Staving off the Cosmic Malthus
The Darwinian argument may be overcome if culture keeps evolving faster than genes and thereby can keep overcoming future genetic adaptations. (Richard Dawkins argues that we can overcome our selfish genes). It may be rebutted that units of culture (what Dawkins calls "memes") themselves are Darwinian competitors and thus also face Malthusian limits, or that future computerized minds may reproduce very quickly and evolve as fast as culture. I won't elaborate on these arguments further here as Robin has got me into a hyper-futuristic mood and I'd like to suggest another way in which we might achieve more "room at the bottom".
Hanson counts atoms in order to estimate the density of information (or of minds) that might be created. But, just as Freeman Dyson, Gerard O'Neill, and others showed that planets are a waste of mass, so that technologically mature civilizations won't have planets, I'll argue here that atoms are a waste of mass-energy, and technologically mature civilizations may not have very many of them. Instead information may be stored in photons and collections of electrons and positrons (for example geonium) may handle most information processing and form the substrate of minds.
Given that a photon can come in a vast number of possibly distinguishable frequencies, the spectrum spanning more than 20 orders of magnitude, we may be able to store at least 10^30 bits per photon. One approach to creating photons is to simply capture the energy of solar nuclear fusions as photons, as we already know how to do -- this should give us about 10^95 bits worth of photons of average energy blue. But we'd have to either wait billions of years for all these fusion reactions to occur naturally in the sun or accelerate them somehow. More completely, the neutrons and protons in the sun, if converted into photons of average energy blue, would give us 10^97 bits and we may not have to wait billions of years if we can figure out how to bring about this hypothetical conversion. This is a fascinating but very speculative bit of physics which I will explore further.
Of course, we will still need some electrons or positrons around to actually process that information and recycle photons. And we still need some neutrons and protons around to fuse for energy to make up for the waste heat, to the extent that geonium computations will be less than perfectly reversible. Unless we are very clever and figure out how to make solid structures that don't blow up out of electrons and positrons, we will need some magnetic tanks made out of traditional heavy atoms to hold the geonium. Worse, the strong tendency for baryon number to be conserved makes cracking protons difficult and perhaps impossible. Protons are made out of three quarks, and while cracking quarks is quite possible (particles with two quarks but zero net baryon number decay spontaneously into particles with no quarks), the tendency for baryon numbers to be conserved at the energy levels used by current particle accelerators suggests that cracking the proton, if we can even figure out how to do it, may require vast amounts of energy, so that only a tiny fraction of the sun's neutrons and protons might be converted before we run out of energy from the fusion of the remaining nuclei. Right now we know how to crack the neutron into a proton and electron, but we don't know how to crack the proton. To be feasible we will have to discover a way to "catalyze" proton decay, by analogy to how the activation energies of chemical reactions can be lowered by catalysts.
If feasible, converting wasteful atoms into more useful photons would give us many orders of magnitude more room at the bottom. Staving off Malthus then becomes a question of how much information can be stored in a photon, and of how quickly electrons or positrons can process those photons.
We still face Heisenberg uncertainty as a limit on how quickly these photonic memories can be recalled. The product of the measured time of arrival of a photon and its measured energy (and thus the number of distinguishable frequencies) has a fixed uncertainty -- if we measure the time with greater precision, we can distinguish fewer frequencies, and vice versa. This sets a finite limit on the rate at which we can process the information stored in the photons. Seth Lloyd has calculated that 1 kilogram of mass converted into energy can perform at most 10^50 operations per second. So future civilizations could only stave off Malthus by going photonic -- Malthus will still eventually catch up, assuming Darwinian competition in reproduction remains.
In addition to classical bits stored as photon frequencies, an exponentially higher number of quantum bits (qubits) might be stored in the entangled states of these photons. However, to use some number of these qubits requires destroying an exponentially larger amount of them. Thus, against exponential population growth memory storage itself remains cheap, but recalling memories or thinking about things becomes exponentially expensive. Qubit minds might stave off Malthus by hibernating for exponentially longer periods of time, waking up only to observe an exponentially decreasing number of interesting events.
My argument that we may figure out how to crack three-quark particles like neutrons and protons into photons relies on the probability, due to the imbalance of protons and anti-protons (and neutrons and anti-neutrons) in the observable universe, that baryon number (a property of quarks) is not necessarily conserved, and is falsifiable in that sense: if for example we discover with better telescopes that the amount of antimatter in the universe is the same as the amount of matter, that will at least strongly suggest that even at Big Bang energies baryon number is conserved, rendering the possibility of ever converting the quarks which constitute most of the mass of neutrons and protons into non-quarkish things (like electrons, positrons or photons) extremely unlikely. It's also somewhat imminently testable insofar as if LHC and similar colliders continue to fail to crack the proton, that further dims prospects. Feasibility, however, is not so testable: one could argue that, even if baryon number was not conserved in the Big Bang, and even if we soon discover how to crack the proton in high-energy colliders, we may never figure out a method, analogous to catalysis in chemical reactions, to crack protons at economically low energies or to productively recycle the energies used to perform the conversions rather than it being dispersed as waste heat.
(h/t: the phrase "Cosmic Malthus" to describe Hanson's theory is from commenter Norman at Robin's blog).