some machine that quickly and easily pulled
  carbon out of the atmosphere

I want this so we can colonize Venus.

It's pretty simple really - just put back all the binding energy we gained from burning up that fossil fuel, minus what earth was able to absorb in the meantime. Hint: Start as early as possible, because the risk for positive feedbacks to nullify your efforts grows every year.

Isn't Venus almost devoid of hydrogen? We're going need a lot of it to make water.

I wish I lived in your world. Mine only seems to be getting more and more divided. None of the leaders of the free (or unfree) world seem to have any desire right now to 'unite' it

Leaders? No. But many people do.

I thought it was the other way around? Until this year, all the leaders were all in on globalization, more open borders (in spirit if not in name) and huge free trade areas. The people revolted and put nationalism in charge in the forms of Brexit and Trump.

Global unity sounds like a dystopian nightmare to me. Are you sure you're not projecting here?

Present day reality lives like a dystopian nightmare to me. Pretty sure I'm not projecting. (God I hope I'm not!)

Global unity sounds to me like world peace. Maybe not every individual would be peaceful, but we could finally put away our silly flags.

Who rules this global unity? A government in Washington? London? The UN? People in different cultures want different things from their country. Just look at the US right now. Split down the middle between what kind of leadership there should be right now. And the US is fairly simple in that most people are happy to pigeon hole themselves as either liberal or conservative. On other countries things are more complicated. Ethnic groups who hate one another. Opposing Religions. Separatists. Unionists. In many countries there are separatist movements who want to split the country into smaller countries, because they don't feel like they are adequately represented in the majority.

It's a lot more complex than ditching the silly flags.

If the present day is a 'dystopian nightmare' to you, then I'm pretty sure you're projecting. Out of interest, if you feel we are in such a situation now, what would you classify the Soviet Union between the fifties and the eighties, or Nazi Germany, as?