Children of Time

I've been watching my way through Deep Space Nine recently, and I just finished watching the episode Children of Time¹. Normally, I'm fairly forgiving of things that don't make sense in Star Trek, that's just to be expected because that's the sort of show it is, but there was something about this particular episode that I could not allow to pass by.

The premise is that the crew of Defiant finds a planet inhabited by their own descendants. Apparently as they try to leave, they're going to hit some space magic and go back in time 200 years.

Now, you may notice that I used the word "descendants" there, not "children" or even "grandchildren". Bashir meets his "great-great-great-great-granddaughter".

Let me run that by you again. Six generations. Two-hundred years.

And that's not where the madness ends. The planet has a population of 8,000. The Defiant's crew is 49 people, one of whom is terminally ill at this point. If every couple in each generation had an average of four children, that's still only a population of about 3,000 in six generations². Never minding that each generation could only have lived about thirty years.

And not only that, but Dax is on its fourth host³ since the accident (including Jadzia). From what I recall being told in earlier episodes, Jadzia herself could still be alive after 200 years. Even assuming she died young and her half-human offspring had a shorter life-span, there's still no way it could be onto body number four.

Just what the hell was going on on this bizarre colony? How did the writers arrive at these numbers, and how did they get through the script editing and so forth? How did no one go "Hold on a minute, 200 years doesn't seem like quite enough. Why don't we bump that number up a bit?"

Just what the fuck happened here?

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¹ Last week, when I wrote this.
² If my maths is wrong, let me know. I'm fairly certain that 8,000 is too high though.
³ Dax is a brainslug, Jadzia is its host body. But it's a nice brainslug, like a Tok'ra.