Digital Immortality
Hyperspeculation follows. The idea is to demonstrate some remote limits, not make sober assessments of probable outcomes.
Blogging, Twitter, and Uploading
We are not creating vastly more "Literature", but in an age of blogs and facebook and twitter, we are storing vast amounts of our experience and conscious thoughts online. We will find more efficient ways to do this, more channels from brain to computer, and learn to capture other outputs, like facial expression, pheromones, body chemistry, etc. As the twitter generation ages, and some suffer from memory loss, individuals will cross a threshold where more of their accessable knowledge and experience is stored on computers than in their brains. Although existing software cannot assemble this knowledge into a personality, or even an autonomous extension of individual will, we are approaching that capability. eBay, Craigslist, and automated market trading are the bare beginnings of this.
More information, with less speculation, will be captured about average individuals born in the 21st century than for any famous individual of the past. No king, surrounded by a retinue of observers and scribes, will leave as much personal information as a convenience store clerk in the future. Our digital records are far more traceable to verifiable events than any history, biography, or scripture of the past.
Imagine enough durable, redundant storage in deep space to keep track of these memories, along with measurements and images of the physical environment in which they formed. Assume that at death, brains are cryonically preserved, retaining evidence of the physical hardware and chemical state that held those memories. The brains are scanned and digitized, and that huge data set is added to the externally captured memories. While physical continuity is interrupted, in time it will be possible to combine all that data into an artificial mind, with memories, relationships, and goals closely resembling the original.
Indeed, such reconstructions may become "realer than real", better able to learn and grow and influence the environment than the original biological brain. More likely, though, the biological and computational brains will be merged, very tightly linked, with the biological brain withering with age, while in-skull and out-of-skull computation and communication grows. At some point, the bio-brain dies, and the atoms are recycled into new humans. The computational brain can now travel freely, at the speed of light.
This is not true 100% immortal identity. But for those of us who identify ourselves by memories, relationships, and goals, and who lose conscious continuity every time we sleep, this may be a difference in degree only.
Energy and Computation for Quintillions of Minds
DysonShell is a wild speculation about the construction of a 50AU shell around the solar system, capturing the 99.99%+ of the sun's energy traveling past the planets of the solar system into empty interstellar space. The energy can be used for computation, but some can be used to maintain vast amounts of self-correcting energy storage.
The shell temperature is perhaps 56K, and the power density is 550 milliwatts per square meter. A computational bit change at 56K is on the order of kT, or 5 meV (milli electronVolts), so we might be able to perform 6E20 operations per square meter per second; this is four orders of magnitude larger than Ralph Merkel's speculation on the computation power of the human brain. A 50 AU (7.5e12 meter) shell contains about 1.5E23 of those square meters. If the solar system gives birth to a 100 million human minds per year, and the sun's lifetime is 10 billion years, that will require "only" 1E18 sites, only a few parts per million of the total.
Far more minds may be "born digital", or born as the descendants of earthlife around other stars. Even with great wisdom, abundant energy, and off planet support, the earth may not be able to endure 10 billion people in the very long term. With present destructive technologies (primarily traditional agriculture) the Earth would eventually be "used up" by less than a billion people. However, I am assuming we will eventually get things right, and we will learn how to adapt our demands to what an enhanced natural world is capable of providing over the very long term.
A 50 AU shell is 14 light hours across. Traveling between opposite sides of the shell at the speed of light will be faster than traveling to the opposite side of the earth in jet airplanes.
The sun is growing hotter, and the inner edge of the "Goldilocks zone" will sweep past the earth in less than 500 million years. Even with technological enhancements, and shifting the earth's orbit, we probably won't be able to support organic life on the earth after the sun evolves into a red giant in 10 billion years. But we will have quadrillions of minds for billions of years to invent workarounds; I don't have to do that here.
Information storage
Besides all that thinking, we will be storing memories and protecting them, and that would rapidly outstrip the storage capacity of the atoms available. So the real limit will be memory. A room temperature silicon NVRAM has an activation energy on the order of 1eV and a failure rate of 1 bit per 1Gbit array per 1 year or so at 300K (WAG). We can correct shell memory far more often if it is continuously powered. An error rate "figure of merit" might be bits * time * exp( -ActivationEnergy/kT ), or 1E9*3E7*exp( -1/0.026 ), about 1 second. The average survival time per bit is 1 billion years. If we use a lower energy process with 100meV activation energies, and 5meV temperature, the survival time per bit drops to 16 years, about half a billion seconds. Assuming we need to perform 100 logical operations at 5meV each to test and correct a bit, 0.5eV total, and do it every 5 million seconds, we need to expend 1E-7 eV/sec-bit (or 1.6e-26 watts/bit) on memory maintenance. If half our power (250 milliwatts per centimeter squared) maintains this memory, then we can store and maintain about 1e25 bits per square meter.
But there is probably no way to to that with a few grams of matter. Atoms, not power, will be the limit for storage. Assuming a more reasonable 1e21 bits per square meter, then a meter-squared mind accumulating 1e4 bits of memories per second, could accumulate that many memories in 3 billion years. We can assume sharing and networking of some of those memories between many minds, which may require less association for observations and facts, more storage for associations.
Conclusion
It is silly to predict 100 years into the future, much less 10 billion. However, with the technologies we can imagine today, there is room for enormous growth in the amount of intelligence the solar system can support; that intelligence can create a far more abundant and comfortable future for itself, so the extrapolations above are both inaccurate and far too pessimistic. The question is not whether there is an abundant future - there will be - but how we personally can help establish and participate in it.