Introduction

If humanity remains on Earth alone and we continue to sustain positive rates of population growth then the human population would become so vast and densely packed that it would outweigh the Earth in just a few thousand years at modest rates of population growth. Over time, the material of the Earth would effectively have to be converted into human flesh. The sphere upon we which live would be reduced as the fleshy outer layer of humans increased. This would have to be the ultimate Malthusian Catastrophe scenario.

This is, of course, a plainly silly scenario. Hopefully we will instead learn to "live of the land" throughout the solar system and beyond. Even if we didn't, then Malthusian population collapse is a far more likely and grim scenario than an ever increasing human population that consumes the Earth. Of course, a more hopeful scenario than a Malthusian Catastrophe (if we remain on Earth) is that we actually learn to live sustainably. Time will tell just how "hopeful" this last scenario is, given the constant tendency of national governments to promote population growth rather than restrain it. Personally, I find this last option  - although more hopeful than a Malthusian Catastrophe - somewhat sad as all the future possibilities of our species are restricted to just the Earth.

Nonetheless, I hope it proves salutary to calculate the speed of a hypothetical global ecophagy by a growing human population. To do so I've assumed variable annual rates of growth between 1% and 2% (inclusive) as representative of recent human population growth.

Note that the term ecophagy was introduced by Robert Freitas Jr in relation to what is commonly referred to as the "grey goo" problem (Freitas, 2001).

Malthus

Thomas Robert Malthus was one of the first and most influential writers on the problem of overpopulation, and he included a scenario on the global arena of the Earth (Malthus, 1798):

"But to make the argument more general and less interrupted by the partial views of emigration, let us take the whole earth, instead of one spot, and suppose that the restraints to population were universally removed. If the subsistence for man that the earth affords was to be increased every twenty-five years by a quantity equal to what the whole world at present produces, this would allow the power of production in the earth to be absolutely unlimited, and its ratio of increase much grater than we can conceive that any possible exertions of mankind could make it." Taking the population of the world at any number, a thousand millions for instance, the human species would increase in the ratio of - 1,  2,  4,  8,  16, 32, 64, 128, 256, 512, etc. and subsistence as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 etc. In two centuries and a quarter, the population would be to the means of subsistence as 512 to 10: in three centuries as 4096 to 13, and in two thousand years the difference would be almost incalculable, though the produce in that time would have increased to an immense extent."

The Exponentialist view is that Malthus presented a flawed argument based on the premises that population grows geometrically (exponentially) and food grows arithmetically (linearly). To simplify his argument, Malthus assumed constant rates of growth. Instead, it the Exponentialist position is that food grows  exponentially as does population, and that both do so via variable rates of growth. See Reverend Thomas Malthus - An Exponentialist View for more.

For an analysis of more recent warnings on global human population catastrophe by well known authors see my articles Paul R. Erhlich and the Prophets of Doom - An Exponentialist View and Albert Bartlett - An Exponentialist View. These articles also include an analysis and rebuttal of counter arguments by Cornucopians Julian Simon and Ronald Bailey to the essentially Malthusian arguments of Ehrlich and Bartlett respectively. In essence, Malthusian arguments are seen to naively rely on a (positive) constant or fixed rate of growth to illustrate their point about the unsustainability of human population growth. This is a weakness in the argument exploited by Cornucopians who then fail to realise (also naively) that variable rates of growth are just as unstainable and just as powerful as constant rates of growth.

Population Doubling

Using the Rule of 70 the time it takes a population to double is 70 years if the annual growth rate is a constant 1%, and 35 years if the annual growth is a constant 2%. The global human population doubled from 3 billion in 1960 to 6 billion in 1999. This entailed variable annual growth rates which were mostly between 1% and 2%. Note therefore that variable rates lead to variable double periods, and that these double periods are comparable to those for constant growth rates.

For more on the population doubling read my article on The Mechanism of Population Doubling.

Eating the Earth

So how quickly would humanity outweigh the Earth? Never mind whether we should, or whether we can. The important thing is to understand the speed at which a human population could outweigh the Earth. In 1974 science-fiction author Isaac Asimov asked the same question. His assumptions were (Asimov, 1974 [2], p.58):

• Average weight of a human being = 60 kg
• Annual Growth Rate = 2%
• Population doubling period = 35 years
• Weight of the Earth (estimate) = 6 x 10 ²⁴ kg = 6,000,000,000,000,000,000,000,000 kg

His answer was not quite1,600 years (Asimov, 1974 [2], p.58). Asimov also calculated that, if the growth rate remained constant at 2% per annum, then the human population would outweigh the entire solar system (including the sun) by 4,220 A.D. and by 6,700 A.D. our population would outweigh the weight of the known universe (Asimov, 1974 [2], p.58). For another Isaac Asimov example, see Isaac Asimov - An Exponentialist View for more.

Here's my own calculation, with my own assumptions including heavier people and variable growth rates (using the Rule of 70):

Assumptions / Notes:

• Average weight of a human being = 80 kg
• Total land area of the Earth = 148,940,000,000 m²
• Total surface area of the Earth= 510,072,000,000 m²
• Weight of the Earth (estimate) = 5.98 x 10 ²⁴ kg = 5,980,000,000,000,000,000,000,000 kg

Allowing for a bonus doubling, humanity would outweigh the Earth in somewhere between 1,575 years to 3,150 years. This is true of any constant rate of growth between 1 and 2% per annum (inclusive). It is also true if the growth rate varies year to year within these upper and lower growth rates (inclusive). The higher our global human population annual growth rate then the less time we have before catastrophic population collapse.

By comparison, you might also like to read about another nightmare scenario in which "grey goo" (comprised of theoretical self-replicating molecular nanotechnology assemblers ) consumes the Earth within just two days (see Grey Goo - An Exponentialist View).

A Surface Layer of Humanity

Of course there are other considerations that I've ignored for simplicity's sake above. Something would have to give - in terms of population collapse - long before the 1,575 years to 3,150 years timeframe described above.

Imagine human population density rising so that in roughly only 200 to 400 years (depending upon the growth rate) there is exactly one person per square metre of land. This is much like the scenario described in John Brunner's 1968 science-fiction novel Stand On Zanzibar. Set in 2010 with a remarkably accurate estimated world population of 7 billion, through the title of the novel Brunner asks his readers to imagine them all packed shoulder to shoulder onto the island of Zanzibar (area 1554 km²), though in the novel this scenario is not actually the case.

As indicated in the table above (assuming variable growth rates between 1% and 2%) , human population density would rise to such an extent that there would be one person per square metre of the total Earth's surface (land and water areas combine) in roughly 250 to 550 years - that's 510,072,000,000 people - over half a trillion people. We would have to live in even taller and more extensive high-rise buildings than we do now, dig deep caverns into the Earth, or live under the oceans in domed cities, or do all of these things.

Eventually, between 1,575 years to 3,150 years from now, it would no longer be appropriate to average the human population over a two-dimensional surface. With over two hundred billion people  per square metre of the total Earth's surface area (105,553,116,266,496,000,000,000 people / 510,072,000,000 m²  = 206,937,679,909), we would be living in a third dimension of humanity of kilometres thick. This is why we can confidently predict that sustained population growth between 1% and 2% (inclusive) will lead to a Malthusian Catastrophe long before the 1,575 years to 3,150 years timeframe described above.

Zero Sum Game

Darwin realised that the "struggle for existence" on Earth is a zero sum game, with expansion one population being at the expense of another population with his concept of what I call Darwin's wedge (Darwin, 1859, pp 117-119):

"In looking at Nature, it is most necessary to keep the foregoing considerations in mind - never to forget that every single organic being around us may be said to be striving to the utmost to increase in numbers; that each lives by a struggle at some period of its life; that heavy destruction inevitably falls either on the young or old, during each generation or at recurrent intervals. Lighten any check, mitigate the destruction ever so little, and the number of the species will almost instantaneously increase to any amount. The face of Nature may be compared to a yielding surface, with ten thousand sharp wedges packed close together and driven inwards by incessant blows, sometimes one wedge being struck, and then another with greater force."

Asimov gives a more recent example of a similar argument. Taking into account the fact that the fixed amount of solar radiation hitting the earth supports an estimated 200 million tons of biomass on Earth, he argued that (Asimov, 1974 [1], p.208):

"Every time the human population increases in mass by one ton, the mass of non-human animal life must decrease by one ton to make room."

With a population doubling rate of 47 years Asimov calculated humanity would replace the entire biomass in just 624 years. In other words, the total Earth biomass would be composed entirely of humans in 624 years time.

Asimov's Bathroom Metaphor

Cornucopians (for example Julian Simon and Ronald Bailey),  self-proclaimed techno-optimists (James Trefil) and others continue to refute various prophets of population doom by listing the numerous failed predictions they have made (all of which are based on constant rates of growth and constant population doubling times). Science and technology, it is claimed, can always be relied upon to save the day (Trefil, 1997, p.121):

"Techno-optimists (of which I am one) argue that advances in technology will continually increase the resources available so that any ecosystem can support its human population even as it grows."

Trefil therefore puts no upper limit on Earth's population. For a man of science Trefil's techno-optimism is hopelessly misplaced if humanity remains restricted to the ecosystem we know as Earth. Yet Trefil's statement above suggests that such a possibility is real, and that the Earth alone can support a population of literally any size.

If the population on Earth continues to grow (at any mix of positive rates) then inevitably the seething mass of humanity will outweigh the Earth (based on what the Earth weighs today). Perhaps Trefil's techno-optimism relies on future technologies such as K. Eric Drexler's molecular nanotechnology, or MNT (refer K. Eric Drexler - An Exponentialist View for more). After all, here we are considering the finite supply of molecules on Earth. Yet even MNT cannot create more molecules when the finite supply on Earth is used up. Trefil should heed Drexler's warning of the exponential power of population to overrun any resource base (Drexler, 1990):

"Concern about population and resources will remain important because the exponential growth of  replicators (such as people) can eventually overrun any finite resource base."

Or perhaps Trefil envisages that enough material will be mined throughout the solar system and brought back to Earth in order to accommodate and feed the 105,553,116,266,496,000,000,000 people that will exist after 44 population doublings from a 6 billion start? If so, then the fleshy kilometres-deep surface layer of humanity will inevitably affect the gravitational balance between the Earth and the Sun as the Earth (with our huge population on it) would now be double its mass. Or perhaps Trefil hasn't actually thought his unqualified techno-optimism through? Still, at least in this scenario we will not have conducted human global ecophagy. Instead we will have brought back to Earth an equivalent Earth-sized mass of the rest of the solar system and eaten it.

What would it be like to live on such a future Earth, with the equivalent the Earth's mass in humanity added on the surface? As Asimov put it in his bathroom metaphor (Freedman, 2005):

"...democracy cannot survive overpopulation. Human dignity cannot survive it. Convenience and decency cannot survive it."

Trefil and other techno-optimists would do well to heed Asimov's warning about the limitations of science to maintain a food supply for a growing population (Asimov, 1974 [1], p.207):

"Science, in other words, cannot keep up with populations no matter what it does."

Refer Isaac Asimov - An Exponentialist View for more on Asimov's views on overpopulation.

Space Is Virtually Limitless, But Earth Is Not

So far we've assumed that the growing human population is restricted to Earth. This may not be the case - indeed, I hope it is not the case and that small founder human populations flourish in space and "green the galaxy" as proposed by Marshall T. Savage (see Marshall T. Savage - An Exponentialist View for more). Space represents the best long-term hope for a prolonged future for our species. 

However, space is not the answer to Earth's overpopulation. The main reason will be that the rate of migration from Earth into space would be practically too small to make much difference to Earth's growing population. Space advocate Carl Sagan appreciated this point, arguing that with a global population growing by 240,000 per day our practical capacity to ship people in space falls very short (p19, Sagan, 1998). Also, as noted by K. Eric Drexler, a space faring population will itself still periodically face limits to growth even in the limitless bounds of space , with each planet colonised, and each solar system colonised. Still, as Drexler notes, "...opening space will burst our limits to growth." Refer K. Eric Drexler - An Exponentialist View for more.

Whether or not we do colonise space, the global human population that remains on Earth will still need to learn to live sustainably and within limits. In other words, human population growth on Earth will stop because it must. For now at least, apart from a handful of astronauts, we are stuck on the "crowded spaceship" (Asimov, 1974[2]) called Earth.

Drowning Children Beneath The Stars

Of course, as a species, we could attempt to live sustainably here on Earth at the expense of a future amongst the stars. Personally I find the idea of failing to colonise space small-minded and sad - equivalent to drowning all those future unborn children beneath a star-lit night:

DROWNING CHILDREN BENEATH THE STARS

Lives lost in love and honest human needs;
And others, blind with ugly human greeds.

National visions tide to the ballot box,
The people of Earth fragmented like rocks.
Green-blue eggshell cracked from within.
So many children will pay for this sin.

 Too many knowing eyes, knowing too late,
Looking back with sadness, and some with hate.

Eyes lifting up, looking out, sinking down;
An ocean of life all ready to drown.

David A. Coutts

It is argued that the huge government expense of space colonisation should be used to end poverty and promote technologies for sustainable living here on Earth. However, this is likely to be a false dichotomy. Instead, the growing List of Private Space Companies indicates that the commercialisation of space will allow us to "mine the sky" (Lewis, 1997) and use the vast untapped resources of our own solar system to help sustain life on Earth and in space. So it need not be a difficult choice between sustainability or space colonisation options. Instead it could be a much easier option of sustainability through space colonisation or "saving our world by seeking others" (Cockell, 2007).

However, unless we favour doubling the mass of the Earth (or more) in Trefil's limitless growth techno-optimistic future, I suspect that by far the greatest population growth will not be sustained on Earth but in space as suggested by Drexler and Savage.

Conclusion

Approximate as the above calculations are, if we do attempt to sustain these sorts of positive rates of population growth on Earth (between 1% and 2% per annum [inclusive]) then the Earth's population will face catastrophic population collapse not in millennia but in centuries. We cannot sustain such growth rates on the Earth for even one thousand years - the idea is not just silly, it is a Malthusian nightmare. Just look at the numbers of people after each doubling. Even at a 1% growth rate, that's around 50 trillion people living on Earth within a thousand years.

Even if our global human population growth rate slowed to just 0.1% per annum, that's a doubling time of roughly 700 years and our population would outweigh the Earth in just 31,500 years. Ours would become a mere cameo role in the grand drama of evolution, measured in mere tens of thousands of years, with the drama of evolution stretching back billions of years and continuing after our demise for many more billions of years to come.

As a species we have to learn when it is appropriate to live sustainably within limits to growth, whilst at the same time not denying ourselves any opportunities to expand beyond the Earth and carry life to the stars. We need to learn to balance sustainability and growth.

However, the one key practical message I would like to impart in this article is that variable rates of growth are just as unstainable and just as powerful as constant rates of growth. The dire warnings of Asimov, Bartlett, Malthus, Ehrlich and others are not invalidated just because populations grow and double at variable rates. 

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References

Asimov, Isaac. The Stars In Their Courses. Panther. 1974 [1]

Asimov, Isaac. Earth Our Crowded Spaceship. Abelard-Schuman.1974 [2]. written for young adults

Freedman, Carl (editor), Conversations with Isaac Asimov. University Press of Mississippi. 2005.

Cockell, Charles S.. Space on Earth - Saving Our World By Seeking Others. Macmillan. 2007.

Darwin, Charles. Origin of Species. 1859.

Drexler, K. Eric. Engines Of Creation - The Coming Era of Nanotechnology. Oxford University Press. 1990.

Freitas Jr, Robert A., Some Limits to Global Ecophagy by Biovorous Nanoreplicators, with Public Policy Recommendations. The Foresight Institute (website 14th September, 2009). 2001

Lewis, John S.. Mining the Sky: Untold Riches from the Asteroids, Comets, and Planets. Perseus Publishing. 1997.

Malthus, Thomas Robert, An Essay on the Principle of Population. J. Johnson. Library of Economics and Liberty. 1798. (1st edition)

Sagan, Carl. Billions and Billions. Headline. 1998.

Trefil, James S.. One hundred one things you don't know about science and no one else does either. (Google Books link, website accessed 14th September, 2009). Mariner Books. 1997.

Send email to exponentialist@optusnet.com.au with questions or comments about this web site.
Copyright 2009 David A. Coutts
Last modified: 08 October, 2009