Anything that can be written down as a program can be computed given the right memory and enough time.
Explanations are a form of information, and information can only be processed in basically one way—with computation of the kind invented by Babbage and Turing.
Computers are universal, in the sense that given the right program, they can perform any transformation of information whatsoever, including the creation of explanations and other knowledge.
Now, there are only two possible limitations to that. One is the lack of computer memory (i.e. of information-storage capacity) and the other is the lack of speed (or the lack of time).
We've been improving our memory capacity and our speed of computation for thousands of years with the invention of things like writing, writing implements, even language itself, which enables more than one person to work on the same problem and coordinate their understanding of it. Nowadays, we use computers, and in the future we can use computer implants and so on.
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