Humans are famously bad at predicting the impact of exponential growth. The problem is demonstrated by the following question, often posed to unsuspecting students.

A colony of bacteria grows in a petri dish and doubles in size each day. It fills the dish on the 100th day, triggering a population crash. On what day is the petri dish half full?

The answer is on the 99th day, a result that is mathematically trivial and yet still has the power to surprise. The truth is that humans just haven’t evolved to think intuitively about exponential change.

This difficulty has important implications for our environment and how we should use the resources it offers. The global population has doubled twice in the last hundred years or so. The global economy is doubling in size every 20 years.

A growing number of people are warning that we must avoid the 99th-day scenario—although it is far from clear that we could recognize it if we were in its midst.

One potential solution is for humanity to expand into the solar system. Rocky bodies like the moon and Mars are obvious targets for colonization. And asteroids look like tempting sources of valuable minerals for space miners. Indeed, the prospect of a free-for-all is already stimulating a new space age.

But the solar system is also a limited resource, albeit a large one. And that raises the important question of how we should control its exploitation. In particular, how much of the solar system should be kept as wilderness?

Today, we get an answer thanks to the work of Martin Elvis at the Harvard Smithsonian Center for Astrophysics and Tony Milligan at Kings College London. They have studied the nature of exponential growth and say that our limited ability to predict its impact means we should take this into account when limiting how the solar system can be exploited.

They calculate that humans should be allowed to exploit an eighth of the solar system, with the rest designated as wilderness. And they warn that at current rates of growth, this limit could be reached within 400 years.

The researchers’ reasoning is straightforward. When a system is experiencing exponential growth and has used up an eighth of its resources, it has three periods of doubling left until all the resources are exhausted—a point that Elvis and Milligan call super-exploitation. “Our limited ability to see ahead until such processes are far advanced suggests that we should set ourselves a ‘tripwire’ that gives us at least 3 doubling times as leeway,” they say.

Why three doubling times? In these kinds of systems, small errors of measurement can lead to big errors in predictions. That’s why the researchers do not advocate a stricter limit.  “A more restrictive 1/16 or 1/32 principle has the problem that a minor error in estimating the growth rate can lead to a major error in predicting when super-exploitation will be reached,” they say.            

Neither are they opposed to growth or exploitation, which they see as an important part of humanity’s future. “[The one-eighth principle] excludes only unconstrained or runaway growth,” they say.

So how long have we got? To gauge a realistic level of growth, Elvis and Milligan use iron exploitation since the Industrial Revolution. This has grown at an average rate of 3.5% per year, leading to a doubling every 20 years.

They then calculate how a similar rate of growth would play out on an interplanetary scale. Their calculations suggest that the one-eighth point would be reached in 400 years. At that stage, the next doubling periods would be crucial. “At that point, only 60 years would remain in which to transition the economic system to new ‘steady state’ conditions,” they say.

To prevent this, much of the solar system needs to be protected, but exactly what is a tricky subject. Elvis and Milligan suggest that planets should be protected by surface area and asteroids by volume. The sun should be excluded from the calculations altogether, and Elvis and Milligan say that Jupiter—which has more mass than all the other planets put together—could be excluded too.

Then there is the Kuiper Belt—the belt of icy objects orbiting beyond Neptune—and the much less well-understood Oort Cloud of comets even farther away. Elvis and Milligan say that including these regions in the calculations does not significantly change the conclusions. The mass of material in the Kuiper Belt adds another three doubling times, or 60 years, to the calculations, and the Oort Cloud adds another 80 years.

Either way, time is precious, since there is little prospect of mining other star systems because the distances involved are too great. “Journey times, which are already measured in decades for the Oort Cloud, increase to centuries for anything but microscopic masses at these interstellar distances,” they say. As far as resources are concerned, our solar system is a closed system.

But it should provide plenty, even with a one-eighth limit in place. Elvis and Milligan calculate that it should be possible to build millions of sun-girdling rings with these resources. “That should be enough to go on with, though a Dyson sphere may be out of reach,” they say, referring to the famous idea of Freeman Dyson that a sufficiently advanced, energy-hungry civilization could completely encircle its host star with a sphere that captures all its emitted energy.

The technology required for that is currently beyond humanity.  And so it’s easy to imagine that the idea of protecting the solar system now is somewhat premature.

But the current interest in asteroid mining could change that soon. “The rationale for adopting the one-eighth principle so far in advance is that it may be far easier to implement in-principle restrictions at an early stage, rather than later, when vested and competing interests have come into existence,” they say.

Of course, humanity already protects some parts of the solar system from exploitation. But efforts on Earth have been limited. The US Wilderness Act of 1964 famously protects huge tracts of the United States; the former Soviet Union also protected the Belovezhskaya pushcha, one of the last remaining areas of primeval forest in Europe, although this region in Belarus is now under threat.

And yet only 12% of Earth’s land area is protected, and just 6% of the oceans. When these limits are reached, there will be precious little time to change course.

Elvis and Milligan’s argument is that if we want to prevent a similar failure in space, we need to act now.

Ref: arxiv.org/abs/1905.13681 : How Much of the Solar System Should We Leave as Wilderness?