Asimov - An Exponentialist View
Bartlett - An Exponentialist View
Darwin - An Exponentialist View
Dawkins - An Exponentialist View
Drexler - An Exponentialist View
Ehrlich - An Exponentialist View
Malthus - An Exponentialist View
Sagan - The Secrets of the Universe
Savage - An Exponentialist View
Turchin - An Exponentialist View
Wallace - An Exponentialist View
Witting - An Exponentialist View

Population Doubling Mechanism 

New Malthusian Scale 

External Links:
Living Universe Foundation homepage

The Millennial Project (Colonising The Galaxy in Eight Easy Steps  (Amazon link) - Marshall T. Savage (1992, 1994)

Malthusian Catastrophe article on Wikipedia

Cyanobacteria article on Wikipedia

Photosynthesis article on Wikipedia


 Marshall T. Savage - An Exponentialist View

"The germs of existence contained in this spot of earth, with ample food, and ample room to expand in, would fill millions of worlds in the course of a few thousand years."
(Malthus, 1798).


Marshall T. Savage, founder of the First Millennial Foundation (now the Living Universe Foundation), is also the author of "The Millennial Project: Colonizing The Galaxy In Eight Easy Steps". As you might guess, Savage is firmly in the pro-space camp (as am I). Savage is the antithesis of the prophets of doom and, though the title of his book might fuel the stereotypical view of a naive technophile, Savage provides technical data and references throughout (including extensive endnotes). 

However, it is not the intention of this article is not to examine the feasibility or desirability of colonising space. Instead, this article will examine Savage's explanation of the exponential growth of populations. Also, Savage's references to Malthus and Kardashev will be discussed. 


Savage introduces the problem of the human overpopulation of Earth during the first of his "eight easy steps" in colonising the galaxy. This step is called Aquarius, and involves the building of sea-cities in international waters in a bid to colonise the oceans. 

With a nod to Malthus (see Malthus - An Exponentialist View for more) in a section entitled "Malthusian Blues", Savage explains the need to avoid a man-made catastrophe on Earth if we are to fulfil our destiny in space (Savage, 1992, 1994):

"Our future lies in space, but the Earth is the womb of life, and it will be a long time before we can cut our umbilical cord. The new worlds we wish to create can survive only if the Mother of Life (Gaia) is here to nourish them. If we are to fulfil our Cosmic destiny as the harbingers of Life, we must insure the survival of the planet....Our rapacious demands are overtaxing the ability of Gaia to regenerate herself. The result is a dying planet.

We must find a way to avert this catastrophe."

In a section entitled "Food Glorious Food" Savage again paints a grim pessimistic picture (Savage, 1992, 1994):

"The world is approaching the Malthusian wall. We are running put of arable land, cheap energy, and time. In the immediate future we face crucial shortages of everything but people. Our resource base is shrinking. The planetary ecosystem is already collapsing under the weight of five billion people. How then are we ever going to feed twice that number?"

At least one explicit answer is provided by plant physiologist Lloyd Evans in his 1998 book "Feeding the Ten Billion", 200 years after Malthus wrote his famous essay on population, though Evans admits it won't be easy (Evans, 1998):

"Feeding the ten billion can be done, but to do so sustainably in the face of climate change, equitably in the face of social and regional inequalities, and in [a] time when few seem concerned, remains one of humanity's greatest challenges."

In a clear reference to Paul Ehrlich's "The Population Bomb" (see Ehrlich - An Exponentialist View for more), Savage also offers hope that we can survive mass famine (Savage, 1992, 1994):

"The global ocean can provide enough energy and nutrients for us to survive detonation of the population bomb."

Savage believes that these sea colonies will solve our world food crisis and double our energy supply all without adding to our environmental problems. The argument is that the oceans can be more efficiently farmed (with a focus on blue-green algae), and Ocean Thermal Energy Converters will provide the required energy.

As we have seen, Malthus' name has come to be associated with impending doom and disaster, commonly known as the Malthusian Catastrophe. This is the most obvious interpretation of what Malthus had to say, yet Malthus made it clear that he believed we have always lived beyond our means and that we always would (Malthus, 1798):

"The perpetual tendency of the race of man to increase beyond the means of subsistence is one of the general laws of animated nature, which we can have no reason to expect to change." 

 Also, Malthus quite clearly understood that the key was the connection between food supply and population growth and that this would oscillate periodically (Malthus, 2nd edition, 1817):

"...the tendency to an oscillation or alternation in the increase of population and food in the natural course of their progress."

Hence the Malthusian time bomb is not one great catastrophe, but many smaller catastrophes.

The Malthusian doctrine proposed to combat this state of affairs involved "moral restraint" (abstinence from sex before marriage, late marriage, and sexual restraint during marriage). Malthus didn't expect his doctrine to succeed. Malthus, who was opposed to contraception, abortion and homosexuality would probably be disappointed with modern-day society's more effective response to the problem of overpopulation. However, there is evidence to support the view that the changing role and status of women in society has resulted in families choosing to have fewer children and in having children later in life. Both of these aspects of moral restraint will help reduce population growth rates.

Exponential Growth

Savage does not directly refer to Malthus nor Malthus' book ("An Essay On The Principle Of Population", 1798), nor to Malthus' contribution of a universal growth model for populations. Nonetheless, Savage does explain the significance of exponential growth to life in the eighth of his easy steps to the colonisation of the galaxy - Galactia. In a section entitled "Seed People", uses a card game analogy to compare the forces of entropy (Chaos) and Life (Savage, 1992, 1994):

"Life holds the ultimate trump card in the struggle against Chaos. In the cosmic game, pitting the emerald forces of light against the sable minions of darkness, the deck is stacked in favor of Chaos: the expanses of frozen sterile space are effectively infinite; the hostility and violence of alien worlds and stars are virtually unlimited; even on Earth - the lone bastion of Life - everything ultimately dies. Against these overwhelming forces, Cosmos can play but a single card - exponential growth. Fortunately, in this universe, geometric growth is the trump suit.

The power of exponential growth is of such transcendent magnitude that it will allow us to annihilate annihilation itself. Life is a force of unlimited potency. The capacity of Life to animate the inanimate can overwhelm even the forces of entropy. A single mushroom cap can release a cloud of spores numbering in the hundreds of billions. If all the spores in the world grew at once, they would bury the surface of the earth meters deep in mushrooms. A pair of butterflies could, in just a few hundred generations, produce a mass of descendants outweighing the universe.

Exponential explosions are virtually the sole province of Life. The only other exponential reactions are fleeting events like stellar super-novae. Life is not going to be a transitory event in this universe. We are here to stay...."

This is the stuff of poetry, powerful and emotive. The financial sector might quibble that exponential growth applies to lifeless money. Artificial Life enthusiasts might point out that their virtual life-forms also grow exponentially. Dawkins might argue that memes replicate (see Dawkins - An Exponentialist View for more), and Drexler has high hopes for lifeless nanotechnology (see Drexler - An Exponentialist View for more). However, Savage has matched the following passage from Malthus in his association of exponential growth and Life (Malthus, 1798):

"...all animals, according to the known laws by which they are produced, must have a capacity of increasing in geometrical progression."

Savage mentions the various "dehumanising" reprogenetic options available to humanity to boost our annual rate of growth - genetic engineering, cloning, in vitro gestation etc. Then he takes an extreme historical rate of growth (8% on the US frontier) and states that only 150 colonists growing at that rate could attain Earth's population (5 billion back in 1992) in "just over" 200 years. This is a good concrete example to examine in some detail using my New Malthusian Scale:

1 2 4   8 16 32 64 128 150 256 512 1024
kilopops 1 2 4   8 16 32 64 128   256 512 1024
Megapops 1 2 4   8 16 32 64 128 150 256 512 1024
Gigapops 1 2 4 4.66 8 16 32 64 128   256 512 1024

Table A. 150 colonists growing at a constant 8% for just over 200 years

Note:  1kilopop = 1024 pops, Megapop = 1024 kilopops, 1 Gigapop = 1024 Megapop.

Savage is extrapolating a constant rate of doubling for over 200 years for 150 individuals to get a population of 5 billion (roughly 4.66 Gigapops). At 8% a population doubles roughly every 9 years. To prove this, use your calculator. Multiply 1.01 by 1 (enter 1, press X, enter 1.08, press =) , and then keep pressing "=" until you get 2. It will take you 9 presses to get to 1.999. This is the effect of a fixed 8% compound interest rate. 

Each row on Table A shows 10 population doublings, so 1 row represents 90 years of population doubling. Therefore, after 180 years the 150 individuals would produce a population of 150 Megapops. Only 2 more doublings (another 18 years) takes that figure to 600 Megapops after 198 years. So, one more doubling would put us "just over" 200 years at 207 years. 1200 Megapops equals only 1,258,291,200 people (or 1.17 Gigapops). Savage appears to have it wrong. Even if he was using an approximate doubling time for 8% (which, using the Rule Of 70, would be 8.75 years) he would still be out. However, one shouldn't take Savage's figures as a blueprint. Rather, his figures are intended to show the realism of his dream - they serve to inspire. 

In fact, you would need a starting population of 1024 people (1 kilopop) growing at 8% to reach a population of 4 Gigapops after 198 years (22 doublings), or 8 Gigapops after 207 years (23 doublings). It's also worth noting that Savage is only roughly two population doublings out (double 1.17 Gigapops twice and you have 4.68 Gigapops). 

It is also worth pointing out at this point that Life does not naturally grow at a constant rate of growth, but more typically grows at variable growth rates. For an example using human populations, see Total Midyear World Population for 1950 to 2050 AD from the U.S. Census bureau. Also, as pointed out by Malthus back in 1830 ("A Summary View"), population doubling times also vary:

"The immediate cause of the increase of population is the excess of the births above deaths; and the rate of increase, or the period of doubling, depends upon the proportion which the excess of the births above the deaths bears to the population."

Despite Savage's error, his point is still made. Very few colonists would be required to produce a population of 5 billion if they were growing at 8% per annum. Of course, it is unlikely that such a rate of growth could be sustained without resorting to some of the "dehumanising" measures mentioned by Savage earlier. 

Savage isn't the only exponentialist to get his mathematics wrong, but most people aren't bothered by this. Is this because, 9 times out 10, being roughly right is good enough to prove the point anyway? Or perhaps most people simply don't like dealing with numbers. 

Whatever the case, I firmly believe that an accumulation of such petty oversights by the vast majority of people has resulted in a public failure to appreciate the "trump card" of exponential growth for what it is. It affects our understanding of the past, the present and the future. It affects our understanding of demography (see Ehrlich - An Exponentialist View for more), and evolution (Darwin - An Exponentialist View for more) and nanotechnology 

Blue-Green Algae

Malthus once pointed out what it was that made humans very powerful and numerous (Malthus, 1798):

"The main peculiarity which distinguishes man from other animals, is the means of his support, is the power which he possesses of very greatly increasing these means."

Given Malthus' examples of exponential growth using sheep and grain, I interpret this statement by Malthus as saying that it is our ability to harness the exponential growth of other replicator populations which make humans powerful. In short, farming

Savage, as noted above, puts great faith in the ability of his future sea colonies to farm blue-green algae, in particular Spirulina platensis (Savage, 1992, 1994):

"The marine colonies will be able to produce food so abundantly because they cultivate the simplest, hardiest, and most prolific plant in the known universe - blue-green algae."

They are certainly simple and tough (they've been around for 3.5 billion years, and they live in every niche imaginable), but how prolific are these bacterial life-forms? Well, they are estimated to comprise 70% of Earth's biomass.

According to Savage, algae are important for other reasons, too. Alga's as a whole are responsible for roughly 90% of all photosynthesis on Earth. They produce most of the oxygen that we breath. They are ideal for cultivation in our own oceans, and in future space habitats. A human needs about 540 grams of food a day. Spirulina is ideally suited to human digestion. As Savage points out (Savage, 1992, 1994):

"Under controlled conditions, algae can double their population four times a day....The initial culture needs only 40 grams of algae to produce 600 grams of food, plus having 40 grams left over to start the cycle again....The system is so compact and efficient that all the oxygen and food needs for the entire colony can be produced from a tiny area."

1 2 4 8 16 32 40 64 128 256 512 640 1024
kilopops 1 2 4 8 16 32   64 128 256 512   1024
Megapops 1 2 4 8 16 32   64 128 256 512   1024
Gigapops 1 2 4 8 16 32 40 64 128 256 512 640 1024

Table B. Algae doubling 4 times a day (every 6 hours).

Note:  1kilopop = 1024 pops, Megapop = 1024 kilopops, 1 Gigapop = 1024 Megapop.

In Table B I'm measuring the algae by mass, rather than numbers of individual algae. Following Savage's example, 40 grams of algae will double 4 times in day and produce 640 grams of algae (starting at 40, the doubling series is 80, 160, 320, 640). Hence, the population doubling time is 6 hours.

Given that each row represents 10 population doublings, then each row represents 60 hours. Thus, 40 grams of algae could be cultivated to 40 Gigapops (42,949,672,960 grams) in 60 hours, and 640 Gigapops (6,87,194,767,360 grams) a day later. That's enough to feed 1,272,582,902 people!

Although there are issues with farming blue-green algae, such as the production of harmful toxins, controlled environments can prevent this from happening and screening can detect the presence of toxins. Also, Savage explores how the algae is then processed for human consumption. First, the algae is dried. Then all colour, flavour and odour is removed, resulting in a white powder which is still 85% protein. This can then be used as a supplement to other foods, such as bread.

Some have noted that beauty of our planet as seen from space is also due to "Nature's super food", blue-green algae (Gribbs, 1997):

"As we look out into space and wonder what the next millennium holds for us, we should pause for a moment to consider the words of the first astronauts as they circled the Earth thirty years ago. The Earth, they said, was a wondrous sight when they viewed it from space. It was a beautiful, great orb glittering in the darkness with an iridescent blue-green glow. What they did not realise at the time was that it was a simple micro-organism blue-green algae, which has been patiently maintaining the earth for 3 1/2 billion years, that gives the planet this wondrous glow."

Perhaps the future belongs to those most able to exploit the exponential growth of other life-forms for their own purposes.


In this section of his book Savage notes that humanity is growing at roughly 2% per year (in fact, Savage was using a 1989 figure of 1.74% from Nathan Keyfitz in Scientific American).  Even though the current trend is for a reduction in our growth rate, Savage predicts that two trends will cause a rise in our growth rate - death rates will fall, and life-spans will be extended. Savage also expects the attractiveness of life in space to increase our birth rate. Hence, Savage feels justified in assuming a "modest" rate of growth of 2% for our space colonists. Savage envisions that humanity will colonise the solar system. Given all these assumptions, what sort of demographic future does Savage predict for humanity within the confines of our own solar system? Well, at 2% our population will double every 35 years (Savage, 1992, 1994):

"Over the course of a thousand years, a growth rate of just 2% leads to an increase of one billion fold. In the year 3000 A.D., the population of the solar system could easily exceed five billion billion."

Savage also provides some interim figures (Savage, 1992, 1994):

"By the year 2250, the total population of the solar system is likely to be approaching the trillion mark."

"Half way through the next Millennium, human numbers will have grown to 330 trillion - 66,000 times that of the Earth today."

Savage anticipates that 95% of these people will live in the Asteroid Belt, which he calculates could sustain 7,500 trillion people excluding all the resources of the other planets.

1 2 4 5 8 16 32 64 128 256 512 1024
kilopops 1 2 4   8 16 32 64 128 256 512 1024
Megapops 1 2 4   8 16 32 64 128 256 512 1024
Gigapops 1 2 4 5 8 16 32 64 128 256 512 1024

Table C. A starting population of 5 billion people (=1 Pop) growing at 2% per annum (and a 35 year population doubling time) growing for 1,050 years.

Note:  1kilopop = 1024 pops, Megapop = 1024 kilopops, 1 Gigapop = 1024 Megapop.

At 2% the approximate doubling time (also noted by Savage) is 35 years. Each row on Table C shows ten population doublings, hence each row represents 350 years of population doubling. This means that a population of 5 Gigapops (5,368,709,120 billion - over 5 billion billion) would be reached in 1050 years. This is close enough to prove Savage's point (and in fact the end-notes indicate that Savage is aware that he was approximating this example). 

Perhaps the key false assumption that Savage makes appears to be that the starting population of 5 billion will sustain a growth rate of 2%. Clearly, on Earth, the intention is to reduce population growth rates as far as possible. Today, the growth rate is around 1% (doubling time 70 years) and falling. The long-range predictions are for "stabilisation" or even overall negative growth by the end of this century (see Human Replicators - An Exponentialist View for more). 

Nonetheless, if we assume just 1 million space colonists by 2100 A.D. growing at 2%, that would result in a billion fold increase by 3150 A.D. Of course, 2% could turn out to be a very modest rate of growth.

Meanwhile, what of Earth's population? Even if it was 10 billion, this would be a drop in ocean compared to the rest of the Solar System's 1 million billion!

Of course, a lot can happen in a thousand years or so...


In a section of Solaria entitled "Climb K-2", Savage notes the work done by Soviet astrophysicist Nikolai Kardashev in 1964. Kardashev proposed that space-faring civilisations would pass through 3 levels (and various gradations in between), which are now known as the Kardashev levels:

Solaria was Savage's exploration of climbing K-2, and in the chapter entitled "Galactia" we humans climb K-3. One million years from now, imagine a human civilisation spanning the Milky Way

As far as I have so far been able to determine, Savage is the first person to seriously attempt to use a Malthusian Growth Model for populations growing within a Kardashev framework. The potential of huge populations of replicators to change the universe itself has never been so clearly revealed before. If this thought is coupled with the Dawkins / Deutsch view that knowledge itself is the key attribute of life, then the universe will never seem so vast and empty again (see Dawkins - An Exponentialist View for more).

Home Alone

Like Drexler before him (see K. Eric Drexler - An Exponentialist View), Savage concludes that we are effectively alone. Despite an earnest desire to believe in UFOs and little green men, Savage reaches the sober conclusion that we live in a "Radio Free Universe" (Savage, 1992, 1994):

"The skies are thunderous in their silence; the Moon eloquent in its blankness; the aliens are conclusive in their absence. The extraterrestrials aren't here. They've never been here. They're never coming here. They aren't coming because they don't exist. We are alone."

The Milky Way galaxy, and perhaps the universe beyond, awaits the first population of replicators who reach K-1 and dare to push on. That could be us.



Savage, Marshall T., The Millennial Project: Colonizing The Galaxy In Eight Easy Steps. Little Brown and Company. 1992, 1994.

Evans, L. T., Feeding the Ten Billion Plants and population growth. Cambridge University Press. 1998.

Cribbs, Gillian. Nature's Super Food The Blue-Green Algae Revolution. Trans-Atlantic Publications. 1997.

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

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Copyright 2001 David A. Coutts
Last modified: 15 December, 2011