There may be a little bit of misconception about what actually happens to curtail the civilization’s living the high life for ever and ever. What happens is the cost of extracting resources gets higher. These costs can be tabulated in terms of two things: energy and resources themselves. As the mines have to be dug deeper or ores shipped farther or more ores dug up to be processed, more energy is needed. This is no big deal if you assume there is infinite fusion energy around. Just build another reactor. Problem solved.
No. There are connections. To build another reactor, you need resources, which are getting more and more scarce. So there is a Catch-22. You need resources to build a reactor to get more power and you need more power to get resources to build the reactor. This smells like some square law thing, meaning that things get worse really fast near the end.
To try and understand the processes, let’s build a model. Before doing so, remember that modeling is just another language, like French or Russian, except it is a language of mathematics. What is nice about languages of mathematics is that you can intersperse it with English to make everything clearer, which is particularly hard to do with French or Russian. Spoken languages are meant to be done independently, but mathematical languages are meant to be used with a spoken language. That’s just nice, and everyone should have the right to be taught, properly, how to speak some mathematical languages, like modeling.
That being said, I will reveal the secret behind the curtain of modelers. Modeling is just a way of communicating ideas. A model proves nothing. It is just a tool to try and put numbers into some concepts. You can make a model do anything you want it to, just like you can use English to say anything you want to. To try and convince someone of some idea because it has a model portraying it is deceptive. Models are not science, they are a language of mathematics, no matter how complex they are or who creates them. They convey the ideas of the author, just like an essay does.
I like simple models, because simple models help people understand the interplay of ideas that are quantitative. So, here we will use the maximally simple model.
Consider an alien planet, which at time zero has 500 units of resources. For simplicity, we only think about one resource. It has cities, full of citizens, which depend on the resources and the energy which is produced in their power plants. Let’s just consider averages. At time zero, the city needs 1 unit of resources to get it to time one, and 1 unit of energy from the power plant. The power plant produces its own energy, but in the standard design of the power plant, it needs 0.04 units of resource per year to produce one unit of power. This is averaged over its lifetime, and most of the resource usage comes at the construction phase. Recycling is already figured into these numbers, which are only the net amounts, or the recycling losses, if you prefer.
Resources, net of course, come from some resource extraction operations, like mining, and they need some power to do their job, which we take as 0.1 units to begin. They also consume some resources, which starts as 0.04 as well. This means that, for the one city to function for one unit of time, 1.1 units of energy have to be generated, and 1.14 units of resources are consumed in each unit of time. If resources were like tomatoes on supermarket shelves, all equal and all waiting to be picked up, this model would function linearly, and the last resource would be used up in 500/1.14 units of time, where we are taking 500 as the measure of total resources available on the planet.
But resources get harder to extract and process and make available as there are less and less of them. This means that the power needed and the resources lost in gathering a unit of resources gets larger and larger as the remaining amount diminishes. How fast? For the simplest model, suppose it is inversely proportional to the amount. So, when there are 250 units left, it takes 0.2 units of energy to extract and prepare one unit of resources, plus 0.08 units of the resource itself. Here’s what happens:
What happens is that cheap fusion power just keeps being used to extract more and more resources, which do not go to the city, but to the resources extraction operations and power plant construction, and the city is oblivious of the changes, until near the end, when the power a new plant can provide does not return enough resources to enable its construction. Buried in the assumptions are that fusion fuel is inexpensive, virtually inexhaustible, and it does not negatively impact anything at all. Quite a nice package: cheap fuel, as many reactors as necessary, and resources that go on and on until they don’t.
Never forget by this time, the alien civilization is quite smart, and they wouldn’t be fooled by the seeming unchanging life they lead. Furthermore, they have mastered artificial intelligence, and one would hope the master computer network, or whatever embodies their AI, would tell them that they have only a certain number of time units (maybe these are years or decades) before some resource shortages hit them. Even if there is no visible sign of any resource shortage in the cities, somebody would notice the gradual change in the composition of the infrastructure, meaning more reactors and mines every unit of time.
There is little they can do, other than colonize. Being smart and all, they are already recycling as best as anyone could. The home world is headed back to living on renewable resources, as there won’t be any other ones. This means no industrial equipment, as it all uses resources, except for what can be made out of grown materials and powered by natural forces, such as rain, tides or wind. No hope for visiting Earth if they didn’t make the voyage before the last bit of time, when shortage actually start looking like shortages, and cheap deuterium doesn’t ameliorate it any more.
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