We do not yet know what a computer can't do. Indeed, for nearly one hundred years, the computer has been defined capaciously, as a machine that can do the work of any other machine provided it can be defined logically (Alan Turing). Adopting François Laruelle's parlance, Turing's definition could be renamed the Principle of Sufficient Computation; the definition ensures that the computer can actuate any and all events, provided they are formulated as ideas.
The Principle of Sufficient Computation thus reveals a series of characteristics common in computing:
(1) The centrality of action or practice, understood as a series of commands that may be executed in order to alter the states of a system.
(2) The linking of idea to action, wherein if something can be thought it can be executed, and if something has been executed it was, perforce, previously thought.
(3) Practical omniscience, where knowledge swells to the very limits of knowability, even as those limits have been incontrovertibly demonstrated using logical proof.
(4) A system of judgment based not in morality or politics but in mimesis. Computers thus parrot the old question from the Poetics of Aristotle: Is this copy a well-crafted copy?
So we do not yet know what a computer can't do, mostly because the computer has been doing so much for so long.
And, still, indicators show a variety of alternatives, varieties of computation that reside not so much before or after mainstream computing, but along side it. The varieties of computation would include digital computing (the paradigmatic implementation of the Principle of Sufficient Computation), analog computing (formerly dominant, but today largely overshadowed), dialectical computing (unimaginable using today's chips and software), and non-standard or artificial computing.
Artificial computation was discovered by Laruelle, even as artificial computers have not yet been invented, similar to the discovery of Shor's algorithm prior to any machine capable of implementing it. Synonyms for artificial computation include: non-computation, non-standard computation, compu-fiction, and computer fiction.
Artificial computation is defined, axiomatically, as the withdrawal from the Principle of Sufficient Computation, and hence in terms of:
(1) The preemption of all commands and the neutering of the executable, in favor of pure process as a phenomenon immanent to itself.
(2) The delinking of idea and action as to be absolutely un-exchangeable with each other.
(3) Knowledge as radically finite, existing not as the total aggregation of ever-widening claims about the world, but as a series of axioms in the generic real.
(4) A non-Aristotelian technology of immanence, where technology is not understood in terms of craft or mimesis (whether effective or defective).
Artificial computation is thus not post-computational, but rather, somehow, along side it, as a science "liberated from...the neurosciences or cybernetics" (Laruelle). In this sense artificial computation enacts a generic form of thinking, which, ironically, has thus far remained unthinkable by that overweening discipline of philosophy.