The first connection is between:
The second connection between brain and computer is the old notion that digital circuits, such as computers use, are as expressive as neurons and synapses in their ability to perform brain like processes. This connection has nothing to say about sequentiality, nor consciousness. Kanerva and others have raised the question of whether normal boolean digital circuits can efficiently perform the search like functions that many suspect the brain makes heavy use of. I don’t know. An anecdote is apropos here. Fred Brooks, a prominent IBM computer architect, resisted introduction of ‘content addressable memories’ in the early 60’s. Those who advocated them, he said, always compared their performance with the worst programmed algorithms, not the best. Today Google (and other good search engines) can, given two obscure words, find one document among billions with both words. It does this with clever algorithms and not clever circuits.
Some will note that today’s computers are hardly sequential. They will be checking your e-mail even as they attend carefully to each keystroke you type into a document. Here is a short history of how they developed this ability in the 60’s and 70’s. Since there was a discipline and thorough understanding of the state of a computation, it was possible to enhance the hardware, and write a program, called the kernel, that could switch between many concurrent processes as external events demanded, while preserving the illusion to each process that there was nothing else besides its narrow task that needed attention. People too multitask (originally computer jargon) but not so efficiently and smoothly as computers.