Vajk's Dilemma

© Laurence B. Winn

Mar 1, 2001

It is said, and not entirely without justification, that computer models of the world economy fail to predict real outcomes.

Perhaps the most famous of such computer programs is the Forrester world dynamics model used by the MIT-led Club of Rome that produced the 1972 report The Limits to Growth. Some of the details of that report, being in error, make the entire range of findings subject to derision from interests not well served by a focus on limits.

However, for a first look at a system as chaotic as the world economy, Limits was a very good try. It correctly predicted the current world population of six billion. It was on the mark with its prediction of runaway growth in atmospheric carbon dioxide levels, and it was very likely correct in its prediction of a peak in world material standard of living around 2000. Many present-day prognosticators see the report's predicted 2080 die-off due to famine, disease and war as somewhat optimistic, especially in Africa.

Dennis Meadows, who lead the MIT team and authored the report, did indeed vary the conditions of the model in order to test "what-if" assumptions. If, for example, we had zeroed population growth by 1975, restricted capital growth by requiring that investment equal depreciation and recycled everything, then the model gives us long-term (but not perpetual) equilibrium at an average world income level of around $3 U.S. per day, equally distributed among nations. If we wait until 2000 (oops), equilibrium is no longer sustainable.

There was no model that suggested the possibility of sustainable growth without unlimited resources, which you can get only from space. In the same year Limits was published, then President Richard Nixon shut down the U.S. space program for planetary exploration with human crews, presumably to avoid embarrassing the Communists. For a while after that, optimists persisted in a lot of talk about space habitats, and by 1975, J. Peter Vajk of the University of California's Lawrence Livermore Laboratory had published a paper titled "The Impact of Space Colonization on World Dynamics".

The chief criticism of the Forrester model of world dynamics had been that it consisted of only one "sector", in which the entire world economy was treated as a single "lumped" system, everything averaged. Vajk found that predictions from a two-sector model adequately represented the output of models with as many as 10 sectors, so he settled for the simpler two-sector approach. Then he added a third sector, a space industrial infrastructure ala Gerard K. O'Neill, interacting with the terrestrial economies.

Vajk proposed, as did O'Neill, that the space economy would pay for terrestrial imports with energy, specifically, energy from the sun transmitted to earth by proven microwave technology. (See "Cities in the Sky".)

The two terrestrial sectors he called the developed sector and, insensitively perhaps, the underdeveloped sector (but remember, this is 1975). Vajk was mindful of the ability of mathematical models to predict general happenings, even while missing some important details. For example, his model could not have foreseen the advent of AIDS or the dissolution of the USSR. Food and pollution multipliers were applied to the material standard of living to create an additional "quality of life" function, displayed on the charts with factors such as capital investment, pollution ratio and natural resources.

Assuming an absence of space industrialization until at least 2100, Vajk predicted a world population of around five billion by 2000, substantially off the mark on the optimistic side. This error is most likely from a reduction in assumed birth rates prompted by politically correct consternation over the output of the Forrester model. In the developing countries, quality of life peaks by 1990, and the material standard of living peaks by 2000. Quality of life and material standard of living reach their highest point around 2000 in the developed world at levels at least ten times higher than the developing sector. Quality of life and material standard of living fall to 1900 levels in both sectors by 2100 and continue to fall, albeit more slowly, after that. The downturn in the population of the developing countries in 2080 is the result of increased death rate, not reduced birth rate. In the developed world, population continues to rise through 2100.

If a space industrialization program had begun in 1982, Vajk's model predicts zero net population growth in the developing countries by 2040. The population curve turns over because of a reduced birth rate derived from an improved standard of living, not because of an elevated death rate, as in the first run. The main difference for the developed world is decreased pollution owing to the substitution of clean solar power for energy from fossil fuels. In this scenario, immigration to the space habitats starts by 2000, consisting mainly of people from the developed sector. Immigration from the developing sector almost catches up by 2100. Quality of life starts off at very high levels compared to either terrestrial sector. It falls to developed terrestrial levels in about 2020 due to crowding, and then climbs again.

In Vajk's model, the economic benefits for earth are negligible if space industrialization is delayed until 2002.

No pompous bologne-monger with a vested interest in the status quo ever called Vajk’s model “dead on arrival”. It never got that kind of attention because it never entered the public consciousness, was never called “discredited”, because it never made the news, as the Forrester model did. Even though the model's projections for natural resources were wrong insofar as materials are concerned, they were not necessarily wrong period. Materials are almost infinitely substitutable -- aluminum for steel, ceramics for metals, carbon fibers for nearly anything -- but you still need energy to make it happen. Throw out the term "resources" and substitute "energy", and the early world dynamics models may be just about right.

So here is Vajk's dilemma: Is it nobler to take the best stock and leave home while we can, spreading the spark of humanity through the solar system and beyond, or to huddle together on a spent cinder, sharing resources equally and waiting for a big space rock to deliver our spiritual reward?

Perhaps you should decide before the next election, while we still have time.