The piece is an extract from Arthur C. Clarke's 2001: A Space Odyssey. It was not a standalone piece of literature.
The passage I was trying to remember is as follows:
There were other thinkers, Bowman also found, who held even more exotic views. They did not
believe that really advanced beings would possess organic bodies at all. Sooner or later, as their
scientific knowledge progressed, they would get rid of the fragile, disease-and-accident-prone
homes that Nature had given them, and which doomed them to inevitable death. They would replace
their natural bodies as they wore out - or perhaps even before that - by constructions of metal
and plastic, and would thus achieve immortality. The brain might linger for a little while as the
last remnant of the organic body, directing its mechanical limbs and observing the universe
through its electronic senses - senses far finer and subtler than those that blind evolution could
ever develop.
Even on Earth, the first steps in this direction had been taken. There were millions of men,
doomed in earlier ages, who now lived active and happy lives thanks to artificial limbs, kidneys,
lungs, and hearts. To this process there could be only one conclusion - however far off it might
be.
And eventually even the brain might go. As the seat of consciousness, It was not essential;
the development of electronic intelligence had proved that. The conflict between mind and machine
might be resolved at last in the eternal truce of complete symbiosis.
But was even this the end? A few mystically inclined biologists went still further. They
speculated, taking their cues from the beliefs of many religions, that mind would eventually free
itself from matter. The robot body, like the flesh-and-blood one, would be no more than a steppingstone to something which, long ago, men bad called "spirit."
And if there was anything beyond that, its name could only be God.
Thank you to @OrganicMarble and @jwodder for helping me find the source.
