I think the Greatest Mistake is determined by the player itself. If the player decides to blow Earth up, sobeit.
If they're modeling it off Simmons like they hinted, it wouldn't be a long, over-time buildup (environmental degradation) or something as blunt as a war. It would more likely be an 1) acute event 2) resulting from technological hubris. (Trying not to give much away from Hyperion.)
Then again, I may be reading too much into the parallel. It's completely possible they just lifted the idea of the mistake and not any of the characteristics. Plus, I like the idea of it being either player choice or going entirely unmentioned, maybe with little hints dropped along the way. Letting/making the player's imagination run wild with it seems more powerful than any event they could script.
THE GREAT MISTAKE
From its very first incarnations, the Civilization series has always been grounded in human history. Since 1991, it's tasked players with building empires that would survive and thrive the test of time. Sid Meier's Civilization: Beyond Earth focuses not on the past, but on the future. And it needed a reason to be different, a narrative justification to take the franchise where no Civilization game has gone before.
Firaxis calls it The Great Mistake.
"The state of Earth a couple hundred years from now becomes rather dire," lead designer Anton Strenger told Polygon. "There's a series of events which we call The Great Mistake."
In the science fiction that forms the foundation of Sid Meier's Civilization: Beyond Earth, our home planet is no longer what it used to be. Humanity's future among the stars flows from those events, but Firaxis is making a choice. It knows what happens — everybody there knows what happens, so they can work from a common foundation — but Firaxis isn't going to tell players everything.
"Internally, we've written out exactly what those events are, but for the player, we're leaving it vague and allowing their imagination to fill the gaps," he said.
I hope they don't say.
One of Spider Robinson's books had time travelers coming back to 21st century earth to give us a few gifts to get us through the rough years ahead.
They didn't go into great detail about the catastrophes that had doomed humanity in their timeline, but one of the details they did give was both a funny and horrifying thought.
Nanotechnology with software errors.
Imagine bluescreening nanobots turning half the planet into grey paste.
If it was nanobots how did we not all die? Did we build nanobots to kill nanobots?
Apparently we can't actually have grey goo because they would generate too much heat, but I read that on the internet somewhere so take of that what you will.
The SMAC solution according to the that one wonder move was that they didn't do anything unless you slid in a programming transponder, which makes sense, but it makes me wonder why they couldn't have put in more dramatic technology turns against man scenarios in the game. What's stopping a scientist at the University from building a nanorobot which has its own power source and programming which is to build more of itself?
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I believe that the Great Mistake was giving Gandhi nukes, constructing the Internet wonder, and clearly building the Pyramids in a coastal city in CivBE Earth so that they would end up in the water.
Not sure that they thought so hard to adjust the night sky shot of the Earth though.