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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 6E16 operations per square centimeter per second; this is on the order of Ralph Merkel's speculation on the [[ http://www.merkle.com/brainLimits.html | computation power of the human brain]]. A 50 AU (7.5e12 meter) shell contains about 1E18 of those square centimeters. If the solar system gives birth to 100 million human minds per year, we have enough sites to upload those minds through life and organic death for 10 billion years, the remaining lifetime of the sun. 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 [[ http://www.merkle.com/brainLimits.html | 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.
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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 (25 microwatts per centimeter squared) maintains this memory, then we can store and maintain about 1e21 bits per square centimeter. 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.
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But there is probably no way to to that with a fraction of a milligram of matter. This will probably be the true limit; there won't be enough mass in the solar system for all that memory. At some point, our minds must migrate elsewhere. 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, than 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.

MORE LATER

Digital Immortality

Hyperspeculation follows. The idea is to explore limits, not make sober assessments of probable outcomes.

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.

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 through the whole 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, than 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.

MORE LATER

RwsDigitalImmortality (last edited 2015-01-16 04:55:02 by KeithLofstrom)