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Growing Our Way to Centauri

In a book so stuffed with insights and quirky oddments that it belongs on the shelf of anyone interested in interstellar flight, Carl Sagan and I.S. Shklovskii once made a stunning calculation. Their 1966 volume Intelligent Life in the Universe (San Francisco: Holden-Day) presents the argument that with an average annual growth rate of just 1/3 of one percent, energy demand will outstrip the total solar radiation falling on the Earth by a factor of 100,000 within 2500 years. The re-building of the Solar System into something like a Dyson sphere may be inevitable.

But isn’t it a pipe dream to assume that growth will continue at even these modest levels? That was certainly my initial response, for so many things can throw a spanner into a civilization’s works. But Andrew Kennedy (The Chronolith Project, Seville Spain) takes a hard look at growth issues in a recent paper with interesting results. Kennedy believes that growth is far more tenacious than generally accepted. Economic collapse? Ponder that the average recession time in past centuries was between 8-10 years, whereas all our recessions since the Great Depression are better measured in months rather than years.

Disease? Even the Black Death in Europe exerted only a temporary brake on growth. Figuring a death rate of perhaps one-third of the population (the figure varies widely depending on the source), the population did not rise to pre-1349 levels until 1600. Both warfare and trade were severely reduced. But note what happened next:

…150 years or so afterwards, America had been discovered, improved ship-building and navigation (using the recent Western version of the compass) made journeys to the Far East commonplace, ships had sailed around the world (in AD 1521), and Europe was trading with China and India. The spread of credit-based banking and the invention of double entry bookkeeping had brought investment funds into play, and warfare had picked up again.

Kennedy’s examples from both Europe and the Americas are too numerous to list, but I found his thoughts on climate change interesting. The ‘Little ice Age’ that began at the start of the 14th century produced widespread famine and economic contraction, raising the price of English wheat to six times the norm amidst squalor and desolation. But by 1330, Edward III was turning castles from military installations into palaces even as war continued on the Continent. Wealth was being accumulated, great cathedrals built and the shipping industry revitalized in a trade renaissance fueled by spices, silks, wines and furs. The Bay of Biscay became known as the ‘sea of the English.’

Can the momentum continue? As a medievalist by training, I find Kennedy’s optimism about growth hard to swallow, but then my worldview was shaped by the notion of fortune’s wheel continually turning, as medieval a conceit as is imaginable (though passed along from Rome via Boethius). Nonetheless, the growth argument has a place in interstellar discussions, and Kennedy’s purpose is to apply it to the broader issue of how long an interstellar voyage should be delayed given the expectation that further growth will produce faster spacecraft that will catch the original one.

We’ll look at how Kennedy handles this again shortly, and I also want to bring in the thoughts of Marc Millis, who addressed these issues at the latest New Trends in Astrodynamics conference in Princeton. I have that presentation here and want to get into the meat of an argument that was so neatly captured by A.E. van Vogt in his story “Far Centaurus,” in which interstellar travelers finally reach the Centauri stars only to find that Earthmen with faster ships have landed long before them. Millis calls this issue ‘Zeno’s paradox in reverse.’ More about Zeno, paradoxes and Centauri missions as we move past the Thanksgiving holiday here in the States.

The paper is Kennedy, “Interstellar Travel: The Wait Calculation and the Incentive Trap of Progress,” Journal of the British Interplanetary Society Vol. 59, No. 7 (July, 2006), pp. 239-247.

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  • george scaglione November 21, 2006, 15:36

    how incredibly strange it is that now of all times i see a comment like building a dyson sphere may be inevitable!! was talking to an engineer friend 10 minutes ago about this very thing! he had the reasonable idea that anyone capable of building a dyson sphere would probably have a more sophisticated approach than just simply such a sphere! i added that perhaps they would be capable of some sort of inter demensional approach, virtually creating more space by juggling space time in some ultra sophisticated way! yes it would have to be one advanced species,no kiddding! but…maybe thats why we have not seen evidence of a dyson sphere,we just do not know what to look for! could be. thank you george

  • Zen Blade November 21, 2006, 22:11

    The initial quote confuses me.
    if growth is .33%, then the doubling time is over 200 years… how much larger must our combined energy needs grow before we outstrip the sun’s energy output? These calculations would make it seem that growing the Earth’s economy by 13 doublings (8192 fold increase from 1966 numbers… which is a lot) would outstrip the sun’s output.

    Since 1966 we’ve had one doubling (at least)… actually here is one website with some growth statistics. I’m no expert, but the numbers look consistent with other information I’ve read.
    This would mean we’ve had almost Two Doublings since the mid-60’s.

    How many more years before we are really stretching the resources of the solar system?

    -Zen Blade

  • Ron S November 21, 2006, 22:27

    If the decimal point moved one place to make it 3.3% then the doubling is about 20 years. That seems consistent with Zen’s comment. Is that the source of the error?

  • Adam November 25, 2006, 18:14

    Hi All

    I think Shklovskii and Sagan fubbled the calculation. Growth at 0.3% increases production by just e^7.5 = 1808 times in 2500 years. I think they meant 1%. Even so the wait time merely increases by a factor of 3 for 0.3% growth, which is still a drop in the bucket of deep time.

    Earth intercepts 174,750 TW from the Sun. It reflects 30% and absorbs 122,300 TW. Land area is 29.1% so the land receives 35,600 TW. We use 15 TW currently – 2373 times less than what the Sun provides. In just about 800 years we’ll be using the solar supply levels after 1% growth. Current growth in power needs is 2.6% roughly – higher in the countries rapidly industrialising, much lower in static states in Europe and dirt poor nations elsewhere, and about right in efficiency slackers like USA and Australia.

    If global use stabilises at Australia levels of ~ 12 kW/person then when population peaks at 9.5 billion global potential demand will be ~ 114 TW. Good growth at 2.6% will reach that in 2084, hopefully getting most from advanced fuel-cycle nukes and SPS in Geosynch. The mess caused by using coal, methane clathrates and/or Generation IV nuke fission to reach those levels is unthinkably horrible. We could use ground-based solar, but it’s inherently only 20% as good as in-space solar – great supplemental power when everyone is throwing on an air-conditioner in Summer, but pitiful if we’re all charging electric cars at midnight.


  • Zen Blade November 28, 2006, 21:49

    cool number crunching.