>
And what about concepts like art, love, beauty, morality? Are these also simply "computations" of some sort?Yes, all that we are is contained within our skulls, in some sort of mess of chemical reactions and computations built ontop of those chemical reactions. Our detailed understanding of those reactions and relationships is limited at this point, however there has been nothing to suggest that anything that "is us" is operating outside of the laws of physics.
In other words, we are materialistic.
That leaves the question of if we are algorithmic. According to the Church-Turing-Deutsch principle, we are. Some people, most notably Roger Penrose, disagree.
Penrose's objection to the algorithmic nature of the mind is rooting in Gödel's incompleteness theorems (I suspect you are familiar with his objections, maybe read his books on the topic?). However it is important to remember that Penrose does not argue against a materialistic mind, merely the algorithmic mind. He believes that there are quantum phenomenon in your wetware that are essential to the human mind, and which allow a violation of the Church-Turing-Deutsch principle.
If he is correct (and I believe that he is not. evidence for such a essential quantum phenomenon is absent), then it doesn't really matter. What it would mean is that any computer constructed to run a human-like intelligence would need to take advantage of those same quantum phenomenon. Anything a materialistic (although not algorithmic) mind can do, a sufficiently advanced materialistic computer can do as well.