It seems to me that this question needs certain other things defined to be properly answerable.
Let us start by working with Chaco's assumption that we are devoting all available area to living space. Naturally we want to assume that a person must have enough space to live decently, which involves getting up and stretching one's legs occasionally. But in fact life could easily be sustained in a tiny room of merely 60 square feet - a New York City apartment, for instance.
But we have made a fallacious assumption here. As such high-rise apartments prove, we are not limited to the surface area of the Earth. Rooms stack. In theory, we can stack the buildings as high as structural integrity will permit. We could surpass even this limitation with light pockets of gas, making homes which float in the air. Not to mention that we can dig a few miles into the Earth's crust, or perhaps even make the core somehow livable (cooling, probably).
And suppose that we find building materials and gases so advanced as to allow us hundreds of miles of vertical construction. At this point, our major limitation becomes whatever we define as the limit of the volume of "
Earth"
.
Yet, we still have not considered one possibility. It becomes possible that in the future, we would be sustained in little closet-size tubes, a la
The Matrix. It is also possible, depending upon how we define life, that we may consist solely of disembodied brains, with reproduction done artificially and extraterrestrially. We may even, again with a liberal enough definition, be storable as electrical impulses on hard disks, as conceived by Arthur Clarke. These possibilities drastically decrease the mass, volume, and resources necessary for each human.
I can't really calculate a number with all these unknowns, so I'll pick a scenario. Wikipedia says the volume of Earth, not counting atmosphere, is 1.0832073*10^15 cubic meters. I'll discount the atmosphere to compensate for a teensy bit of the core going unused. The volume of the largest recorded human brain, meanwhile, is around .18 cubic meters. We'll round to .25 for whatever equipment each would support. Therefore, the largest number of Earthling disembodied brains which may be supported at some point is approximately... 4.3 quadrillion.
Multiply that by 5.2 billion years, divide by 18, and it becomes approximately... 1.25 septillion. Plus whoever has already lived, a comparably insignificant figure according to Wikipedia.
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[Last edited by Jatopian at 11-27-2007 12:00 AM : time factor]