Charles Stross, procrastinating:
Charlie's Diary: I'm going to assume no alien invasions or total collapses of technological civilization or significant asteroid impacts, because all three of these are rare in the historical record…. I'm also going to ignore space colonization…. I'm going to assume that we are sufficiently short-sighted and stupid that we keep burning fossil fuels. We're going to add at least 1000 GT of fossil carbon to the atmosphere…. So the climate is going to be rather ... different.
Sea levels will have risen by at least one, and possibly more than ten metres worldwide. Large chunks of sub-Saharan Africa, China, India, Brazil, and the US midwest and south are going to be uninhabitably hot — that is, too hot for non-GM plants and organisms to survive in during heat spikes, and with heat spikes over 44 celsius at night lasting at least two weeks every year (sufficient to kill off anyone without air conditioning). As 80% of today's human population live within 200Km of a coast, there will have been mass migrations and resettlements….
Energy and technology: I think there's a high probability (approaching certainty) that we'll be running on a de-carbonized energy cycle by then….
Political/demographic change ... Five hundred years is a nearly unimaginable gulf from today's perspective. Five centuries ago, the Portuguese conquistadores were beginning their rampage through South America; Martin Luther was finishing his doctorate in theology and thinking about sin: the huge sequence of civil wars that racked Japan for over a century were raging: the Great Powers were still the Chinese empire and the Caliphate (although the latter was undergoing a shift in center of gravity towards Istanbul and the Ottoman empire). The great powers in Europe were Spain and Venice; the English speaking world was a few million barbarians occupying a handful of damp islands on the outer fringes of Europe…. The half-life of a public corporation today is about 30 years: ten half-lives out — 300 years hence — we may expect only one in a million to survive.
Looking forward 500 years requires us to make some assumptions…. We appear to be living close to the peak of a demographic bubble that will see our population max out or be in decline by 2100…. [D]emographically, the world of 2512 isn't going to resemble our world very closely at all, although it's anyone's guess at this stage as to who will prosper…. One key issue is that during the age of cheap oil (i.e. right now) a whole lot of cultural mixing is going on, on an unprecedented, planetary scale. We have become an urban species, and I see no high probability of that state changing and the bulk of humanity reverting to a low-density agricultural (much less hunter-gatherer) lifestyle. Over the next century we're going to be doing a lot more cultural remixing; many niche languages are becoming endangered while 3-5 major languages are becoming global lingua francas — English, Mandarin Chinese, Arabic (although Arabic is balkanized), Spanish, Portuguese….
I'd like to believe in Steven Pinker's pacification hypothesis…. But even if he's right in the long term, there are regressions along the way…. I suspect the hypothetical no-collapse-of-civilization world of 2512 will harbor a myriad of conflicts, but they'll be played out in ways incomprehensible or invisible to us. We're already living into an age when developed nations prefer to send drones instead of human soldiers where possible: and where information war is an actual thing, not just a bullshit marketing proposition. Go forward 500 years and extrapolate from today's Predator drone, analogizing it to a 1500s arquebus ... it's not pretty.
Speaking of regressions: racism and race politics as they exist today are largely a side-effect of the perceived need to find a moral basis from which to defend the African slave trade, followed by rationalisms based on a half-assed reading of evolution. Older strains of racism and intolerance hinge on religious absolutism. Sexism emerges from the defense of patriarchal status. I see none of these constructs as inevitable, and the status of women in particular is drastically affected by the demographic transition….
The biosphere on 2512 Earth isn't going to look much like ours. That we're living through a great extinction event is obvious, and the level of climate change we can expect in five centuries means this will have run mostly to completion. On the other hand, it's almost a certainty that if we're still around in five centuries, we'll have extensive experience in synthetic biology, and not just at the single-celled level….
I'd expect to see lots of — to our eyes — odd vegetation. Freeman Dyson's suggestion of GM mangroves that can grow in salinated intertidal zones and synthesize gasoline…. Variant food crops that can grow in 50 celsius climates and still make stuff we can eat would be a bonus. Modified animal or bird pest species, re-purposed as agricultural stoop labour? It might be easier to work with the intelligences that nature's dropped all around us rather than trying to design artificial ones from scratch. (Think raccoons. Think raccoons programmed to come out at night to harvest and wash fruit because we've invented raccoon Heroin™ and trained them to take their fix in payment for crop-picking. Or something like that.)…
Other neck-sticking-out projections?
I doubt the United States of America will exist in 2512. I doubt the United Kingdom of Great Britain and Northern Ireland will exist in 2512. I doubt that the Peoples Republic of China will exist in 2512. (The Japanese monarchy ... maybe, if they haven't been inundated.) Our existing geopolitical boundaries are going to take a shoeing from rising sea levels and changing demographics. And our existing political arbitration mechanisms are already taking a shoeing from communication and data mining technologies…. I don't expect off-planet trade to amount to much…. [T]here's a hard floor under the energy cost of getting a canned ape into orbit — namely the mass constraint imposed by canned ape plus life support, and the reaction mass and energy needed to shove it up to around 7.5km/s — and we really don't want to be using excessively high energy power sources in a biosphere we have to live in…