THE NEXT GENERATIONS:population dynamics and cultural rules in a generational

spaceship

Luca Cinacchio

University of Torino, Physics Department

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59.77 s 44100 Hz 2 channels

Cinacchio Mathematica UGM 2011.nb 1

Abstract

A generational spaceship is a hypothetical starship that travels at a speed

much slower than that of light, taking for its travel hundreds or tons of

years. The original occupants will leave their descendants to continue

traveling. This scenario will imply dealing with biological, social and moral

problems related with the society inside the ships, and the kinship rules

regulating how the crew can mate, and thus whether the society can

grow, stay stable or die.

This discovery process is the goal of this project.

Cinacchio Mathematica UGM 2011.nb 2

Generations after generations,

will ever the Humankind reach the stars?

We don't know yet if we will be able in the future to build spaceships that

can travel so far to reach other stars and planets outside the solar

system.

According to Einstein theory of Relativity we know that this will take hun-

dreds of years.

But we can already discover if it will be possible to set up a crew and

some kinship rules that allow the original crew to reproduce generations

after generations, and eventually allow the Humankind to reach its final

destination.

Cinacchio Mathematica UGM 2011.nb 3

A generational spaceship as metaphor

of a perfectly closed society

In every society there are kinship rules, dictating who can marry who

(e.g., in some societies you cannot marry your siblings), and different

societies allow different mating. Using the metaphor of a generational

spaceship, in this project I will explore how a closed society can evolve

or die following different kinship rules, and with differents rates of gener-

ated offspring for each new generation.

For any given rule a labeled genealogical tree, ultimately composed of a

sequence of individuals, will be produced: it will be used to supervise the

application of the kinship rule and to illustrate how in that society

humans mate and produce offspring. A particular attention will be payed

to the kinship rule used at the present moment in many of the societies

of the humankind, that allow mating only between people connected by 4

or more kinship degrees.

Applying the selected rules I will try to discover whit what distribution of

probability for the generation of offspring at each new generation the

society inside the spaceship can stay stable and healty, grow exponen-

tially extinguishing the resources or be leaded to extinction.

Different numbers of people in the original crew will be considered, to

discover what is the minimum size of tree which can propogate and what

size is guaranteed to die out.

Cinacchio Mathematica UGM 2011.nb 4

What is a kinship rule?

Kinship is a relationship between any

entities that share a genealogical origin.

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