Steady Growth

There is a notion around that humanity requires steady growth to be healthy and happy. Steady growth clearly cannot continue for long on a finite planet. So there is another related notion around, that interplanetary colonization is required for humanity to be healthy and happy. Even the solar system is finite of course, so interstellar colonization is a natural next step. Why not intergalactic?!

But there are other physical limits that will constrain growth. Of course it could be that we will discover that our notions about physical limits are not accurate. But then our notions about the need for growth could be wrong, too. Any and all of our ideas could be wrong, but still, we're thinking beings; if we expect to succeed with interstellar colonization, we'd better hone the precision of our thinking!

One of the most fundamental physical limits in our theories today is the speed of light. Perhaps we'll find a way to colonize other galaxies, but it will take us a very long time to get to any of them!

Steady growth generally means exponential growth. Over a generation, the growth in whatever segment of the population will grow in proportion to the size of that segment. If health and happiness is to be equitably distributed, and if health and happiness requires growth, then growth will be exponential.

Physics comes in because humans, whatever else they might be, are also physical objects. The disciples of Ray Kurzweil might quibble: perhaps humans, in essence, are actually information. But even information requires some minimal physical substrate to be stored and processed! In any case, I am certainly not proposing that the specific numbers of my back-of-envelope calculations here should be taken with any seriousness. My point here is that steady growth will eventually bump up against the physical limit of the speed of light. I invite everyone to run the numbers as they see fit.

Suppose humanity's domain is some large sphere, centered on the earth presumably, and stretching out through interstellar space toward the distant galaxies. Since humanity is steadily growing, its domain is also growing. If humanity is growing exponentially, the volume of its domain will also be growing exponentially. Of course humanity can grow, to some extent, while in some fixed domain. That's what we've been doing on earth so far.

What exactly the carrying capacity of earth is, that's difficult to say. But, again, there are physical limits. The earth's mass is about 10^13 times the total mass of humanity. If the population grows at a steady 1% per year, then in about 3000 years, the total mass of humanity will exceed the total mass of the planet earth. Obviously we will run into serious trouble long before that; it is difficult to predict the exact course of our battle against limits to growth. The point of my quick calculations here is that they set some quite hard bounds. If humanity is to continue to grow at a steady 1%, certainly before 3000 years have gone by, we will need to be well down the road of interplanetary colonization.

It's easy to run similar numbers for the solar system. In less than 5000 years, the steadily growing mass of humanity will exceed the total mass of the solar system. Probably we will not find a way to digest the sun, so we will need to be colonizing distant stars well before then.

So let's say that we have spread out in the galaxy out to some radius R. If humanity is growing at 1% per year, the volume of its domain must also be growing at 1% per year, and then the radius will need to grow at 0.3% per year. Once that radius hits 300 light years, that steady growth will require the radius to grow more than one light year per year, i.e. faster than the speed of light!

So a reasonable bound on steady growth of 1% per year is that the domain of humanity will hit a hard physical limit at radius 300 light years. That's a volume of about 3 x 10^61 cm. Given the rough density of galactic matter, the total mass in that volume would be about 3 x 10^40 grams. A human weighs about 10^5 grams, so that would be a maximum population of about 3 x 10^35... assuming humans have incorporated all material into their bodies! Today's population is about 10^10, so that's a population growth of a factor of 3 x 10^25. At a steady 1% growth rate, we'll hit the speed of light in about 6000 years.

Of course these rough calculations involve many very unrealistic assumptions. There is no way that humanity will absorb into their bodies the entire mass of galactic matter inside a sphere of radius 300 light years. But even if they could, we'd hit the speed of light in 6000 years, given a steady 1% growth rate. 6000 years is already not an absurdly long time - it's roughly our historical horizon. Absurdly generous assumptions about the success of humanity's battle against the limits to growth already run into limits that are not absurdly far away.