Harper). Given this, the Church-Turing Thesis says that our mechanical computers ought to be able to model anything reality is made of: either reality is theoretically Turing-recognizable given enough compute-power, or reality contains super-Turing phenomena that we could exploit to build super-Turing computers.
Thus, if we accept a couple of assertions that have held up decently so far, it looks as if all parts of our prosaic, everyday reality ought to be amenable to computational modeling, provided we find the right model and throw enough flops at it.
They are assertions, but they've also held up for a damn long time, and we would need some extraordinary evidence to accept the extraordinary claim that those assertions don't hold.