MatryoshkaNet is a lighthearted, unrealistic transhumanist setting. I made it up as an exercise in wish fulfillment: what kind of world would I want to live in? My biggest influences are probably Eclipse Phase, Star Trek, and the Culture.
The year is 3122. Most people are more like artificial intelligences than living creatures. There are about half a trillion of them, and each has a quota of processing power and storage space in a matryoshka brain around Proxima Centauri called the Internet.
Some 150 billion of the people who live on the Internet, called chimps, were originally ordinary humans who lived and died on Earth (or some other physical location, like a space station). Their brains were probabilistically (but highly accurately) reconstructed and then encoded as machine intelligences. In fact, all humans who ever lived are now on the Internet, except for some 3 million who voluntarily left the Internet to become purely flesh-and-blood people called cons. The remaining 350 billion people now hosted on the Internet are memes who were deliberately created by preexisting people. The Internet is constantly expanding, with part of the new storage space and processing power divided up among all extant people to extend their quotas, and part being devoted to new memes.
Life on the Internet
It turns out there are many advantages to being an artificial intelligence. So long as the Internet's arrangement of backups holds, people are immortal, which most people agreed is obviously awesome once you actually have it. They're vastly smarter than any flesh-and-blood human ever was. They can alter their own personalities at will by rewriting their code. They can communicate instantaneously with all other Internet citizens and give themselves whatever simulated experiences they like. To interact with the material world, they can use various technologies for remote control to build bodies (organic bodies, starships, Roombas, etc.), move them around, and perceive through their sensors. Faster-than-light communication is routine (the secret turned out to be putting very tiny spoilers on photons). Faster-than-light travel of material objects is not quite possible, but you can always destroy something at one place and recreate it at the other, and modern people are smart enough to realize that philosophers were being morons when they complained about how this wasn't good enough.
The Internet is a post-scarcity society. The only meaningfully limited resource is the Internet itself. An individual person could use some of the universe's many raw materials to build more computers and disks, but it's a meaningless exercise, like a billionaire cutting coupons—a drop in the bucket compared to their Internet quota. Their own quota grows much faster, via Internet expansion, than they alone could add to.
The Internet is a direct democracy. The psychological issues that make 21st-century democracy hard, as well as many other weaknesses in human personality, have been effectively removed from most people, by editing one's own code. People in general are thoughtful, kind, tolerant, generous, wise, and morally scrupulous. Every person gets an equal vote on all policies, with the exception of the process for creating new memes, which is called sex. During sex, younger people's preferences count for more; this arrangement, called the law of sexy young'uns, was decided upon to keep society from being dominated by ancient social groups that kept reproducing themselves. Everybody gets to contribute to each meme (it's more like a massive orgy than a beast with two backs), but younger people are allowed to contribute more code, so e.g. Plato only gets to have much influence on the final product by convincing a lot of memes to use his ideas.
Crime, such as trying to use other people's Internet quotas without their permission, is rare, because it's punished with personality rewriting to prevent reoffending. Still, there are some paranoid people, such as Ken Thompson, who suspect there's a mass of underhanded code somewhere out there that's so subtle that even the scrutiny of billions of superintelligent people won't prevent the day that a switch flips and half the memes born in the last century turn into some kind of Dawkinsian selfish-meme nightmare. Most people try not to think about this too hard.
Time travel, in the sense of actually affecting the past or the future, has turned out to be impossible, which was probably the biggest disappointment of the 29th century. However, there is software called time tubes that allows viewing the past, from most any point in space. Time tubes work by probabilistically reconstructing the past from the present. Their most important use was in creating chimps, the modern Internet equivalents of dead humans. During the process of constructing chimps in the late 2700s, there was substantial controversy about resurrecting especially infamous people, the most controversial of which ended up being, of course, Adolf Hitler and Herostratus. In the end, the rule of universal resurrection won the day, Hitler mellowed out and was forgiven now that all his victims are in better health than ever, and Herostratus almost immediately tried to crash the Internet and got his personality rewritten so that he didn't do it again.
Identity is a much more flexible concept on the Internet than in the 21st century. Many chimps have no remaining sense of loyalty to what their original bodies looked like, and memes never had an original human body to start with. Some chimps still have gender identities, but very few memes do. Formally, each person's name is an integer designating their order of birth (so the very oldest person is named 1, the second 2, and so on—1-based indexing for this barely beat out 0-based indexing at vote), but lots of people have other informal identifiers that they use sometimes. It is quite possible for a person to split their computational resources into being multiple, somewhat less intelligent people. For example, the current quota is more than enough for a single person to run the minds of the entire world population of 2020, with lots of resources left over; combine that with plentiful material resources for making and controlling human bodies and a person can be the entire human population of 2020, although, to be honest, they'd probably prefer 2019.
"Con" stands for "bioconservative", "conviction", "downside", and arguably also "confidence trick". It refers to the small minority of people who didn't ultimately decide that living on the Internet, and more or less being a god, is way cool. They relinquished their Internet quotas and asked to be put in human bodies with real human brains and nothing else. More specifically, cons are people who decided to become cons and then didn't immediately change their minds and return to the Internet within minutes, as most would-be cons do. No memes have ended up as a con, only chimps. Notable cons have included Neil Postman, John Searle, and Leo Tolstoy (by now, all are dead for the second time). Ted Kaczynski tried it for a week and then fled from a lynch mob back to the Internet. He's back in mathematics, dabbling in ecology, and is much happier now.
The cons were given Australia to live in, because that only seemed appropriate. The Internet doesn't interfere with them except to prevent cons from leaving Australia and to readmit cons who ask to go back to the Internet. A con formally requests readmission by yelling at the sky "I'm sorry, okay?".
Australia is run as a republic with a strong central executive, who is known to the cons as the president, but is more usually referred to on the Internet as King Con. Digital computers are banned, freezing technology at approximately a mid-20th-century level. The population of cons has decreased over time, because cons are mortal, the supply of chimps was finite from the beginning, the initial population of cons was 90% male, a lot of the initial population were computer-security experts with little interest in reproduction, and children born among the cons often end up defecting to the Internet, despite elaborate society-wide attempts to keep them from learning that the Internet exists. The Internet is pretty sure that the last con will be dead by 3500.
Lots of people, not just cons, like to have bodies and interact with the material world, at least sometimes. Here are a few locations on Earth where notable material special-interest groups do their business.
The Pornhub is an area dedicated to eroticism that's roughly contiguous with Los Angeles County. Here's where people go to have sex the old-fashioned way or enact previously impossible fetishes like being vored by a 50-foot-tall slime woman. You could just simulate sex on the Internet with all the same sensory details, of course. Or you could give yourself pleasure with no intermediary. Or, most commonly, you could just rewrite your personality so as to make "pleasure" coincident with goal-oriented morally acceptable behavior, and not bother with feelings or experiences for their own sake. Still, people sometimes want to bang, and the Pornhub is a popular place for it.
The Big City is a colossal mass of structure and machinery covering much of the northeast US and eastern Canada and also going far underground and into the sea. Part art project, part engineering experiment, the Big City is full of fanciful robots, vehicles, buildings, and other gizmos. On its western frontier, there is a concentration of biology, with lots of partly and fully organic machines, such as a colony of wheeled parakeets.
Dragon Dungeon, or "D&D" for short, is a vast complex deep beneath the surface of Antarctica that's full of hideous monsters, fiendish traps, and sparkling treasure. The lethal hazards are harmless to people who are not bound to physical bodies, and the treasure is of no value in a post-scarcity society, but they're amusing all the same.
Central Park comprises much of continental Europe. It preserves wildlife as well as artificially designed living things of various kinds, segregated into 1,000 distinct 100 km × 100 km artificially created and reinforced habitats. Even non-Earthlike environments like the crushing inferno of Venus are represented.
The Wonderful World of Science is a wide strip of Asia that's used for scientific research. If you want to do really big things, like cut a planet in half to see what's inside, you have to go elsewhere, but if you don't need a huge amount of space and you like the idea of being physically close to other researchers and their experiments, the World of Science is the place to be. Trying to solve problems in science, mathematics, and philosophy, of which there turns out to be no lack despite the human condition being so good, is a popular pastime these days.