The calculations assumed that the then-current population growth rate would stay the same (an intentional conceit that he drew attention to after the climax of the calculations had been revealed, a conceit I will repeat here) and he simply noted some interesting milestones as the population grew bigger and bigger. Things like the point when all the living humans standing shoulder to shoulder would cover the entire land area of the Earth, or when the total mass of all the living humans would be equal to the mass of the Earth, or the mass of the solar system, or the mass of the Milky Way galaxy, and ultimately the mass of the entire known universe, when every atom we've ever detected is part of a living human body, an all-human universe.
Annoyingly, I've never been able to remember the exact figures Asimov gave, which takes something of the punch out of this demonstration. It's also quite likely that some of the figures have changed since Asimov wrote that, not least of which is the total mass of the observed universe, because our observations have improved and we've seen more stuff. So, I thought I might as well just repeat his exercise and do an early 21st century update.
I got a little bit stuck on the maths - I'm quite rusty - until I saw this really great lecture by Prof. Albert A. Bartlett, which is clear and simple and to the point, but doesn't go nearly as far as Asimov did. It's definitely worth a watch, to understand how Asimov and I came to our answers.
I'll make a few trivial assumptions here, so feel free to adjust these if you think you know better. They will include:
Mass of one human = 70kg (a rough average, there might be a better figure available somewhere)
The floor area taken up by one standing human: 1 m2
I'll also draw on a few more important figures, calculated by people smarter than me. Sources will be given for each of these, though I'm sure you could find more accurate sources if you cared to hunt for them. They include:
The current total (as of the day I published this) human population: 7.014 billion
The current rate (as of 2009) of human population growth: 1.1%
The Earth's land surface area: 148,940,000 km2
The Earth's mass: 5.9736×1024 kg
The solar system's mass: 1.992 x 1030 kg
The Milky Way's mass: 2.983 x 1042 kg
The mass of the observed universe: 3 × 1052 kg
So when do we hit those kilometer stones? Check my maths, but I believe the assumptions and facts above resolve thusly:
Total living human population standing area = Earth's land surface area in 2,811 years
Total living human population mass = Earth's mass in 2,800 years
Total living human population mass = solar system's mass in under 4,000 years
Total living human population mass = Milky Way's mass in under 6,500 year
Total living human population mass = mass of the observed universe in under 8,500 years
Despite a couple decades of changing data and a population growth rate that's already dropped a bit, that's still all in the same ball park as the figures I remember from Asimov's book. So there you have it: 8,500 years ago, we were 5 million humans, covered in shit and only just getting the hang of domesticated beans and cows, and the maths is telling us that in another 8,500 years we'll have travelled billions of lightyears in all directions and consumed literally EVERYTHING!!!! that we're currently aware of.
Clearly. Not. Possible.
And this is exactly what Malthus, Asimov, Bartlett and now I want to draw your attention to. Picture our available resources as a road. Net consumption of resources drives us down the road, net restoration of them puts us in reverse. And there's a massive fucking concrete wall, all covered in spikes and shit, waiting for us at the end of the road. So frankly, we don't want to touch the accelerator unless we really have to, because even a slow crawl will eventually crush us into the Wall of Unpleasant Death. That wall represents starvation, drought, war over land and resources, avoidable diseases and everything else that a population exceeding its available resources will suffer. It really is bad, horrible stuff. And yet our collective foot is firmly on the accelerator.
(There is, of course, a second spikey death wall at the other end of the road, representing total extinction, so we don't want to just go into full reverse. Ideally, we don't want to move, but the road rolls up and down, so it's harder to stop in some places than others. This metaphor is now officially getting stretched too much.)
We couldn't even reach that first kilometer stone, where humans occupy all of the available land surface on Earth (ignoring for a moment the doubling of Earth's gravity due the doubling of its total mass at around the same time), because even dividing the actual land surface by 100 (by making all homes 100 floors high, a challenging but not insane option, even under double gravity) wouldn't help. The actual land area needed for one human is far greater than 1 m2, somewhere closer to 2,500 m2. We're already using about 11.61% of available land just to grow food for 7 billion humans, and in that future scenario we'd have to feed the same number of humans with only 4.2% (7/150ths of 90%) of available land, and that's assuming we're now using 100% of the land, excluding the 10% set aside for our standing-rooming-only sleeping-pod skyscrapers. At that stage, there are no more wild spaces, apart from non-arable mountains, oceans and other really human-hostile terrains. Even if you're only interested in humans and no other species, that's still not a win, as we've now lost all industrial and recreational space, so we're now just 150 billion farmers, sleeping in broom closets in massive skyscrapers, with nowhere to go but work or bed. There are also no major forests left to give us the oxygen we need to breathe, so we'd have to assume some sort of clever technological alternative to that.
And a couple generations later, we'd all be starving to death anyway, as there just isn't any land left but the population's approaching 300 billion. A couple generations after that, we'd have to make room for 600 billion. So never mind the 8,500 years to the all-human universe, we're going to struggle to cope with just the next few centuries, and the less we change our reproductive habits, the more we'll struggle.
So what to do about it?
Opinions are mixed. A lot of people seem to be quite happy with complete denial. Their own lives are currently tolerable, they lack the imagination to consider things being more shit in only 50 years' time, when they're too old to do much about it, so they don't give a shit about future generations. Let's assume these people are complete cockheads.
A more subtle form of denial is the "technology will fix it" crowd. They see a long history of things that have made massive improvements in humans' ability to survive and thrive another day - fire, the wheel, medicine, skyscrapers, water reclamation, the Green Revolution - and assume A.) that the admittedly huge advantages that these things give will always be repeatable with other, new technologies, 2.) that these assumed advances will always scale to match whatever our population happens to be at the time, and III.) that any waiting periods for that new technology will be tolerably short (within a generation, say). This is not just optimistic, it's impossible. If you don't believe me and you haven't watched Prof. Bartlett's lecture yet, watch it right now, and pay particular attention to the bit about bacteria growing in a bottle.
To be clear, I'm all in favour of colonising space, as far beyond Earth as we can reach. But that'll be slow and unpredictable, and ultimately, it'd just add more bottles for us to fill, unless we also intelligently check our population growth while we colonise. And once again, if population growth continues at the current rate, we've got 6,500 years to conquer and consume the whole Milky Way, the furthest bits of which are 80,000-100,000 lightyears away. In other words, we'd fail. We literally couldn't move through space fast enough to eat a fraction of everything we'd need to survive, even if it was all made of delicious toast, instead of fiery-fusiony stars and the occasional chunk of rock. But of course, this assumes we'd already learned to convert the whole of our own Sun into food 2,500 years earlier, so that's ok.
(There's also a totally delusional but common variation of the "technology will fix it" idea, which is held by the "magic/fairies/deities/space aliens will fix it" crowd. We could spend hours merrily debunking these, but in fact I suspect a lot of people who make these claims really fit better in the pure denialist crowd, and are simply bringing up their pet superstitions as an easy defence against hard and uncomfortable thoughts. The same may be true of some technologists, but at least they have real historical examples behind them, however misguided those examples are.)
The only really viable option is population control. For some reason, though, this freaks people out. I don't think there's any rational reason people have for objecting to it, I believe it's just a very deep-rooted instinctive urge to breed like mad, taking control of people's brains (and I mean this quite literally, if slightly flippantly) and making them generate whatever reasonable-sounding excuses they need to keep pumping out kids. From an evolutionary point of view, nothing could make more sense. Evolution doesn't care if half of us or even 99% of us starve to death this generation, so long as we also produce the next generation.
So someone always brings up China's one-child policy, and they always present it as an absolute disaster, representing the entire concept of population growth control, rather than a single example of a single type of intervention. I'd call it a failure, in that it only lowered the population growth rate without fully stopping it. But the fact that it had other unintended negative consequences? That's not a valid criticism; every real intervention has side effects, and you can't deal with those until you've discovered them, but that doesn't automatically mean the intervention is permanently unworkable. I also really don't buy the argument that people have a right to breed as much as they like; the creation of a whole new person is a hugely significant thing, both for that person and for the whole species. It is not a hobby, nor is it something vital to the parents' survival, and there's no reason (outside of religious dogma and animal instinct) to enshrine it as a fundamental human right.
But there are other options, beyond the Chinese model. I'm always in favour of education as the first response to any social problem, and there's some evidence that general education correlates with lowered growth rates. Specific birth-control education should, all else being equal, produce an even sharper lowering. Teach everyone what I'm telling you here, and I think most people would get it, and enough would take it seriously. Similarly, feminism's had a lowering effect on population growth rates in the West, especially the parts about letting women decide for themselves if and when they want to get knocked up; turns out, fewer wanted that than men have historically assumed. (This assumes that access to birth control is widespread and freely available, which of course it should be.)
But if that's not enough? Perhaps I'm over-optimistic. Instead, do we penalise breeders? Reward non-breeders? Both? Only permit breeding with a licence, with only a limited number of licences to be had? Somehow make breeding beyond your allotted limit medically impossible? Encouraging more varieties of non-reproductive sex more often could be an interesting one. It's all quite difficult and easily gets bogged down in real and imagined controversies. But it must be addressed, or it's the spikey, horrible Wall of Unpleasant Death that'll address us instead.
For a start, though, I think leading by example is good. Share this information, teach people the (really, really simple) maths behind it, and for fuck's sakes, stop breeding. I certainly won't. If you don't have kids yet, please don't add to the problem. It's no good when people say, "Oh, but we're only having one or two, just enough to replace each parent," when the majority of the world's breeders don't do the same yet. Then your one or two kids are just extras on top of the existing growth. That's like being careful to only light one match at a time while standing in a house that's burning down. If you really want to make a mathematically worthwhile difference, don't add any new babies at all AND ALSO do your bit to discourage others from breeding, so that your net effect is subtractive.
And if you've already had a kid or two, then you should now work extra hard to compensate for the additive effect you've already dumped on us. And also be extra careful in future, as accidents can happen (as many of you will already have discovered).
And for those of you who've already chosen to have three kids or more... For fuck's sakes!
The bottom line is that our reproductive instincts and the breeding culture we've built around those for the last few millennia are no longer appropriate. Our population is not in the thousands, limited to one environment, where we could easily be wiped out. It would take nearly as much effort to kill all the humans today as it did to end the dinosaurs 65 million years ago (and even then some of the small feathery ones survived). We can take our foot off the accelerator now. Realising this and adapting to it is going to be a massive new challenge for humanity, possibly the single biggest mental obstacle we've faced as a species. I don't promise Utopia if we do get a grip on our groins in time, but I do promise hell on Earth if we don't.