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As Iain M. Banks said in A Few Notes on the Culture, the population growth was very slow, as the convention was that each person should give birth to one child.

As the life expectancies remain constant in about 350-400 years, and immigration is not encouraged, how can the number of citizens increase from 31 trillion in 22nd century CE (told in Look to Windward) to 50 trillion in 29th century (told in Surface Detail)? Only by new built machines?

Note: The Culture population growth is about 0.068% yearly in that period, compared to current 0.05% in Europe, 0.75% in North America and 1.1% in the world.

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    He also mentions that "In practice, the population grows slowly. (And sporadically, in addition, for other reasons, as we'll come to later.)"* – Valorum Mar 2 '17 at 13:37
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    I thought people expected to 'have' two children - one as a man and one as woman. Hence the Genar-Hofoen Dajeil sub-plot in Excession – Glimmervoid Mar 2 '17 at 14:05
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    Does the Culture really discourage immigration? ISTR individuals or even whole civilizations can join the Culture, if their beliefs are compatible with Culture standards. – Royal Canadian Bandit Mar 2 '17 at 14:15
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    @Glimmervoid: if we assume it takes two to make a child, we are still at one per person. – ths Mar 2 '17 at 16:07
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    I'm also not sure that the Culture does not encourage immigration. I believe people and groups can join the culture, in fact do so by simply stating they are part of the culture and acting like it. – DJClayworth Mar 2 '17 at 16:47
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Surly it depends on when people have children.

If you live to 500 but have a child at 20, and they have a child at 20 you can easily cover that population growth. There would just be a lot of concurrent generations living.

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    Yes, you are right, but this cannot be maintained in time for a long time (the culture exist for thousands of years) – greuze Mar 3 '17 at 10:58
  • @greuze: Exactly, the death rate of those baby boomers would catch up with the birth rate, evening out the overall population increase. So there would be an equal amount of concurrent generations dying. – user100501 May 18 '18 at 15:27
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The Culture is inclusive, in that nothing is really forbidden. While the convention is that people will on average have only one child per person, there will always be those for whom having lots of children is a personal imperative.

This can be seen even in the world today, while conventionally in the West the classic family size is "2.4" children there are people who will significantly exceed that. The Bateses and Duggars in the US at the point of the article in 2012 had 19 Children each, despite the convention that families have 2.4 children. Imagine the family sizes if they lived to be 350!

The mention of "sporadic" growth in the notes suggests one of two things to me. Immigration or absorption of civilizations, which has been discussed in the comments on the OP. Or having babies suddenly becomes fashionable in a cyclical pattern. Over a 350 year life period, during most of which the individual is fertile leaves open the possibility of large numbers of people having an "extra" child if they've already had the standard quota, but having a baby has suddenly become a meme. While culture civilization is mature, not everyone in it has to be.

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I think Royal Canadian Bandit nailed it in the comments. The expansion of the Culture's population is achieved through the influence and acceptance of other civilisations into it rather than making lots of babies. I'd venture further, however, and say that it is deliberate, or at least wilfully tolerated. Although Iain Banks does say in his notes that the Culture does not "actively encourage immigration", in the very next sentence he articulates the means of their expansion:

Contact's preferred methods are intended to help other civilisations develop their own potential as a whole, and are designed to neither leech away their best and brightest, nor turn such civilisations into miniature versions of the Culture.

Since "potential" is from the perspective of the Culture, it is defined by Culture values. Therefore, Contact mentors other civilisations towards a future state that is morally in line with that of the culture itself, at which point it is indistinguishable and becomes a part of it by default. While its conscious aim is not to turn them into mini-Cultures, the end result is just that.

Flere-Imsaho in The Player of Games provides one of many examples of the purposeful influencing of a civilisation's path to one more closely aligned with the Cultire's values, implying careful consideration of the options to achieve the desired end-state (spoiler alert).

"The Empire's been ripe to fall for decades; it needed a big push, but it could always go. Coming in 'all guns blazing' as you put it is almost never the right approach; Azad - the game itself - had to be discredited. It was what had held the Empire together all these years - the linchpin; but that made it the most vulnerable point too."

As well as the means, Banks also discusses the Minds' and humans' benign motivations for meddling:

Interest - the delight in experience, in understanding - comes from the unknown; understanding is a process as well as a state, denoting the shift from the unknown to the known, from the random to the ordered...

The humans of the Culture, having solved all the obvious problems of their shared pasts to be free from hunger, want, disease and the fear of natural disaster and attack, would find it a slightly empty existence only and merely enjoying themselves, and so need the good-works of the Contact section to let them feel vicariously useful.

Guiding another race towards your own set of principles is morally ambiguous to say the least and the Culture is acutely aware of this. In Use of Weapons Sma sums this up nicely when justifying the existence of Special Circumstances:

“We think we’re right; we even think we can prove it, but we can never be sure; there are always arguments against us. There is no certainty; least of all in Special Circumstances, where the rules are different.”

This acknowledgement of the limits of their own knowledge supports the idea that they are doing it all out of curiosity. And as true scientists they appear open to the idea that other races could influence them in turn (rules being different), albeit through the concentric layers of SC, then Contact, then the civilisation as a whole. They and Iain Banks are perhaps a little embarrassed by the hypocrisy of their actions, but they can't help themselves.

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