[Halc (OP)]

I am putting this in General Science since it is a general question addressing many problems in several unrelated fields.  The premise is artificial, out of necessity, but the answer should be real.  The idea is to get you to think.

Statement of the premise:
Suppose the world is flat and indefinitely large.  Everything else is more or less the same as the way we know it.  Humans are confined to say a continent, but then let loose.  The rest of the world is filled with the same sorts of plants and animals that existed say 1000 years ago. There is day and night, and seasons, not particularly explained.  Gravity is continuous at any altitude (which is consistent with a flat object).  It's a little like Niven's Ringworld, except not round, and infinite.

The question:
At what long term pace would humans move into new territory?  The answer to that isn't as important as thinking of ways that would limit the long term pace.  You can take any technology with you, but you will need to refuel/replace any of it as needed. Positing infinitely durable toys is against the spirit of the question.

Obviously it can't just be one group of people like Lewis and Clark.  The lead people will get wiped out now and then.  Towns will need to be built to 'feed and breed', so to speak, and to support the 'front line' effort. One problem might be what incentive would be needed to keep up this effort indefinitely, but I think evolution would take care of that. A group of people genetically inclined to move at a greater pace will get there first and will be the ones to populate the lands.

Anyway, the idea is to come up with some aspect of the effort and see if it might be a candidate for the thing that most limits the pace.

[alancalverd]

You could use the recent history of North America as a model. Given that the indigenous population was sparse and living in a low-tech equilibrium, the arrival of Europeans approximates to the sudden injection of unlimited technology and a potentially infinite number of people into fairly virgin but generally fertile territory. And 500 years later, 17% of the USA and 5% of Canada is cultivated, compared with 65% in Bangladesh. Surprisingly, only 25% of the UK is listed as cultivated, though most of the rest is managed grazing.

The UK and Bangladesh being decidedly "old" countries, it seems that the asymptote depends very much on geography: tropical flood plain farming will support a much larger population than sub-arctic hill grazing, and even in a young, hi-tech country  like Australia,  exploitation of natural resources is limited by the availability of water. 

[Bored chemist]

When the first person arrives, the "world" is populated.

However, that's semantics and probably not what you had in mind.

I have visions of something like this happening.
https://en.wikipedia.org/wiki/Fairy_ring

[Halc (OP)]

You could use the recent history of North America as a model.

Pretty much, yes.  Given that model, we can use a convention of west being our frontier, and east being whence they come.

Given that the indigenous population was sparse and living in a low-tech equilibrium,

In my example, there would be no indigenous population.  But since they were a help about as much as they were a hindrance, I don't think they made a lot of difference as to how long it took people to push said frontier.

the arrival of Europeans approximates to the sudden injection of unlimited technology and a potentially infinite number of people into fairly virgin but generally fertile territory.

Not unlimited technology.  Only as limited as Europe managed to be when it made the move to push to the next continent.  That's a huge factor in my scenario is to try to decide what level of technology would be.  Sure, you'd probably not want to push the frontier like that until you have rudiments like iron tools and maybe guns, but the higher the technology you use, the longer they will have to wait for that technology before moving on.
Take electronics for instance.  Suppose Europeans push to America today armed with year 2000 level technology.  How long before America can reproduce all the factories and such needed to produce that technology?  100 years?  That's not unreasonable, since I think it would take 100 years given say 1800 tech as well.  That's part of the debate of this thread: Go high tech or low tech...

Yes, you point out that the frontier will always have untapped resources that are more used up in the older world.  A sufficiently old world will have consumed them all and must rely on an equilibrium based in renewable resources.  Nowhere on Earth has yet achieved that state, so we don't have much of a model of it.

The UK and Bangladesh being decidedly "old" countries

In my scenario, all of Europe would be populated, but still 'young' countries, having only recently been populated.  The old countries all all much further east.  One of the problems is how one might go about communicating or trading with them. Eventually the distances render both of those prohibitively uneconomical.

it seems that the asymptote depends very much on geography: tropical flood plain farming will support a much larger population than sub-arctic hill grazing, and even in a young, hi-tech country  like Australia,  exploitation of natural resources is limited by the availability of water.

Yes, with each push of the frontier, the challenges will be different to a point.  I'm keeping it somewhat sane by saying the same sort of biology is everywhere.  You can't go so far that you can no longer digest the local fruits.  That's more of a problem with traveling to another planet with completely alien life.  Realistically, an infinite flat world would all evolve from identical beginnings, but wouldn't go in the same direction at all.  Eventually one might find a place for instance where photosynthesis never evolved, and good friggin luck trying to survive in such a place.  So I put as part of the premise that we don't have to consider issue like that one.

[Halc (OP)]

I have visions of something like this happening.
https://en.wikipedia.org/wiki/Fairy_ring

Yea, like that. A forest fire, especially one with no wind, creates a similar pattern. As I mention in the prior post, the old world would either die out from consumption of resources or drop into a lower energy renewable mode. Either way, they would likely be of little assistance to the frontier efforts.

[EddieSWog]

Humans shall see in the long run.

Its a near hit, right. They did miss...

[chris]

Humans shall see in the long run.

Its a near hit, right. They did miss...

What are you talking about?

[Halc (OP)]

I had initially been working on an assumption that given arbitrarily long time, the distance between the height of technology and the frontier would also become arbitrarily long.  But the Fairy ring comment throws a wrench into that.  The top technology is necessarily going to exist in the center of the ring (if people still occupy it), but it is based on a sustainable economy, probably of little interest to the people on the ring itself which is based on a gilded economy.  Technology from there is what is of interest to the frontier, and it exists a finite distance away.

No need to walk or expect to be completely primitive at the frontier.  We can give them some vehicles designed for unimproved terrain, and those vehicles and other toys can be maintained/replaced from behind the lines so long as the lines don't advance too fast.  But we're trying to optimize the speed at which those lines advance.

[Akoji]

Thanks for the info