One helpful rule for determining at least part of what necessities a seeding team would need on the ground on their new planet is this: bring whatever you need to reproduce what you brought. If replication can be achieved, and some expansion produced on top of that, the new colony will be able to survive and prosper, barring catastrophes.
This design rule has two implications. One is that the materials included should be as simple to manufacture, whatever that means for the state of technology that exists in the alien civilization, as possible. The other is that the production equipment must be, in and of itself, self-replicating. It needs to be made of parts it can make.
There is a broader context. Manufacturing is only one item within the concept of self-replication. The other is materials. There must be replicatable equipment able to find and extract all the necessary materials, from raw sources found on the planet. Clearly the premium is on reducing the different materials needed to the absolute minimum, and make that minimum up from easy to find and easy to extract materials as far as possible. This may involve departing from exact replication, but sticking to the replication of function. One clear example is the use of the local equivalent of trees to replace uses of plastic in some parts of the equipment. Another would be the use of extracted plant oils to replace synthetic oils used in the original equipment.
A third consideration involves transport. There will not be much ability to move long distances. This means materials found need to be local. If mining is needed, and it probably will, underground mineral resources need to be close at hand. If Earth is any guide, minerals are not located near one another. Having two mines, for dissimilar minerals, near one another is the rare exception. The story of Earth is of locating minerals and other natural sources anywhere on the planet, and transporting it, by one means or another, to the central sites for processing and converting to the usable form of the elements or minerals needed for various types of equipment.
Even early trade on Earth between distant locals was more in basic materials rather than manufactured items. Copper, tin, iron, and other metals usually had to be brought long distances. This implies that there will need to be careful planning on how to, for example, only use iron for construction, and only use additives to it which are easily found. On Earth, our technology does not go in that direction, as we are in a phase of our history where materials of all sorts are still plentiful here on the planet. There is little need to try and reduce the variety used. Instead, pressing forward with more capability, for example, more strength for less weight, more processing capability in less volume, more flexibility, more heat capacity, more of any number of different attributes is what is desired. Materials are on Earth still sufficiently low in the fraction of cost of items to allow a wide selection of them to be incorporated into anything. This would not be the case with a settlement expedition to another planet.
It might be that there are a dozen different natural materials that will suffice to meet the functional replication requirement. Some of these might be mined, others exist on the surface. If one is fossil fuels, and the planet is so fortunate to have them easily available, some drilling might be necessary. Here is the first indication of a minimum size for the landing party. If there are a dozen sites from which materials of different sites need to be extracted, there would need to be either some robotic equipment or some biological organism, an alien or an intello, present at the dozen sites. If it were aliens, this provides an indication of how many aliens would be needed. At each site, perhaps three, and another fifty at the landing site, leading to only a hundred or so.
For robotics, there is a question as to whether a useful robot can be built using a minimum number of materials. For any of the materials extraction sites, the robot would have to have some degree of mobility, as well as a high degree of artificial intelligence. Both of these would be simply provided on the aliens’ home planet, but making them out of a minimum number of materials might be beyond the reach of even asymptotic technology. Intellos might be simpler to grow and train, but there is a time constraint involved here. It might be that aliens are required at each site, and at the very least, to be able to travel to the sites.
Transport of minerals over long distances on a raw planet cannot easily be done over land. Building air transport would likely involve more difficulties than water transport, if such things are possible on the new planet.
Simply thinking about the struggle to colonize a planet indicates the aliens may be initially building an infrastructure, very thin, that relates closely to their earlier era of pre-technology life on their home planet. There are some aspects of technology that could be transferred to the clone planet, but in many areas of life, primitive methods might have to be used. The primitive life of the aliens would have depended on some characteristics of their own planet. They may or may not have had pack animals, and these could be bred on the colony planet. There may not have been many open bodies of water on the home planet, and they may have turned to air travel early in their technological climb. We know about dirigibles, but never made use of them. Perhaps some alien worlds have, and if so, they would be likely transported to the new world if conditions were the same there
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When we on Earth think of asymptotic technology, the natural thing to think about is increasing capability in every possible way, maximizing all the attributes listed above and more. But asymptotic technology is much more than that. It is the complete knowledge of technology, and this means being able to perform functions with less energy, less materials, less recycling losses, less wear, less computation, less and less and less. This phase of asymptotic technology, the one we are not as familiar with, is the one that will play a critical role in equipping the landing party, and will be what determines the minimal size of the party. This minimal technology, in conjunction with some carryovers of primitive infrastructure, probably defines what a clone world would look like during the earliest period of its existence.
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