mkline55

2013-Jun-28, 04:10 PM

It's Friday. The mind wanders.

You've probably seen the argument that galactic expansion would be exponential. Two colonies become four. Four become eight. Eight become sixteen. Sixteen become 32. And so forth, and in very short time, the entire galaxy becomes overcrowded. Actually, about 44 successive generations would do the trick to reach 1 billion planets. The trouble is, it simply cannot work that way.

Suppose some life form set out to conquer the galaxy. Call it "conquer", "explore", "populate", "terraform", or whatever. I'll stick with "conquer".

We'll need some assumptions. First, assume the technology exists to build a colonizing starship that can survive up to 200 years of interstellar travel. Just for arguments sake, assume the ship can accelerate to 10% of light speed within a relatively short period of time, coast for most of the journey toward its destination, and decellerate to match velocity with whatever target. Vary these numbers to suit your own speculation.

How the passengers are managed, although likely of personal importance to themselves, is inconsequential to the discussion, provided the ship can safely put the passengers onto a livable planet/moon, and that the population is sufficiently sized and trained/trainable to rapidly expand industry and population. Assume each population is capable of doubling every twenty years after arrival, and that the entire industry will be capable of building and populating another generation of starships from the ground up in just ten generations, or two hundred years.

With the entire galaxy to choose from, where would you go first? Well, you have a maximum range of twenty light years. I'd expect travel to proceed first to the nearest extra-solar likely-livable planets.

Let's say there were forty such planets within twenty light years. Also assume that the distribution of planets throughout the majority of the galaxy is somewhat similar. That seems really, really generous, but bear with me. I'll swing the pendulum the other way for comparison.

So you start from day zero and send out forty ships. Maybe you only send one a year for forty years, and maybe there's just a one-day super launch. After that initial launches, there could be follow-up launches to the same destinations, but there just are no additional likely targets. Two hundred years later, those first ships have all landed and began to establish colonies A1 through A40. Assume 100% success. They grow all of the necessary industries for building new starships such as mining, refining, energy management, farming, etc. etc. etc. Over the next two hundred years the population is roughly one thousand times larger than what initially arrived, and has sufficient resources to send a new generation of starships abroad.

So it's been four hundred years, some more, some less, since the first starships left, and now these forty first-generation colonies decide to launch their own colony ships. Where do they go?

For each of the first-generation colonies, about fifteen of the potential forty targets are already populated by similar first-generation endeavors. For those nearest the original star, they would likely find that most of their potential destinations are already populated. Let's say that leaves twenty-five uninhabited targets for each colony. Most of those twenty-five targets are also within range of one or more other colonies. At best, each colony has only a couple undisputed targets. The rest are more or less up for grabs. So that's where the trouble starts. It's where the term "conquer" comes into play.

The most rapid expansion possible would be somewhat spherical. After only a few generations, each additional expansion would only be to a few more destinations. Even ignoring the disk shape of the galaxy, growth practically levels off. One becomes 41, becomes 60, becomes 71, becomes 79, becomes 89. No exponential expansion. At ten additional planets every 400 years, it takes 40 billion years to populate 1 billion planets. Ouch!

Don't like that? Okay. Let's say there are just two viable targets within range of any colony. Ships leave for both targets at year zero. By year 400 both are ready to expand again. Each has only two potential destinations. One is somewhere far away. The other is right back where you started from. So, by generation two, you already have at best a linear growth. One becomes 3. Three becomes 5, becomes 7, becomes 9, etc. Again, no exponential growth. At two new colonies every 400 years, it takes 200 billion years to populate 1 billion planets.

You could make other assumptions. Suppose colonies could grow to full maturity in just ten years. Suppose travel could occur at 1/2 light speed and for as long as 1000 years. Or suppose the destination planets were not all that livable, and it takes 1000 years to reach maturity. You could assume anything. This is just speculation after all. Plus, it's Friday.

You've probably seen the argument that galactic expansion would be exponential. Two colonies become four. Four become eight. Eight become sixteen. Sixteen become 32. And so forth, and in very short time, the entire galaxy becomes overcrowded. Actually, about 44 successive generations would do the trick to reach 1 billion planets. The trouble is, it simply cannot work that way.

Suppose some life form set out to conquer the galaxy. Call it "conquer", "explore", "populate", "terraform", or whatever. I'll stick with "conquer".

We'll need some assumptions. First, assume the technology exists to build a colonizing starship that can survive up to 200 years of interstellar travel. Just for arguments sake, assume the ship can accelerate to 10% of light speed within a relatively short period of time, coast for most of the journey toward its destination, and decellerate to match velocity with whatever target. Vary these numbers to suit your own speculation.

How the passengers are managed, although likely of personal importance to themselves, is inconsequential to the discussion, provided the ship can safely put the passengers onto a livable planet/moon, and that the population is sufficiently sized and trained/trainable to rapidly expand industry and population. Assume each population is capable of doubling every twenty years after arrival, and that the entire industry will be capable of building and populating another generation of starships from the ground up in just ten generations, or two hundred years.

With the entire galaxy to choose from, where would you go first? Well, you have a maximum range of twenty light years. I'd expect travel to proceed first to the nearest extra-solar likely-livable planets.

Let's say there were forty such planets within twenty light years. Also assume that the distribution of planets throughout the majority of the galaxy is somewhat similar. That seems really, really generous, but bear with me. I'll swing the pendulum the other way for comparison.

So you start from day zero and send out forty ships. Maybe you only send one a year for forty years, and maybe there's just a one-day super launch. After that initial launches, there could be follow-up launches to the same destinations, but there just are no additional likely targets. Two hundred years later, those first ships have all landed and began to establish colonies A1 through A40. Assume 100% success. They grow all of the necessary industries for building new starships such as mining, refining, energy management, farming, etc. etc. etc. Over the next two hundred years the population is roughly one thousand times larger than what initially arrived, and has sufficient resources to send a new generation of starships abroad.

So it's been four hundred years, some more, some less, since the first starships left, and now these forty first-generation colonies decide to launch their own colony ships. Where do they go?

For each of the first-generation colonies, about fifteen of the potential forty targets are already populated by similar first-generation endeavors. For those nearest the original star, they would likely find that most of their potential destinations are already populated. Let's say that leaves twenty-five uninhabited targets for each colony. Most of those twenty-five targets are also within range of one or more other colonies. At best, each colony has only a couple undisputed targets. The rest are more or less up for grabs. So that's where the trouble starts. It's where the term "conquer" comes into play.

The most rapid expansion possible would be somewhat spherical. After only a few generations, each additional expansion would only be to a few more destinations. Even ignoring the disk shape of the galaxy, growth practically levels off. One becomes 41, becomes 60, becomes 71, becomes 79, becomes 89. No exponential expansion. At ten additional planets every 400 years, it takes 40 billion years to populate 1 billion planets. Ouch!

Don't like that? Okay. Let's say there are just two viable targets within range of any colony. Ships leave for both targets at year zero. By year 400 both are ready to expand again. Each has only two potential destinations. One is somewhere far away. The other is right back where you started from. So, by generation two, you already have at best a linear growth. One becomes 3. Three becomes 5, becomes 7, becomes 9, etc. Again, no exponential growth. At two new colonies every 400 years, it takes 200 billion years to populate 1 billion planets.

You could make other assumptions. Suppose colonies could grow to full maturity in just ten years. Suppose travel could occur at 1/2 light speed and for as long as 1000 years. Or suppose the destination planets were not all that livable, and it takes 1000 years to reach maturity. You could assume anything. This is just speculation after all. Plus, it's Friday.