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Two Computers & An Ethernet Cable -- Also A Computer?

Say we want to run a computation on two computers, with a
network cable between them. This gets very complicated -- one
must make all sorts of provisions for network failure, failure
of one machine, &c -- unless one is willing to fail fast, to
fail the whole thing if any component fails.

After examining this problem for quite some time, I wonder if
the network computer is not really a computer, in the sense of
a general purpose computer, but rather a lesser machine, not
able to run all the algorithms that a general purpose computer
can run. However, I lack the formal tools to say anything
about this. Is there a clear case to be made one way or the
other? What's a good book to start with, assuming I would like
to demonstrate it for myself?