What will the world be like on 2100?

I might be excused for hazarding guesses I know to be wrong, via my own reasoning, but if I had to guess I would make these guesses:

• The USA will remain the worlds most powerful and significant nation.
• China growth will stop somewhere just under US GDP because its export dependency places a limit upon its growth.  Japan, Taiwan and Korea have grown rich but have not been able to break out of the limitation to their economies and China will face the same problem.
• The EU and the Euro wills survive, but expansion will be extremely slow if not stopped, and the EU's lack of strong central government, UK full participation, and the weak Federal system in Germany will make it a basket case Confederation.  They will not be able to break it up, but given the political situation in the UK and Germany they will not be able to fix it.  So the EU will be a critical economic and R&D centre but nothing more.
• Despite current problems India will slowly emerge as a global power, just much more slowly than people were thinking a few years ago.  India has massive problems to overcome, more than China did, but it also has strengths of education and ingenuity that will enable it to overcome it.
• It will be hotter, but global warming impacts on population will be tiny.  Things will be a bit more uncomfortable or harder to do, but civilisation will adjust.
• The world population will be smaller than it is today, but not radically smaller, to take a guess I would say maybe 5 billion.
• Capitalism and Representative Democracy will not be the global standard, the end of History stuff will end up being a flop.  Half the world's population will live in authoritarian regimes, Capitalism in the West will be dependent on Government power and spending, and many more nations will be openly Socialist, though not really in the Cuba or USSR model and not in a consistent or well worked out way.

BUT:

Well this is really impossible to answer in any real detail.  We can make guesses about the population, the GDP, the climate and the relative distribution of wealth, but we can not get the fine level of details right like the people who will come to power, the ideologies that will emerge, or the specific things that will be created and adopted.

And human society is a highly chaotic system, small variations in initial conditions will create great difference over relatively short time frames.  Clearly these variations are far smaller than our ability to measure of even quantify.

For example take the birth of one person. In 1912 Alan Turing was born.  His contribution to WWII may have, by itself, made sure the Allies were ready to invade France by 1944, meaning Western Europe was Capitalist and Democratic, meaning they would grow uncompetitive and in debt buying massive amounts from China.  The entire global structure may have been different if Turing was never born, it the Enigma code was broken 6 months later and the German U-boat war was able to delay the Allied landing in Normandy by a year giving the Russians time to win the war entirely.  Maybe.

But also the pace of computer development without a few brilliant men like Turing would clearly have been different.  

So it is really impossible to make any solid predictions about anything in detail more than a few years out, and this inability to make solid predictions on detail make it impossible to make firm predictions about the overall picture.