It’s pretty difficult to imagine a world relatively far after a technological singularity. It’s important to understand the the most important limitation for such a civilization is the speed of light. Therefore any such civilization will put a lot of efforts into trying to breach that barrier by creating fast than light travelling methods or materials in which the speed of light is increased. For the sake of simplicty I will assume here that that’s not possible.
Computronium
Not let’s come to the basics of a post-singularity civilization: Computation. After greater than human intelligence is developed, progress will be very very fast, so we can expect to have a rather ultimate atomic computation substance, called atomic computronium. How fast could this computronium be?
Computronium computation
Here I will just give very rough estimates to get the area of orders of magnitude about right. I’m not an expert in this field, so I may be horribly wrong, but even that won’t affect the qualitative results a lot. For my guestimations I used an essay on the question “How fast is the brain?” and some rather old texts from Hans Moravec:
Let’s assume that atomic computronium consists of groups of atoms which calculate with visible light, which has a wavelength between 400-800nm or 1.3-2.7 lfs (light femtoseconds, the distance light moves in a femto second, which is a millionth billionth of a second). These computations with photons would make computations on the femtosecond scale possible, so we would basically have a PetaHertz computer (which is about a million times faster than what we have today). How many atoms do we need per computation unit? Let’s assume that we need about 1000 atoms for a single calculation, which would result in the computronium doing 10^12 computations per atom and second.
What kinds of atoms will be used? That’s hard to tell. Using lots of carbon or silicon would make sense, because those materials are widely available and have good chemical properties. But possibly many heavier elements are needed, so let’s assume an average atomic weight of 50 g/mol (about 6*10^23 atoms would weigh 50 g). Perhaps some very spongy of foamy structure of that material is needed for some reasons, for example making compliated three-dimensional structures possible, so let’s assume for the sake of simplity that computronium only weighs 1 g/cm³. At that density one cm³ would contain about 10^22 atoms, together doing 10^34 operations per second. That’s as much as 10^18 humans can do in a second, if we assume that a normal human does 10^16 operations a second. A volume of the human brain filled with computronium would match more than 10^21 humans, which is roughly as much as could fit into our whole galaxy if every star had about one inhabitable planet.
Computronium memory
We’ve seen that the computation speed is immense, but what about memory? If we rather store the information in low-energy photons instead of the atoms themselves, then we could get a storage density of about one Megabit per atom at the very physical limits. Thus, for our kind of computronium we can assume one kilobit per atom relatively safely. Our cube of one cm side length could store 10^25 bits of information. If we assume that a human brain can store 1000 Terabit of information, then our small cube could contain 10^10 human minds, that’s more than the current human population of earth. Here we see that memory would probably pose a much bigger problem when simulating human minds on computronium than raw computing speed.
As a side note, you could store all of your mind’s content on a couple of today’s harddrives for a total cost of less than 10 000 €! The real problem for this kind of storage is just the extraction of that data. If the human brain could be scanned in a resolution that’s high enough and in a manner that’s cheap enough, making a brain scan would be an interesting alternative to cryopreservation of the brain.
Thinking speed of uploads in computronium
Now, we will consider rather “average” post-humans which could use about 10 Petabit for a start. A mind of a post-human would fit into one cubic millimeter. At what speed could such a post-human compared to one of today’s humans think? As 1 mm of computronium does 10^15 times more operations per second one would assume that the thinking speed is that much higher. But that’s a too simple approximation, because for holistic / integrated / conscious thinking the whole brain has to take part in the computations, so we have to consider how quickly the information is transmitted in the computation medium. Say humans need about 300 milliseconds = 3*10^-1 seconds for an isolated conscious “think”. Light needs about 3 picoseconds = 3*10^-12 seconds to pass through one millimeter of space. Therefore, such post-humans run on computronium could think about 100 billion times faster than regular humans – at least on an integrated level which would allow conscious thoughts.
Energy and waste heat
Makting those estimates we have completely ignored problems like energy consumption and the creation of waste heat. Those factors could reduce the performance of computronium dramatically, so that everything has to be slowed down by some orders of magnitude to prevent overheating or too high energy consumption rates. Those problems could be countered by almost always using resersible operations which don’t increase entropy. But for information processing you need at least some irreversible operations and for conscious thinking where you don’t just want to percieve (and remember) the results of your thoughts, but also your very thoughts themselves, you will probably need a lot of irreversible operations. Anyway, I guess it is still safe to say that post-humans will think at least a thousand times faster than the humans of our time.
Nucleotronium
Until now we just considered atomic computronium, but what if we could use compressed nuclear matter, like the stuff which can be found in white dwarfs and neutron stars, for computation? The diameter of an atomic nucleus is about 100 000 times smaller than the diameter of the atom itself, so will everything be five orders of magnitude better? Probably it’s not that simple. Let’s take a closer look at some possible nuclear computronium, or nucleotronium.
Nulceotronium computation
Instead of using visible light, nucleotronium would use gamma rays for computation. The wavelength of gamma rays lies in the picometer or the light zeptosecond scale (10^21 zeptoseconds = 1 second). ZettaHertz (10^21 Hertz) computing might be technologically extremely complicated, because using nuclear matter in a meaningful way that allows effective computation is everything but a trivial task. But post-humans are perhaps clever enough just to need 10 000 nucleons for a single computation, so we would end up with around 10^17 computations per nucleon and second, which is actually 100 000 times faster than atomic computronium.
Nucleotronium memory and thinking speed
Memory could maybe be stored in quantum states of nuclei, perhaps at a rate of one bit per 10 nuclei. Because the density of nuclear material is about 15 orders of magnitude higher than that of normal matter, a volume of just one cubic nanometer would contain about 10^16 nuclei, storing a whole Petabit, which is at least enough for a human upload. Light would only need 3 attoseconds to run through the whole of that nanobrain, making that human think 10^17 times faster than a normal flesher. Such an uploaded human would experience the whole lifetime of our cosmos until now in only about 4 seconds of objective time! Interestingly, the approximation of thinking speed in nucleotronium based on limitation from the speed of light coincides with the approximation based on raw computing power. Therefore, there’s not much room for computing anything else but the pure thinking processes if an uploaded mind runs at maximum speed. That mind would have to create its own world, which means it has to dream all the time. But I think, dreaming for billions of years will get boring, sooner or later.
Problems with nucleotronium
Wait a minute! How can we use superdense nuclear matter for computation when that is only found in white dwarfs and neutron stars in nature? In order to create the pressure in a white dwarf you would basically have to build … a white dwarf! So, if you don’t want to let our homestar collapse into such a star or travel to another star system you would have to be more creative. Maybe you don’t need extreme pressure to create states of matter with extremely high density. There are quite exotic states of matter such like Bose-Einstein condensates, which have various interesting properties. Even if Bose-Einstein condensates might not be useful for creating high density nuclear computers we may find another way to do so. While it’s hard to think of a really practical method for us to create nucleotronium now doesn’t mean that it is improssible, but just not easy for us to do.
However, there is a problem which is rather obvious: You would need a whole lot a energy to get matter to accept that kind of unnatural state. That, in turn, means this nuclear matter will emit that whole lot of energy in an instant if it leaves that unnatural state. Form that point of view, having a nuclear computer is roughly equivalent to possessing a nuclear bomb which could go of accidentally if the machinery preserving the exotic matter state malfunctions. Hence the possession and control of nucleotronium will most likely be strictly politically regulated, if not prohibited entirely.
Computing with phonons
Instead of using photons you could use phonons for computation in atomic or nuclear computronium. According to the background information of the sci-fi universe Orion’s Arm a phononic computer would be faster than a photonic one, but the data for a 1 cm³ computer given there are 5*10^21 operations per second and 5*10^20 bits of memory, which is actually worse than the type of atomic computronium I have speculated about.
Plasmatrononium
While computronium and nucleotronium probably would need extensive cooling, there is also the theoretical possibility to compute with very hot plasma. What properties would some kind of plasma computronium or plasmatronium have? According to an article in the issue from 2005 January of Spektrum der Wissenschaft (German version of Scientific American) by Seth Lloyd and Y. Jack Ng the memory would be about the same as the one of photonic memory computronium while every particle would compute up tp 10^20 operations per second, which is eight orders of magnitude faster than that of atomic computronium. Plasmatronium probably wouldn’t be used for simulating conscious thoughts, but rather for less complex programs which need an awful lot of calculations, for example simulating virtual worlds in extremely high resolution.
Black Hole computing
According to the same article as mentioned above it could be possible to use tiny black holes for extremely rapid computations. A small black hole of 1 kg mass and a radius of 10^-27 meters would calculate 10^35 operations per second and store 10^16 bits of memory and evaporate into Hawking radiation after 10^-21 seconds. A post-human mind of 10 Petabit injected into such a black hole would operate at a speed 10^19 times faster than a normal human brain would do. It’s probably the most excentric computation machine in our universe. A nucleotronium computer with 10^18 nuclei would store 10^17 bits and run also run at 10^35 operations at second, so it would do roughly the same job, but use up 100 cubic nanomters of space. It’s quite probable that black hole computers would not be practical at all, because the size and complexity of the machinery needed for extracting the information from the Hawking radiation, to create those black holes and to feed them with the right input would reduce the efficiency of the whole black hole computer below that of usual nucleotronium (unless it is not possible to build efficient nucleotronium at all, of course).
Storing information in dark energy
Another information which can be deduced from the already mentioned article is that dark energy (if it actually exists) could store up to one Exabit per cubic nanometer, which is a thousand times more than a cubic nanometer of nucelotronium could contain. If we could find a way to manipulate dark energy effectively it could be used as ultimate data storage.
Quarktronium
Maybe there is some other way to use quarks and gluons for computing except in the form contained in nucleons. Such a form of quark nucleotronium, or quarktronium could be a few orders of magnitude faster than nucleotronium. The likeliest scenario I can imagine is that quarktronium would compare to nucleotronium as plasmatronium compares to normal atomic computronium.
Computation on spacetime itself
Until now we considered particles for our computations, but what if spacetime is a grid of discrete elements of spacetime units? If we could store information directly (instead of using any “material” particles) in that discrete grid and somehow make computations with it, we would have the absolutely ultimate computer. The feasibility of that approach depends on the exact structure of spacetime, which isn’t known, yet. However, if it is possible to develop such technology, it would most likely be so advanced that all other technologies would be abandoned, and the civilization that invented it would simply transcend so thoroughly that we would see no signs of its existence. It would surely also be able to remove all signs of it ever having existed on this level of reality, which is a possible explanation for the Fermi Paradox.
Quantum computing
All former considerations were of a rather classical nature, so what happens if we include possibilities like quantum computation? At least it would provide a dramatic speedup for a lot of algortihms and would make it possible to simulate physical problems and virtual realities at levels of precision which are only found in the real material world. However, it is hard to tell whether quantum computing can be used to speed up conscious thinking. After all, quantum physics is just a result of the relationship between subjectivity and objectivity, which is a new insight I have attained recently and will explain at some time in more detail. Maybe there would be no advantages of simulating minds or even just parts of a single brain on a quantum computer, and maybe strange phenomena, which are so absolutely weird that even I am unable to imagine them, would occur when doing so.
Quantum effects are everywhere
You could insist that all those kinds of computation substrates I have mentioned above are all at working at quantum levels, so that all of them would be basically quantum computers. While it’s true that quantum effects play a vast role in those computers that doesn’t turn them into quantum computers in the way they are defined. For a real quantum computer you need to create entangled quantum states; the more the better (the more qubits). Entanglement doesn’t appear just accidentally but has to be enforced artificially, which is rather complicated. Therefore we would still see a difference between “classical” computing and “entanglement” computing. It would be a good idea to call quantum computers entanglement computers instead, in order to resolve some ambiguosness.
Conclusion
While there may be a lot different kinds of optimal computation substrates for various jobs, the bulk of all computational matter will most likely consist of atomic computronium. Other kind of computers will need great amounts of energy and therefore will be reserved for special purposes, if they are used at all. Those energy requirements make it highly likely that those high-energy substrates will be placed in artificial satellites in a low orbit around the sun.
If it is possible to store information in dark energy, this possibility will be used, otherwise most information will reside in atomic computronium memory, mainly because of its low energy requirements. In any case, people living in such computation substrates will be able to think extraordinarily fast and be able to live in virtual worlds which don’t leave much to desire.
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