By "spacefaring" I mean the ability to live in/utilize space (asteroid mines, fast travel like lightspeed, harnessing greater energy sources, terraforming planets, etc.)
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The only reason for us not being able to get to that point is if we kill ourselves off. We could go into another dark age (albeit a short one) and still be able to make it in time. If nothing goes wrong we'll probably be space faring within the next 100 years easy.