Solution They Have Not Had Time to Reach Us

Had we but world enough, and time.

Andrew Marvell, To His Coy Mistress

A common reaction when people first hear of the Fermi paradox is: "Oh, they have not had time to reach us." Hart, in his influential paper on the absence of ETCs, called this the temporal explanation of the paradox.

As we saw on page 4, Hart argued that this explanation is not tenable. To recap, he reasoned that if an ETC sends colonization ships to nearby stars at a speed 0.1c, and if the colonies in turn send out their own colonization ships, then that ETC would quickly colonize the Galaxy. If the ships did not pause between trips, then a colonization wavefront would sweep through the Galaxy at a speed of 0.1c. If the time between voyages was about the same as the voyage time itself (travelers have to rest, after all), then the colonization wavefront would move at 0.05c, so it could travel from one end of the Galaxy to the other in 0.6 to 1.2 million years. For ease of use, we can say that the Galactic colonization time is 1 million years.89

One million years is a long time on an individual level; it is a long time even at the level of an entire mammalian species. But it extremely short compared to the total time available for colonization. Consider the various time scales involved in terms of the Universal Year. The Galactic colonization time corresponds to just 41 minutes 40 seconds — less than one half of a soccer match. on this timescale, civilizations may have been popping into existence since the late spring months, and there seems to be no compelling reason why the first ETC could not have arisen by about May Day. So although the first species with the inclination and ability to engage in interstellar travel might have arisen at any time in the 8 months between May and December, according to Hart the temporal explanation asks us to accept that this species started traveling no earlier than 11:18 P.M. on 31 December. It would be a remarkable coincidence if mankind emerged so soon after the emergence of the first star-faring civilization.

Hart's argument is compelling, but one can dispute a number of his assumptions. An obvious problem is the speed of the colonization wavefront, which Hart assumes to be a large fraction of the speed of individual spacecraft. As Sagan pointed out: "Rome was not built in a day — although one can cross it on foot in a few hours." In other words, for the city of Rome, the speed of the "colonization wavefront" was an infinitesimal fraction of the speed of the craft used to "colonize" it. More explicitly, throughout all of human history there has never been a colonization wavefront that moved anything like as fast as the speed of individual craft. Why should it be any different for a civilization busy colonizing the Galaxy?

Hart calculated his Galactic colonization time simply by dividing the diameter of the Galaxy by an assumed travel speed. Several authors have developed more sophisticated computer models of Galactic colonization and thereby arrived at more plausible colonization times. Eric Jones analyzed a model in which colonization was driven by population growth.90 He assumed a population growth rate of 0.03 per year and an emigration rate of 0.0003 per year (which was the emigration rate during the European colonization of North America in the 18th century). His model showed that, under these assumptions, a single space-faring ETC could colonize the Galaxy in 5 million years. In subsequent analyses he offered a preferred colonization time of 60 million years (though this time can be made larger with different assumptions for the rates of emigration and population growth). Of course, 60 million years is much longer than Hart's colonization time; but it is still too short to permit a temporal explanation of the Fermi paradox. On a human scale, a process that takes 60 million years is not even glacially slow; but on a cosmic scale the colonization wave moves like a flash flood through the Galaxy.

However, Jones himself made assumptions that can be disputed. For example, Newman and Sagan argued that Galactic colonization cannot be driven by the demands of population growth.91 Look at mankind. In the last century, the world population more than tripled in size. If the population were to continue to grow at that rate, and if we wished to maintain Earth's present population density, then in a few hundred years a colonization wavefront would be moving at light speed. Once we reached that point, the population growth rate would have to decline! This is an extreme example, but it demonstrates that ETCs will not establish colonies as a means of avoiding overcrowding on the home planet. In the long run, they cannot outrun the problems caused by an exponentially increasing population — they simply cannot travel fast enough. A civilization has to curb its population growth regardless of whether it develops space travel. Newman and Sagan therefore modeled Galactic colonization as a diffusion process,92 and applied the well known mathematics of diffusion to a particular colonization model. Their results seemed to show that if ETCs practice zero population growth, then the nearest civilization would reach Earth only if it had a lifetime of 13 billion years. This is long enough to provide a temporal explanation of why extraterrestrials are not here (though it does not necessarily explain why we do not hear from them).

The Newman-Sagan model was subject to criticism. In their model, it turns out that the Galactic colonization time is rather insensitive to the speed of interstellar travel. What matters is the time taken to establish a planetary colony, which in turn depends upon the population growth rate. Newman and Sagan assumed very low population growth rates — rates that many people find too conservative. Even if one accepts their rates for population growth, there is a problem with their conclusion. The differential rotation of the Galaxy turns the expansion zone into a spiral, rather like path of a drop of thick cream when you slowly stir it into a cup of coffee. Take this factor into account and the Galactic colonization time shortens dramatically. A final criticism: even if advanced ETCs are not driven to expansion by population pressure, would they not explore the Galaxy out of curiosity?

Yet other models have been analyzed.93 For example, a recent calculation by Ian Crawford suggests that the Galaxy can be colonized in as little as 3.75 million years. The biggest uncertainty in this figure is not the speed of interstellar spaceships, but the time it takes for colonies to establish themselves and then send out their own spaceships. And Fogg, in developing his interdict scenario, analyzed the results of a model in which ETCs arise at the rate of 1 every 1000 years, and 1 in 100 of these ETCs attempts to colonize the Galaxy. His model provided the time to "fill" the Galaxy for different speeds of colonization wavefront. Even under the most pessimistic assumptions, he found that ETCs filled the Galaxy in 500 million years, which is short compared to the age of the Galaxy and makes it difficult to support a temporal explanation of the paradox.

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