It is a fact of nature that certain objects inhabiting this physical world are capable of evoking conscious awareness. Among such objects are healthy living human brains (at least when attached to human bodies). We do not know what other physical systems might be capable of this feat. There is a point of view which asserts that a sufficiently powerful computer, suitably programmed, could also evoke awareness. Indeed, it is not infrequently maintained that this conclusion would be a necessary implication of any completely scientific viewpoint. It is argued that the brain's function is simply "information processing" — the activity that computers also indulge in, sometimes very much more effectively than human brains. Although there are many activities in which the brain remains a more effective instrument than any computer system constructed to date, it is only a matter of time — so the argument runs -before computers will vastly exceed the capabilities of brains in all significant respects. Of course, opinions might differ widely as to the timescales involved. Some say that we shall be superseded in less than forty years (cf. Moravec 1988), whilst others argue that it will be many centuries, perhaps even millenia, before computers will overtake us, though eventually they must do so — if we do not destroy ourselves first!